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!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJRoot Entry FWordDocumentul11Table+V Data
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D , *\b'
o` WHO Child Growth Standards
Length/height-for-age, weight-for-age, weight-for-length,
weight-for-height and body mass index-for-age
Methods and development
1 year 2 years 3 years 4 years 5 years
WHO Child Growth Standards
Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age
Methods and development
Department of Nutrition for Health and Development
WHO Library Cataloguing-in-Publication Data
WHO child growth standards : length/height-for-age, weight-for-age, weight-for-length, weight-for-
height and body mass index-for-age : methods and development.
Coordinating team: Mercedes de Onis ... [et al.].
Anthropometry. 2. Anthropometry - methods. 3. Body weights and measures - standards. 4. Child development. 5. Growth. 6. Reference standards. 7. Nutrition assessment. I. de Onis, Mercedes. II. World Health Organization. III. Title: World Health Organization child growth standards.
ISBN 92 4 154693 X (NLM classification: WS 103)
World Health Organization 2006
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should be addressed to WHO Press, at the above address (fax: +41 22 791 4806; email: permissions@who.int).
The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the World Health Organization concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Dotted lines on maps represent approximate border lines for which there may not yet be full agreement.
The mention of specific companies or of certain manufacturers products does not imply that they are endorsed or recommended by the World Health Organization in preference to others of a similar nature that are not mentioned. Errors and omissions excepted, the names of proprietary products are distinguished by initial capital letters.
All reasonable precautions have been taken by WHO to verify the information contained in this publication. However, the published material is being distributed without warranty of any kind, either express or implied. The responsibility for the interpretation and use of the material lies with the reader. In no event shall the World Health Organization be liable for damages arising from its use.
Printed in France
Members of the WHO Multicentre Growth Reference Study Group
Coordinating Team
Mercedes de Onis [Study Coordinator], Adelheid Onyango, Elaine Borghi, Amani Siyam, Alain Pinol (Department of Nutrition for Health and Development, World Health Organization).
Executive Committee
Cutberto Garza [Chair], Mercedes de Onis, Jose Martines, Reynaldo Martorell, Cesar G. Victora (up to October 2002), Maharaj K. Bhan (from November 2002).
Steering Committee
Coordinating Centre (WHO, Geneva): Mercedes de Onis, Jose Martines, Adelheid Onyango, Alain Pinol.
Investigators (by country): Cesar G. Victora and Cora Luiza Arajo (Brazil), Anna Lartey and William B. Owusu (Ghana), Maharaj K. Bhan and Nita Bhandari (India), Kaare R. Norum and Gunn-Elin Aa. Bjoerneboe (Norway), Ali Jaffer Mohamed (Oman), Kathryn G. Dewey (USA).
United Nations Agency Representatives: Cutberto Garza (UNU), Krishna Belbase (UNICEF).
Advisory Group
Maureen Black, Wm. Cameron Chumlea, Tim Cole, Edward Frongillo, Laurence Grummer-Strawn, Reynaldo Martorell, Roger Shrimpton, Jan Van den Broeck. For the work presented in this document, Huiqi Pan, Robert Rigby, Mikis Stasinopoulos and Stef van Buuren, participated in an advisory capacity.
Participating countries and investigators
Brazil: Cora Luiza Arajo, Cesar G. Victora, Elaine Albernaz, Elaine Tomasi, Rita de Cssia Fossati da Silveira, Gisele Nader (Departamento de Nutrio and Departamento de Medicina Social, Universidade Federal de Pelotas; and Ncleo de Pediatria and Escola de Psicologia, Universidade Catlica de Pelotas).
Ghana: Anna Lartey, William B. Owusu, Isabella Sagoe-Moses, Veronica Gomez, Charles Sagoe-Moses (Department of Nutrition and Food Science, University of Ghana; and Ghana Health Service).
India: Nita Bhandari, Maharaj K. Bhan, Sunita Taneja, Temsunaro Rongsen, Jyotsna Chetia, Pooja Sharma, Rajiv Bahl (All India Institute of Medical Sciences).
Norway: Gunn-Elin Aa. Bjoerneboe, Anne Baerug, Elisabeth Tufte, Kaare R. Norum, Karin Rudvin, Hilde Nysaether (Directorate of Health and Social Affairs; National Breastfeeding Centre, Rikshospitalet University Hospital; and Institute for Nutrition Research, University of Oslo).
Oman: Ali Jaffer Mohamed, Deena Alasfoor, Nitya S. Prakash, Ruth M. Mabry, Hanadi Jamaan Al Rajab, Sahar Abdou Helmi (Ministry of Health).
USA: Kathryn G. Dewey, Laurie A. Nommsen-Rivers, Roberta J. Cohen, M. Jane Heinig (University of California, Davis).
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Acknowledgements
The WHO Child Growth Standards were constructed by the Coordinating Team in the Department of Nutrition for Health and Development of the World Health Organization.
The Study Group is indebted to the parents, children and more than 200 field staff that participated in the WHO Multicentre Growth Reference Study. The generous contribution of many individuals that provided expertise and advice was also crucial to the development of the growth standards.
The project has received funding from the Bill & Melinda Gates Foundation, the Netherlands Minister for Development Cooperation, the Norwegian Royal Ministry of Foreign Affairs, and the United States Department of Agriculture (USDA). Financial support was also provided by the Ministry of Health of Oman, the United States National Institutes of Health, the Brazilian Ministry of Health and Ministry of Science and Technology, the Canadian International Development Agency, the United Nations University, the Arab Gulf Fund for United Nations Development, the Office of the WHO Representative to India, and the Department of Child and Adolescent Health and Development.
iv
Contents
Executive summaryxvii1.Introduction12.Methodology32.1Design of the WHO Multicentre Growth Reference Study32.2Anthropometry methods32.3Sample description42.4Data cleaning procedures and exclusions52.5Statistical methods for constructing the growth curves73.Construction of the length/height-for-age standards133.1Indicator-specific methodology133.2Length/height-for-age for boys133.2.1Sample size133.2.2Model selection and results143.2.3WHO standards and their comparison with NCHS and CDC 2000 references32Charts33Tables37Comparison with NCHS45Comparison with CDC 2000463.3Length/height-for-age for girls473.3.1Sample size473.3.2Model selection and results473.3.3WHO standards and their comparison with NCHS and CDC 2000 references59Charts60Tables64Comparison with NCHS72Comparison with CDC 2000733.4Comparisons between boys and girls743.4.1WHO753.4.2NCHS763.4.3CDC 2000774.Construction of the weight-for-age standards794.1Indicator-specific methodology794.2Weight-for-age for boys794.2.1Sample size794.2.2Model selection and results794.2.3WHO standards and their comparison with NCHS and CDC 2000 references94Charts95Tables97Comparison with NCHS105Comparison with CDC 20001064.3Weight-for-age for girls1074.3.1Sample size1074.3.2Model selection and results1074.3.3WHO standards and their comparison with NCHS and CDC 2000 references122Charts123Tables125Comparison with NCHS133Comparison with CDC 20001344.4Comparisons between boys and girls1354.4.1WHO1364.4.2NCHS137
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4.4.3CDC 20001385.Construction of the weight-for-length and weight-for-height standards1395.1Indicator-specific methodology1395.2Weight-for-length/height for boys1395.2.1Sample size1395.2.2Model selection and results1405.2.3WHO standards and their comparison with NCHS and CDC 2000 references153Charts154Tables158Comparison with NCHS176Comparison with CDC 20001785.3Weight-for-length/height for girls1805.3.1Sample size1805.3.2Model selection and results1805.3.3WHO standards and their comparison with NCHS and CDC 2000 references194Charts195Tables199Comparison with NCHS217Comparison with CDC 20002195.4 Comparisons between boys and girls2215.4.1WHO2225.4.2NCHS2245.4.3CDC 20002266.Construction of the body mass index-for-age standards2296.1Indicator-specific methodology2296.2BMI-for-age for boys2306.2.1Sample size2306.2.2Model selection and results230Length-based BMI-for-age for boys230Height-based BMI-for-age for boys2416.2.3WHO standards and their comparison with CDC 2000 reference249Charts250Tables254Comparison with CDC 20002626.3BMI-for-age for girls2636.3.1Sample size2636.3.2Model selection and results263Length-based BMI-for-age for girls263Height-based BMI-for-age for girls2756.3.3WHO standards and their comparison with CDC 2000 reference284Charts285Tables289Comparison with CDC 20002976.4 Comparisons between boys and girls2986.4.1WHO2996.4.2CDC 20003007. Computation of centiles and z-scores for length/height-for-age, weight-for-age,weight-for-length, weight-for-height and BMI-for-age3018.Conclusion3059.Bibliography309Appendix A. Model specifications of the WHO child growth standards312
vi
Figures
Figure 1Worm plots of z-scores for candidate model with df()=11 and df()=6with age transformation age0.35 for length/height-for-age for boys16Figure 2Fitting of and curves of Model 1 for length/height-for-age for boys(dotted line) and their respective sample estimates (points with solid line)17Figure 3Centile residuals from fitting Model 1 for length/height-for-age from0 to 24 months for boys18Figure 4Centile residuals from fitting Model 1 for length/height-for-age from24 to 71 months for boys18Figure 5Worm plots of z-scores for Model 1 for length/height-for-age for boys19Figure 6Worm plots of z-scores for Model 2 for length/height-for-age for boys24Figure 73rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:length-for-age for boys from birth to 24 months28Figure 85th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:length-for-age for boys from birth to 24 months29Figure 93rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:height-for-age for boys from 24 to 71 months30Figure 105th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:height-for-age for boys from 24 to 71 months31Figure 11WHO length-for-age z-scores for boys from birth to 24 months33Figure 12WHO height-for-age z-scores for boys from 24 to 60 months34Figure 13WHO length-for-age percentiles for boys from birth to 24 months35Figure 14WHO height-for-age percentiles for boys from 24 to 60 months36Figure 15Comparison of WHO with NCHS length/height-for-age z-scores for boys45Figure 16Comparison of WHO with CDC 2000 length/height-for-age z-scores for boys46Figure 17Fitting of the and curves of Model 1 for length/height-for-age for girls(dotted line) and their respective sample estimates (points with solid line)49Figure 18Centile residuals from fitting Model 1 for length/height-for-age from0 to 24 months for girls50Figure 19Centile residuals from fitting Model 1 for length/height-for-age from24 to 71 months for girls50Figure 20Worm plots of z-scores for Model 1 for length/height-for-age for girls51Figure 213rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:length-for-age for girls from birth to 24 months55Figure 225th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:length-for-age for girls from birth to 24 months56Figure 233rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:height-for-age for girls from 24 to 71 months57Figure 245th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:height-for-age for girls from 24 to 71 months58Figure 25WHO length-for-age z-scores for girls from birth to 24 months60Figure 26WHO height-for-age z-scores for girls from 24 to 60 months61
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Figure 27WHO length-for-age percentiles for girls from birth to 24 months62Figure 28WHO height-for-age percentiles for girls from 24 to 60 months63Figure 29Comparison of WHO with NCHS length/height-for-age z-scores for girls72Figure 30Comparison of WHO with CDC 2000 length/height-for-age z-scores for girls73Figure 31Comparison of boys' and girls' WHO length/height-for-age z-scores75Figure 32Comparison of boys' and girls' NCHS length/height-for-age z-scores76Figure 33Comparison of boys' and girls' CDC 2000 length/height-for-age z-scores77Figure 34Worm plots of z-scores for Model 1 for weight-for-age for boys81Figure 35Fitting of the , , and curves of Model 2 for weight-for-age for boysfrom 0 to 71 months (dotted line) and their respective sample estimates(points with solid line)84Figure 36Centile residuals from fitting Model 2 for weight-for-age from0 to 24 months for boys85Figure 37Centile residuals from fitting Model 2 for weight-for-age from24 to 71 months for boys85Figure 38Worm plots of z-scores for Model 2 for weight-for-age for boys86Figure 393rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-age for boys from birth to 24 months90Figure 405th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-age for boys from birth to 24 months91Figure 413rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-age for boys from 24 to 71 months92Figure 425th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-age for boys from 24 to 71 months93Figure 43WHO weight-for-age z-scores for boys from birth to 60 months95Figure 44WHO weight-for-age percentiles for boys from birth to 60 months96Figure 45Comparison of WHO with NCHS weight-for-age z-scores for boys105Figure 46Comparison of WHO with CDC 2000 weight-for-age z-scores for boys106Figure 47Cubic splines fitted for the curve with varying numbers of degrees of freedom110Figure 48Fitting of the , , and curves of Model 3 for weight-for-age for girlsfrom 0 to 71 months (dotted line) and their respective sample estimates(points with solid line)113Figure 49Centile residuals from fitting Model 3 for weight-for-age from0 to 24 months for girls114Figure 50Centile residuals from fitting Model 3 for weight-for-age from24 to 71 months for girls114Figure 51Worm plots of z-scores for Model 3 for weight-for-age for girls115Figure 523rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-age for girls from birth to 24 months118Figure 535th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-age for girls from birth to 24 months119
viii
Figure 543rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-age for girls from 24 to 71 months120Figure 555th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-age for girls from 24 to 71 months121Figure 56WHO weight-for-age z-scores for girls from birth to 60 months123Figure 57WHO weight-for-age percentiles for girls from birth to 60 months124Figure 58Comparison of WHO with NCHS weight-for-age z-scores for girls133Figure 59Comparison of WHO with CDC 2000 weight-for-age z-scores for girls134Figure 60Comparison of boys' and girls' WHO weight-for-age z-scores136Figure 61Comparison of boys' and girls' NCHS weight-for-age z-scores137Figure 62Comparison of boys' and girls' CDC 2000 weight-for-age z-scores138Figure 63Worm plots of z-scores for Model 1 for weight-for-length/height for boys141Figure 64Fitting of the , , and curves of Model 2 for weight-for-length/heightfor boys (dotted line) and their respective sample estimates (points withsolid line)143Figure 65Centile residuals from fitting Model 2 for weight-for-length/height for boys144Figure 66Worm plots of z-scores for Model 2 for weight-for-length/height for boys146Figure 673rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-length for boys149Figure 685th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-length for boys150Figure 693rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-height for boys151Figure 705th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-height for boys152Figure 71WHO weight-for-length z-scores for boys from 45 to 110 cm154Figure 72WHO weight-for-height z-scores for boys from 65 to 120 cm155Figure 73WHO weight-for-length percentiles for boys from 45 to 110 cm156Figure 74WHO weight-for-height percentiles for boys from 65 to 120 cm157Figure 75Comparison of WHO with NCHS weight-for-length z-scores for boys176Figure 76Comparison of WHO with NCHS weight-for-height z-scores for boys177Figure 77Comparison of WHO with CDC 2000 weight-for-length z-scores for boys178Figure 78Comparison of WHO with CDC 2000 weight-for-height z-scores for boys179Figure 79Fitting of the , , and curves of Model 2 for weight-for-length/heightfor girls (dotted line) and their respective sample estimates (points withsolid line)183Figure 80Centile residuals from fitting Model 2 for weight-for-length/height for girls184Figure 81Worm plots of z-scores for Model 2 for weight-for-length/height for girls186Figure 823rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-length for girls190
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Figure 835th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-length for girls191Figure 843rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:weight-for-height for girls192Figure 855th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:weight-for-height for girls193Figure 86WHO weight-for-length z-scores for girls195Figure 87WHO weight-for-height z-scores for girls196Figure 88WHO weight-for-length percentiles for girls197Figure 89WHO weight-for-height percentiles for girls198Figure 90Comparison of WHO with NCHS weight-for-length z-scores for girls217Figure 91Comparison of WHO with NCHS weight-for-height z-scores for girls218Figure 92Comparison of WHO with CDC 2000 weight-for-length z-scores for girls219Figure 93Comparison of WHO with CDC 2000 weight-for-height z-scores for girls220Figure 94Comparison of boys' and girls' WHO weight-for-length z-scores222Figure 95Comparison of boys' and girls' WHO weight-for-height z-scores223Figure 96Comparison of boys' and girls' NCHS weight-for-length z-scores224Figure 97Comparison of boys' and girls' NCHS weight-for-height z-scores225Figure 98Comparison of boys' and girls' CDC 2000 weight-for-length z-scores226Figure 99Comparison of boys' and girls' CDC 2000 weight-for-height z-scores227Figure 100Worm plots of z-scores for Model 1 for length-based BMI-for-age for boys232Figure 101Fitting of the , , and curves of Model 2 for length-based BMI-for-agefrom 0 to 24 months for boys (dotted line) and their respective sampleestimates (points with solid line)234Figure 102Centile residuals from fitting Model 2 for length-based BMI-for-age from0 to 24 months for boys235Figure 103Worm plots of z-scores for Model 2 for length-based BMI-for-age for boys236Figure 1043rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:length-based BMI-for-age for boys from birth to 24 months239Figure 1055th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:length-based BMI-for-age for boys from birth to 24 months240Figure 106Fitting of the , , and curves of Model 1 for height-based BMI-for-agefrom 18 to 71 months for boys (dotted line) and their respective sampleestimates (points with solid line)242Figure 107Centile residuals from fitting Model 1 for height-based BMI-for-age from18 to 71 months for boys243Figure 108Worm plots of z-scores for Model 1 for height-based BMI-for-age for boys246Figure 1093rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:height-based BMI-for-age for boys from 24 to 71 months247Figure 1105th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:height-based BMI-for-age for boys from 24 to 71 months248
x
Figure 111 WHO length-based BMI-for-age z-scores for boys from birth to 24 months250Figure 112 WHO height-based BMI-for-age z-scores for boys from 24 to 60 months251Figure 113 WHO length-based BMI-for-age percentiles for boys from birth to 24 months252Figure 114 WHO height-based BMI-for-age percentiles for boys from 24 to 60 months253Figure 115 Comparison of WHO with CDC 2000 BMI-for-age z-scores for boys262Figure 116 Cubic splines fitted for the curve with varying numbers of degrees of freedom265Figure 117 Worm plots of z-scores for Model 1 for length-based BMI-for-age for girls267Figure 118 Fitting of the , , and curves of Model 2 for length-based BMI-for-agefrom 0 to 24 months for girls (dotted line) and their respective sampleestimates (points with solid line)268Figure 119 Centile residuals from fitting Model 2 for length-based BMI-for-age from0 to 24 months for girls269Figure 120 Worm plots of z-scores for Model 2 for length-based BMI-for-age for girls270Figure 121 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:length-based BMI-for-age for girls from birth to 24 months273Figure 122 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:length-based BMI-for-age for girls from birth to 24 months274Figure 123 Cubic splines fitted for the curve with varying numbers of degrees of freedom276Figure 124 Fitting of the , , and curves of Model 1 for height-based BMI-for-agefrom 18 to 71 months for girls (dotted line) and their respective sampleestimates (points with solid line)277Figure 125 Centile residuals from fitting Model 1 for height-based BMI-for-age from18 to 71 months for girls278Figure 126 Worm plots of z-scores for Model 1 for height-based BMI-for-age for girls279Figure 127 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values:height-based BMI-for-age for girls from 24 to 71 months282Figure 128 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values:height-based BMI-for-age for girls from 24 to 71 months283Figure 129 WHO length-based BMI-for-age z-scores for girls from birth to 24 months285Figure 130 WHO height-based BMI-for-age z-scores for girls from 24 to 60 months286Figure 131 WHO length-based BMI-for-age percentiles for girls from birth to 24 months287Figure 132 WHO height-based BMI-for-age percentiles for girls from 24 to 60 months288Figure 133 Comparison of WHO with CDC 2000 BMI-for-age z-scores for girls297Figure 134 Comparison of boys' and girls' WHO BMI-for-age z-scores299Figure 135 Comparison of boys' and girls' CDC 2000 BMI-for-age z-scores300Figure 136 Examples of children ranked according to the WHO BMI-for-age standards303
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Tables
Table 1Total sample and number of compliant children in the longitudinal component4Table 2Comparison of mean size at birth for compliant newborns and those thatcontributed only birth measurements5Table 3Total sample of children in the cross-sectional component5Table 4Total sample of children in the cross-sectional component by number ofvisits and total number of records5Table 5Number of observations by sex and study component included and excludedon the basis of weight-for-length/height6Table 6Number of observations used in the construction of the WHO child growthstandards by sex and anthropometric indicator7Table 7Interpretation of various patterns in the worm plot10Table 8Summary of differences between recumbent length and standing height ina sample of children measured both ways13Table 9Longitudinal sample sizes for length/height-for-age for boys14Table 10Cross-sectional sample sizes for length/height-for-age for boys14Table 11Global deviance (GD) for models within the class BCPE(x=age, df()=10,df()=6, =1, =2) for length/height-for-age for boys14Table 12Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for length/height-for-age for boys15Table 13Observed proportions of children with measurements below the fittedcentiles from Model 1, length/height-for-age for boys20Table 14Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=12, df()=6,=1, =2)] for length/height-for-age for boys22Table 15Goodness-of-fit summary for models BCPE(x=age0.35, df()=12, df()=6,df()=?, =2) for length/height-for-age for boys23Table 16Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=12, df()=6,df()=6, =2)] for length/height-for-age for boys25Table 17Observed proportions of children with measurements below the fittedcentiles from Model 2, length/height-for-age for boys26Table 18Length-for-age for boys, age in weeks37Table 19Length-for-age for boys, age in years and months39Table 20Height-for age for boys, age in years and months41Table 21Longitudinal sample sizes for length/height-for-age for girls47Table 22Cross-sectional sample sizes for length/height-for-age for girls47Table 23Global deviance (GD) for models within the class BCPE(x=age, df()=10,df()=6, =1, =2) for length/height-for-age for girls48Table 24Goodness-of-fit summary for models using the BCPE distribution with fixed=1 and =2 for length/height-for-age for girls48Table 25Observed proportions of children with measurements below the fittedcentiles from Model 1, length/height-for-age for girls52
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Table 26Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=10, df()=5,=1, =2)] for length/height-for-age for girls54Table 27Length-for-age for girls, age in weeks64Table 28Length-for-age for girls, age in years and months66Table 29Height-for-age for girls, age in years and months68Table 30Longitudinal sample sizes for weight-for-age for boys79Table 31Cross-sectional sample sizes for weight-for-age for boys79Table 32Global deviance (GD) for models within the class BCPE(x=age, df()=9,df()=4, df()=4, =2) for weight-for-age for boys80Table 33Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for weight-for-age for boys80Table 34Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=11, df()=7,=1, =2)] for weight-for-age for boys82Table 35Goodness-of-fit summary for models BCPE(x=age0.35, df()=11, df()=7,df()=?, =2) for weight-for-age for boys83Table 36Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=11, df()=7,df()=2, =2)] for weight-for-age for boys87Table 37Observed proportions of children with measurements below the fittedcentiles from Model 2, weight-for-age for boys88Table 38Weight-for-age for boys, age in weeks97Table 39Weight-for-age for boys, age in years and months99Table 40Longitudinal sample sizes for weight-for-age for girls107Table 41Cross-sectional sample sizes for weight-for-age for girls107Table 42Global deviance (GD) for models within the class BCPE(x=age, df()=9,df()=4, df()=4, =2) for weight-for-age for girls108Table 43Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for weight-for-age for girls108Table 44Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=11, df()=7,=1, =2)] for weight-for-age for girls109Table 45Goodness-of-fit summary for models BCPE(x= age0.35, df()=11, df()=7,df()=?, =2) for weight-for-age for girls110Table 46Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=11, df()=7,df()=5, =2)] for weight-for-age for girls111Table 47Q-test for z-scores from Model 3 [BCPE(x=age0.35, df()=11, df()=7,df()=3, =2)] for weight-for-age for girls112Table 48Observed proportions of children with measurements below the fittedcentiles from Model 3, weight-for-age for girls116Table 49Weight-for-age for girls, age in weeks125Table 50Weight-for-age for girls, age in years and months127Table 51Sample sizes for boys' weight-for-length/height by length interval139Table 52Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for weight-for-length/height for boys140
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Table 53Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7),df()=13, df()=6, =1, =2)] for weight-for-length/height for boys142Table 54Goodness-of-fit summary for models BCPE(x=length (or height+0.7),df()=13, df()=6, df()=?, =2) for weight-for-length/height for boys142Table 55Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7),df()=13, df()=6, df()=1, =2)] for weight-for-length/height for boys145Table 56Observed proportions of children with measurements below the fittedcentiles from Model 2, weight-for-length/height for boys147Table 57Weight-for-length for boys158Table 58Weight-for-height for boys168Table 59Sample sizes for girls' weight-for-length/height by length interval180Table 60Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for weight-for-length/height for girls181Table 61Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7),df()=12, df()=4, =1, =2)] for weight-for-length/height for girls182Table 62Goodness-of-fit summary for models BCPE(x=length (or height+0.7),df()=12, df()=4, df()=?, =2) for weight-for-length/height for girls183Table 63Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7),df()=12, df()=4, df()=1, =2)] for weight-for-length/height for girls185Table 64Q-test for z-scores from model BCPE(x=length (or height+0.7), df()=12,df()=4, df()=1, =2.13) for weight-for-length/height for girls187Table 65Observed proportions of children with measurements below the fittedcentiles from Model 2, weight-for-length/height for girls188Table 66Weight-for-length for girls199Table 67Weight-for-height for girls209Table 68Longitudinal sample sizes for BMI-for-age for boys230Table 69Cross-sectional sample sizes for BMI-for-age for boys230Table 70Global deviance (GD) for models within the class BCPE(x=age, df()=9,df()=4, df()=4, =2) for length-based BMI-for-age for boys231Table 71Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for length-based BMI-for-age for boys231Table 72Q-test for z-scores from Model 1 [BCPE(x=age0.05, df()=10, df()=4,=1, =2)] for length-based BMI-for-age for boys233Table 73Goodness-of-fit summary for models BCPE(x=age0.05, df()=10, df()=4,df()=?, =2) for length-based BMI-for-age for boys233Table 74Q-test for z-scores from Model 2 [BCPE(x=age0.05, df()=10, df()=4,df()=3, =2)] for length-based BMI-for-age for boys237Table 75Observed proportions of children with measurements below the fittedcentiles from Model 2, length-based BMI-for-age for boys238Table 76Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for height-based BMI-for-age for boys241Table 77Goodness-of-fit summary for models BCPE(x=age, df()=4, df()=3,df()=?, =2) for height-based BMI-for-age for boys242
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Table 78Observed proportions of children with measurements below the fittedcentiles from Model 1, height-based BMI-for-age for boys244Table 79Q-test for z-scores from Model 1 [BCPE(x=age, df()=4, df()=3,df()=3, =2)] for height-based BMI-for-age for boys245Table 80Length-based BMI-for-age for boys, age in weeks254Table 81Length-based BMI-for-age for boys, age in years and months256Table 82Height-based BMI-for-age for boys, age in years and months258Table 83Longitudinal sample sizes for BMI-for-age for girls263Table 84Cross-sectional sample sizes for BMI-for-age for girls263Table 85Global deviance (GD) for models within the class BCPE(x=age,df()=9, df()=4, df()=4, =2) for length-based BMI-for-age for girls264Table 86Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for length-based BMI-for-age for girls264Table 87Q-test for z-scores from Model 1 [BCPE(x=age0.05, df()=10, df()=3,=1, =2)] for length-based BMI-for-age for girls266Table 88Goodness-of-fit summary for models BCPE(x=age0.05, df()=10, df()=3,df()=?, =2) for length-based BMI-for-age for girls267Table 89Q-test for z-scores from Model 2 [BCPE(x=age0.05, df()=10, df()=3,df()=3, =2)] for length-based BMI-for-age for girls271Table 90Observed proportions of children with measurements below the fittedcentiles from Model 2 for length-based BMI-for-age for girls272Table 91Goodness-of-fit summary for models using the BCPE distribution withfixed =1 and =2 for height-based BMI-for-age for girls275Table 92Goodness-of-fit summary for models BCPE(x=age, df()=4, df()=4,df()=?, =2) for height-based BMI-for-age for girls276Table 93Q-test for z-scores from Model 1 [BCPE(x=age, df()=4, df()=4,df()=1, =2)] for height-based BMI-for age for girls280Table 94Observed proportions of children with measurements below the fittedcentiles from Model 1 for height-based BMI-for-age for girls281Table 95Length-based BMI-for-age for girls, age in weeks289Table 96Length-based BMI-for-age for girls, age in years and months291Table 97Height-based BMI-for-age for girls, age in years and months293
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Glossary
BCPE
Body mass index (BMI)
Box-Cox transformation
Coefficient of variation
Cubic spline
Cut-off
Degrees of freedom (df)
Kurtosis
P-value
Q-test
Skewness
Standard deviation score (SD) Worm plots
Z-score
The Box-Cox power exponential distribution.
The median of the Box-Cox power exponential distribution.
The approximate coefficient of variation of the Box-Cox power exponential distribution related to the variance.
The power of the Box-Cox transformation (to the normal distribution) of the Box-Cox power exponential distribution - related to the skewness.
The power exponential parameter of the Box-Cox power exponential distribution related to the kurtosis.
The power of the age (or length/height) transformation.
The ratio weight (in kg) / recumbent length or standing height (in m2).
A power transformation to the normal distribution.
The ratio of the standard deviation to the mean.
A piecewise third-order polynomial function that passes through a set of m (or degrees of freedom) control points; it can have a very simple form locally, yet be globally flexible and smooth.
A designated limit beyond which a subject or observation is classified according to a pre-set condition.
The number of control points used to fit the cubic splines.
An attribute of a distribution describing "peakedness". A high kurtosis portrays a distribution with fat tails in contrast to a low kurtosis, which portrays a distribution with skinny tails.
The probability of falsely rejecting the hypothesis being tested. In this report all p-values were compared to a level of significance set to 0.05.
A statistical test which combines overall and local tests assessing departures from the normal distribution with respect to median, variance, skewness and kurtosis.
A statistical term used to describe a distribution's asymmetry in relation to a normal distribution.
See z-score.
A set of detrended Q-Q plots plots that compare the distribution of a given set of observations to the normal distribution.
The deviation of an individual's value from the median value of a reference population, divided by the standard deviation of the reference population (or transformed to normal distribution).
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Executive summary
In 1993 the World Health Organization (WHO) undertook a comprehensive review of the uses and interpretation of anthropometric references. The review concluded that the NCHS/WHO growth reference, which had been recommended for international use since the late 1970s, did not adequately represent early childhood growth and that new growth curves were necessary. The World Health Assembly endorsed this recommendation in 1994. In response WHO undertook the Multicentre Growth Reference Study (MGRS) between 1997 and 2003 to generate new curves for assessing the growth and development of children the world over.
The MGRS combined a longitudinal follow-up from birth to 24 months and a cross-sectional survey of children aged 18 to 71 months. Primary growth data and related information were gathered from 8440 healthy breastfed infants and young children from widely diverse ethnic backgrounds and cultural settings (Brazil, Ghana, India, Norway, Oman and USA). The MGRS is unique in that it was purposely designed to produce a standard by selecting healthy children living under conditions likely to favour the achievement of their full genetic growth potential. Furthermore, the mothers of the children selected for the construction of the standards engaged in fundamental health-promoting practices, namely breastfeeding and not smoking.
This report presents the first set of WHO Child Growth Standards (i.e. length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index (BMI)-for-age) and describes the methodical process followed in their development. The first step in this process was a consultative expert review of some 30 growth curve construction methods, including types of distributions and smoothing techniques to identify the best approach to constructing the standards. Next was the selection of a software package flexible enough to allow the comparative testing of the alternative methods used to generate the growth curves. Then the selected approach was applied systematically to search for the best models to fit the data for each indicator.
The Box-Cox-power-exponential (BCPE) method, with curve smoothing by cubic splines was selected for constructing the WHO child growth curves. The BCPE accommodates various kinds of distributions, from normal to skewed or kurtotic. The age-based indicators originating at birth required a power-transformation to stretch the age scale (x-axis) as a preliminary step to fitting the curves. For each set of curves, the search for the best model specification began by examining various combinations of degrees of freedom to fit the median and variance estimator curves. When data had a non-normal distribution, degrees of freedom for parameters to model skewness and kurtosis were added to the initial model and adequacy of fit evaluated. Apart from length/height-for-age, which followed a normal distribution, the other standards required the modelling of skewness, but not kurtosis. The diagnostic tools used iteratively to detect possible model misfits and biases in the fitted curves included various tests of local and global goodness of fit, worm plots and residual plots. Patterns of differences between empirical and fitted percentiles were also examined, as were proportions of observed versus expected percentages of children with measurements below selected percentiles.
The methodology described above was followed to generate % for boys and girls aged 0 to 60 months
percentile and z-score curves for length/height-for-age, weight-for-age, weight-for-length, weight-for-height and BMI-for-age. The last standard is an addition to the set of indicators previously available as part of the NCHS/WHO reference. In-depth descriptions are presented of how each sex-specific standard was constructed. Also presented are comparisons of the new WHO standards with the NCHS/WHO growth reference and the CDC 2000 growth charts.
To interpret differences between the WHO standards and the NCHS/WHO reference it is important to understand that they reflect differences not only in the populations used, but also in the methodologies applied to construct the two sets of growth curves. To address the significant skewness of the NCHS/WHO sample's weight-for-age and weight-for-height, separate standard deviations were
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calculated for distributions below and above the median for each of the two indicators. This approach is limited in fitting skewed data, especially at the extreme tails of the distribution, since it only partially adjusts for the skewness inherent in the weight-based indicators. The WHO standards, on the other hand, employed LMS-based methods that fit skewed data adequately and generate fitted curves that follow closely the empirical data. Like the WHO standards, construction of the CDC 2000 growth charts was also based on the LMS method and, therefore, differences between this reference and the WHO standards are largely a reflection of differences in the populations on which the two sets of curves were based.
Length/height-for-age. The standard for linear growth has a part based on length (length-for-age, 0 to 24 months) and another on height (height-for-age, 2 to 5 years). The two parts were constructed using the same model but the final curves reflect the average difference between recumbent length and standing height. By design, children between 18 and 30 months in the cross-sectional component of the MGRS had both length and height measurements taken. The average difference between the two measurements in this set of 1625 children was 0.73 cm. To fit a single model for the whole age range, 0.7 cm was therefore added to the cross-sectional height values before merging them with the longitudinal sample's length data. After the model was fitted, the median curve was shifted back downwards by 0.7 cm for ages above two years, and the coefficient of variation curve adjusted to the new median values to construct the height-for-age growth curves. The same power transformation of age was applied to stretch the age scale for each of the sexes before fitting cubic splines to generate their respective growth curves. The boys' curves required a model with higher degrees of freedom to fit both the median and coefficient of variation curves. The data for both sexes followed the normal distribution.
Weight-for-age. The weights of the longitudinal and cross-sectional samples were merged without any adjustments and a single model was fitted to generate one continuous set of curves constituting each sex-specific weight-for-age standard. The same power transformation was applied to both boys' and girls' age before fitting the curve construction model. The weight data for both sexes were skewed, so in specifying the model, the parameter related to skewness was fitted in addition to the median and the approximate coefficient of variation. In modelling skewness the girls' curves required more degrees of freedom to fit a curve for this parameter.
Weight-for-length/height. The construction of the weight-for-length (45 to 110 cm) and weight-for-height (65 to 120 cm) standards followed a procedure similar to that applied to construct the length/height-for-age standards. That is, to fit a single model, 0.7 cm was added to the cross-sectional height values, and after the model was fitted, the weight-for-length centile curves in the length interval 65.7 to 120.7 cm were shifted back by 0.7 cm to derive the weight-for-height standards corresponding to the height range 65 cm to 120 cm. The lower limit of the weight-for-length standards (45 cm) was chosen to cover up to approximately -2 SD girls' length at birth. The upper limit for the weight-for-height standards was influenced by the need to accommodate the tallest children at age 60 months, that is, 120 cm is approximately +2 SD boys' height-for-age at 60 months. The overlap between the upper end of the weight-for-length standards and the lower end of the weight-for-height standards is intended to facilitate their application in severely undernourished populations and emergency settings.
There was no evidence that a length/height transformation similar to that described for age was required for constructing the weight-for-length/height standards. The modelling of the median and variance curves followed the procedure described for the first two standards. Results from the final model for girls' weight-for-length/height suggested the need to investigate potential improvements in the curves by modelling kurtosis. Adjustment for kurtosis, however had a negligible impact on the final centiles. Therefore, considering that modelling the fourth parameter would increase complexity in application of the standards and create inconsistency between the sexes, the final curves were generated without adjusting for kurtosis. The degrees of freedom for the median and variance curves varied between the boys' and girls' standards. The fact that the weight-for-length/height indicator combines different velocities for the two measurements involved (weight and length/height) at
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overlapping ages likely explains the slight wiggle in the final WHO standards (for both boys and girls) as also observed in other references.
Body mass index-for-age. Body mass index is the ratio weight (in kg)/recumbent length or standing height (in m2). To address the difference between length and height, the approach used for constructing the BMI-for-age standards was different from that described for length/height-for-age. Because BMI is a ratio with squared length or height in the denominator, adding 0.7 cm to the height values and back-transforming them after fitting was not feasible. The solution adopted was to construct the standards for the younger and the older children separately based on two sets of data with an overlapping range of ages below and above 24 months. To construct the BMI-for-age standard based on length (0 to 2 years), the longitudinal sample's length data and the cross-sectional sample's height data (18 to 30 months) were combined after adding 0.7 cm to the height values. Analogously, to construct the standard from 2 to 5 years, the cross-sectional sample's height plus the longitudinal sample's length data (18 to 24 months) were combined after subtracting 0.7 cm from the length values. Thus, a common set of data from 18 to 30 months was used to generate the BMI standards for the younger and the older children. The resulting disjunction between the two standards thus in essence reflects the 0.7 cm difference between length and height. This does not mean, however, that a child at a specific age will have the same length- and height-based BMI-for-age z-score as this is mathematically impossible given the nature of the BMI ratio.
An age power transformation as described for the other age-based standards was required before constructing the length-based BMI-for-age curves. No such transformation was necessary for the height-based BMI-for-age. The WHO length- and height-based BMI-for-age standards do not overlap, i.e. the length-based interval ends at 730 days and the height-based interval starts at 731 days. Cubic spline fitting was achieved with variable degrees of freedom for the length- versus height-based standards, and also for the boys' versus girls' final curves.
Technical aspects of the standards. The method used to construct the WHO standards generally relied on the Box-Cox power exponential distribution and the final selected models simplified to the LMS model. As a result, the computation of percentiles and z-scores for these standards uses formulae based on the LMS method. However, a restriction was imposed on all indicators to enable the derivation of percentiles only within the interval corresponding to z-scores between -3 and 3. The underlying reasoning is that percentiles beyond 3 SD are invariant to changes in equivalent z-scores. The loss accruing to this restriction is small since the inclusion range corresponds to the 0.135th to 99.865th percentiles.
The weight-based indicators presented right-skewed distributions. When modelled correctly, right skewness has the effect of making distances between positive z-scores increase progressively the farther away they are from the median, while distances between negative z-scores decrease progressively. The LMS method fits skewed data adequately by using a Box-Cox normal distribution, which follows the empirical data closely. The drawback, however, is that the outer tails of the distribution are highly affected by extreme data points even if only very few. A restricted application of the LMS method was thus used for the construction of the WHO weight-based indicators, limiting the Box-Cox normal distribution to the interval corresponding to z-scores where empirical data were available (i.e. between -3 SD and 3 SD). Beyond these limits, the standard deviation at each age (or length/height) was fixed to the distance between 2 SD and 3 SD, respectively. This approach avoids making assumptions about the distribution of data beyond the limits of the observed values.
Epidemiological aspects of the standards. As expected, there are notable differences with the NCHS/WHO reference that vary by age, sex, anthropometric measure and specific percentile or z-score curve. Differences are particularly important in infancy. Stunting will be greater throughout childhood when assessed using the new WHO standards compared to the NCHS/WHO reference. The growth pattern of breastfed infants will result in a substantial increase in rates of underweight during the first half of infancy and a decrease thereafter. For wasting, the main difference is during infancy
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when wasting rates will be substantially higher using the new WHO standards. With respect to overweight, use of the new WHO standards will result in a greater prevalence that will vary by age, sex and nutritional status of the index population.
The growth standards presented in this report provide a technically robust tool that represents the best description of physiological growth for children under five years of age. The standards depict normal early childhood growth under optimal environmental conditions and can be used to assess children everywhere, regardless of ethnicity, socioeconomic status and type of feeding.
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INTRODUCTION
Growth charts are an essential component of the paediatric toolkit. Their value resides in helping to determine the degree to which physiological needs for growth and development are met during the important childhood period. Beyond their usefulness in assessing children's nutritional status, many governmental and United Nations agencies rely on growth charts to measure the general well-being of populations, formulate health and related policies, and plan interventions and monitor their effectiveness.
The origin of the WHO Child Growth Standards dates back to the early 1990s when a group of experts was appointed to conduct a meticulous evaluation of the National Center for Health Statistics/World Health Organization (NCHS/WHO) growth reference that had been recommended for international use since the late 1970s (WHO, 1995). The limitations of the NCHS/WHO reference have been documented (WHO Working Group on Infant Growth, 1994; de Onis and Yip, 1996; de Onis and Habicht, 1996). The data used to construct the reference covering birth to three years of age came from a longitudinal study of children of European ancestry from a single community in the USA. These children were measured every three months, which is inadequate to describe the rapid and changing rate of growth in early infancy. Also, the statistical methods available at the time the NCHS/WHO growth curves were constructed were too limited to correctly model the pattern and variability of growth. As a result, the NCHS/WHO curves do not adequately represent early childhood growth.
The initial phase of the expert group's work documented the deficiencies of the reference and led to a plan for developing new growth charts that would show how children should grow in all countries rather than merely describing how they grew at a particular time and place. The experts underscored the importance of ensuring that the new growth charts were consistent with "best" health practices (Garza and de Onis, 2004).
A logical outcome of this plan was the WHO Multicentre Growth Reference Study (MGRS), which was implemented between 1997 and 2003 (de Onis et al., 2004a). The MGRS is unique in that it was purposely designed to produce a standard rather than a reference. Although standards and references both serve as a basis for comparison, each enables a different interpretation. Since a standard defines how children should grow, deviations from the pattern it describes are evidence of abnormal growth. A reference, on the other hand, does not provide as sound a basis for such value judgments, although in practice references often are mistakenly used as standards.
The MGRS data provide a solid foundation for developing a standard because they are based on healthy children living under conditions likely to favour achievement of their full genetic growth potential. Furthermore, the mothers of the children selected for the construction of the standards engaged in fundamental health-promoting practices, namely breastfeeding and not smoking (de Onis et al., 2004b).
A second feature of the study that makes it attractive as a basis for an internationally applicable standard is that it included children from a diverse set of countries: Brazil, Ghana, India, Norway, Oman and the USA. By selecting privileged, healthy populations the study reduced the impact of environmental variation. Assessment of differences in linear growth among the child populations of the MGRS shows a striking similarity among the six sites, with only about 3% of variability in length being due to differences among sites compared to 70% due to differences among individuals (WHO Multicentre Growth Reference Study Group, 2006a). Thus, excluding any site has little effect on the 3rd, 50th, and 97th percentile values, and pooling data from all sites is entirely justified. The remarkable similarity in growth during early childhood across human populations is consistent with genomic comparisons among diverse continental groups reporting a high degree of inter-population homogeneity (Rosenberg, 2002; King and Motulsky, 2002; Jorde and Wooding, 2004). Nevertheless, the MGRS sample has considerable built-in ethnic or genetic variability in addition to cultural variation in how children are nurtured, which further strengthens the standards' universal applicability.
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2 Introduction
A key characteristic of the new standards is that they explicitly identify breastfeeding as the biological norm and establish the breastfed child as the normative model for growth and development (WHO Multicentre Growth Reference Study Group, 2006b). Another distinguishing feature of the new standards is that they include windows of achievement for six gross motor developmental milestones which are presented elsewhere (WHO Multicentre Growth Reference Study Group, 2006c). Although WHO in the past issued recommendations concerning attained physical growth, it had not previously made any recommendations for assessing motor development.
This report presents the first set of WHO Child Growth Standards and describes the methods used to construct the standards for length/height-for-age, weight-for-age, weight-for length, weight-for-height and BMI-for-age. It also compares the new standards with the NCHS/WHO growth reference (WHO, 1983) and the 2000 CDC growth charts (Kuczmarski, 2002). Electronic copies of the WHO growth charts and tables together with tools developed to facilitate their use are available on the Web:
www.who.int/childgrowth/en.
METHODOLOGY
2.1 Design of the WHO Multicentre Growth Reference Study
The MGRS (July 1997 December 2003) was a population-based study that took place in the cities of Davis, California, USA; Muscat, Oman; Oslo, Norway; and Pelotas, Brazil; and in selected affluent neighbourhoods of Accra, Ghana and South Delhi, India. The MGRS protocol and its implementation in the six sites are described in detail elsewhere (de Onis et al., 2004a). Briefly, the MGRS combined a longitudinal component from birth to 24 months with a cross-sectional component of children aged 18 71 months. In the longitudinal component, mothers and newborns were screened and enrolled at birth and visited at home a total of 21 times on weeks 1, 2, 4 and 6; monthly from 2 12 months; and bimonthly in the second year. In the cross-sectional component, children aged 18 71 months were measured once, except in the two sites (Brazil and USA) that used a mixed-longitudinal design in which some children were measured two or three times at three-month intervals. Both recumbent length and standing height were measured for all children aged 18 30 months. Data were collected on anthropometry, motor development, feeding practices, child morbidity, perinatal factors, and socioeconomic, demographic and environmental characteristics (de Onis et al., 2004b).
The study populations lived in socioeconomic conditions favourable to growth and where mobility was low, e"20% of mothers followed WHO feeding recommendations and breastfeeding support was available (de Onis et al., 2004b). Individual inclusion criteria were: no known health or environmental constraints to growth, mothers willing to follow MGRS feeding recommendations (i.e. exclusive or predominant breastfeeding for at least 4 months, introduction of complementary foods by the age of 6 months, and continued partial breastfeeding up to at least 12 months), no maternal smoking before and after delivery, single term birth, and absence of significant morbidity (de Onis et al., 2004b).
As part of the site-selection process in Ghana, India and Oman, surveys were conducted to identify socioeconomic characteristics that could be used to select groups whose growth was not environmentally constrained (Owusu et al., 2004; Bhandari et al., 2002; Mohamed et al., 2004). Local criteria for screening newborns, based on parental education and/or income levels, were developed from those surveys. Pre-existing survey data for this purpose were available from Brazil, Norway and the USA. Of the 13 741 mother-infant pairs screened for the longitudinal component, about 83% were ineligible (WHO Multicentre Growth Reference Study Group, 2006d). Families low socioeconomic status was the most common reason for ineligibility in Brazil, Ghana, India and Oman, whereas parental refusal was the main reason for non-participation in Norway and USA (WHO Multicentre Growth Reference Study Group, 2006d). For the cross-sectional component, 69% of the 21 510 subjects screened were excluded for reasons similar to those observed in the longitudinal component.
Term low-birth-weight (<2500 g) infants (2.3%) were not excluded. Since it is likely that in well-off populations such infants represent small but normal children, their exclusion would have artificially distorted the standards lower percentiles. Eligibility criteria for the cross-sectional component were the same as those for the longitudinal component with the exception of infant feeding practices. A minimum of three months of any breastfeeding was required for participants in the study s cross-sectional component.
2.2 Anthropometry methods
Data collection teams were trained at each site during the study's preparatory phase, at which time measurement techniques were standardized against one of two MGRS anthropometry experts. During the study, bimonthly standardization sessions were conducted at each site. Once a year the anthropometry expert visited each site to participate in these sessions (de Onis et al., 2004c). Results from the anthropometry standardization sessions have been reported elsewhere (WHO Multicentre Growth Reference Study Group, 2006e). For the longitudinal component of the study, screening teams measured newborns within 24 hours of delivery, and follow-up teams conducted home visits until 24 months of age. The follow-up teams were also responsible for taking measurements in the cross-sectional component involving children aged 18 71 months (de Onis et al., 2004b).
- 3 -
4 Methodology
The MGRS data included weight and head circumference at all ages, recumbent length (longitudinal component), height (cross-sectional component), and arm circumference, triceps and subscapular skinfolds (all children aged e"3 months). However, this report presents only the standards based on length or height and weight. Observers working in pairs collected anthropometric data. Each observer independently measured and recorded a complete set of measurements, after which the two compared their readings. If any pair of readings exceeded the maximum allowable difference for a given variable (e.g. weight, 100 g; length/height, 7 mm), both observers once again independently measured and recorded a second and, if necessary, a third set of readings for the variable(s) in question (de Onis et al., 2004c).
All study sites used identical measuring equipment. Instruments needed to be highly accurate and precise, yet sturdy and portable to enable them to be carried back and forth on home visits. Length was measured with the portable Harpenden Infantometer (range 30 110 cm, with digit counter readings precise to 1 mm). The Harpenden Portable Stadiometer (range 65 206 cm, digit counter reading) was used for measuring adult and child heights. Portable electronic scales with a taring capability, calibrated to 0.1 kg (i.e. UNICEF Electronic Scale 890 or UNISCALE), were used to measure weight. Length and height were recorded to the last completed unit rather than to the nearest unit. To correct for the systematic negative bias introduced by this practice, 0.05 cm (i.e. half of the smallest measurement unit) was added to each measurement before analysis. This correction did not apply to weight, which was rounded off to the nearest 100 g. Full details of the instruments used and how measurements were taken are provided elsewhere (de Onis et al., 2004c).
2.3 Sample description
The total sample size for the longitudinal and cross-sectional components from all six sites was 8440 children. A total of 1743 children were enrolled in the longitudinal sample, six of whom were excluded for morbidities affecting growth (4 cases of repeated episodes of diarrhoea, 1 case of repeated episodes of malaria, and 1 case of protein-energy malnutrition) leaving a sample of 1737 children (894 boys and 843 girls). Of these, the mothers of 882 children (428 boys and 454 girls) complied fully with the MGRS infant-feeding and no-smoking criteria and completed the follow-up period of 24 months (96% of compliant children completed the 24-month follow-up) (Table 1). The other 855 children contributed only birth measurements, as they either failed to comply with the study's infant-feeding and no-smoking criteria or dropped out before 24 months. The reason for using these measurements was to increase the sample size at birth to minimize the left-edge effect. The size at birth of these 855 children was similar to that of the compliant sample (Table 2). The total number of records for the longitudinal component was 19 900.
Table 1 Total sample and number of compliant children in the longitudinal component
SiteNCompliantaBoysGirlsTotalBrazil309293766Ghana328103124227India3018489173Norway3007573148Oman2917376149USA2086455119All1737428454882
Compliant with infant-feeding and no-smoking criteria and completed the 24-month follow-up.
Methodology5
Table 2 Comparison of mean size at birth for compliant newborns and those that contributed only birth measurements
MeasurementCompliantaNon-compliantN=882N=855Weight (g)33253306Length (cm)49.649.5Head circumference (cm)34.134.2
Compliant with infant-feeding and no-smoking criteria and completed the 24-month follow-up.
The cross-sectional sample comprised 6697 children. Of these, 28 were excluded for medical conditions affecting growth (20 cases of protein-energy malnutrition, five cases of haemolytic anaemia G6PD deficiency, two cases of renal tubulo-interstitial disease, and one case of Crohn disease) leaving a final sample of 6669 children (3450 boys and 3219 girls) (Table 3). The total number of records in the cross-sectional component was 8306 as some children in Brazil and the USA were measured two or three times at three-month intervals (Table 4). A full description of the MGRS sample with regard to screening, recruitment, sample attrition and compliance, as well as the baseline characteristics of the study sample is provided elsewhere (WHO Multicentre Growth Reference Study Group, 2006d).
Table 3 Total sample of children in the cross-sectional component
SiteBoysGirlsTotalBrazil237243480Ghana6847191403India8406471487Norway7256601385Oman7147241438USA250226476All345032196669
Table 4 Total sample of children in the cross-sectional component by number of visits and total number of records
SiteBrazilGhanaIndiaNorwayOmanUSAAllOne visit341403148713851438555802Two visits3600006197Three visits4100000360770No. of children48014031487138514384766669No. of records1336140314871385143812578306
2.4 Data cleaning procedures and exclusions
Data cleaning
The MGRS data management protocol (Onyango et al., 2004) was designed to create and manage a large databank of information collected from multiple sites over a period of several years. Data collection and processing instruments were prepared centrally and used in a standardized fashion across sites. The data management system contained internal validation features for timely detection of data errors and its standard operating procedures stipulated a method of master file updating and correction that maintained a clear trail for data-auditing purposes. Each site was responsible for collecting, entering, verifying and validating data, and for creating site-level master files. Data from
6 Methodology
the sites were sent to WHO/HQ every month for master file consolidation and more extensive quality control checking. All errors identified were communicated to the site for correction at source.
After data collection was completed at a given site, a period of about 6 months was dedicated to in-depth data quality checking and master file cleaning. Detailed validation reports, descriptive statistics and plots were produced from the site s master files. For the longitudinal component, each anthropometric measurement was plotted for every child from birth to the end of his/her participation. These plots were examined individually for any questionable patterns. Query lists from these analyses were sent to the site for investigation and correction, or confirmation, as required. As with the data collection process, the site data manager prepared correction batches to update the master files. The updated master files were then sent to WHO/HQ and this iterative quality assurance process continued until all identifiable problems had been detected and corrected. The rigorous implementation of what was a highly demanding protocol yielded very high-quality data.
Data exclusions
To avoid the influence of unhealthy weights for length/height, observations falling above +3 SD and below -3 SD of the sample median were excluded prior to constructing the standards. For the cross-sectional sample, the +2 SD cut-off (i.e. 97.7 percentile) was applied instead of +3 SD as the sample was exceedingly skewed to the right, indicating the need to identify and exclude high weights for height. This cut-off was considered to be conservative given that various definitions of overweight all apply lower cut-offs than the one used (Daniels et al., 2005; Koplan et al., 2005).
To derive the above-mentioned cut-offs based on the sex-specific weight-for-length/height indicator, the weight median and coefficient of variation curves were modelled continuously across length/height using an approach that accounted for the sample's asymmetry as described below. The data were split into two sets: one set with all points above the median and another with all points below the median. For each of the two sets, mirror values were generated to create symmetrically distributed values around the median for the upper and lower sets. The generation of mirror data was necessary to simulate a symmetric distribution based on the distinct variabilities of the upper and lower sets. For each of the mirror data sets, median and coefficient of variation curves were estimated continuously across the length/height range using the LMS method (Cole and Green, 1992) fixing L=1, i.e. fitting a normal distribution to the data for each specific length/height value, to derive the corresponding cut-offs. In total, only a small proportion of observations were excluded for unhealthy weight-for-length/height: 185 (1.4%) for boys and 155 (1.1%) for girls, most of which were in the upper end of the cross-sectional sample distribution (Table 5).
Table 5 Number of observations by sex and study component included and excluded on the basis of weight-for-length/height
BoysLS%CS%Total%Included923399.3413597.213 36898.6ExcludedLower110.120.1130.1Upper560.61162.71721.3Total9300100.04253100.013 553100.0
GirlsLS%CS%Total%Included974099.6388697.213 62698.9ExcludedLower70.130.1100.1Upper350.31102.71451.0Total9782100.03999100.013 781100.0
LS, Longitudinal study; CS, Cross-sectional study.
Methodology7
In addition, a few influential observations for indicators other than weight-for-height were excluded when constructing the individual standards: for weight-for-age boys, 4 (0.03%) and girls, 1 (0.01%) observations and, for length/height-for-age boys, 3 (0.02%) and girls, 2 (0.01%) observations. These observations were set to missing in the final data set and therefore did not contribute to the construction of the weight-for-length/height and body mass index-for-age standards. The final number of observations used in the construction of the WHO child growth standards is shown in Table 6.
Table 6 Number of observations used in the construction of the WHO child growth standards by sex and anthropometric indicator
IndicatorGirlsBoysTotalWeight-for-length/height13 62313 36226 985Weight-for-age14 05613 79727 853Length/height-for-age13 78313 55127 334BMI-for-age13 62313 36226 985
2.5 Statistical methods for constructing the growth curves
The construction of the growth curves followed a careful, methodical process. This involved:
detailed examination of existing methods, including types of distributions and smoothing techniques, in order to identify the best possible approach;
selection of a software package flexible enough to allow comparative testing of alternative methods and the actual generation of the curves;
systematic application of the selected approach to the data to generate the models that best fit the data.
A group of statisticians and growth experts met at WHO/HQ to review possible choices of methods and to define a strategy and criteria for selecting the most appropriate model for the MGRS data (Borghi et al., 2006). As many as 30 construction methods for attained growth curves were examined. The group recommended that methods based on selected distributions be compared and combined with two smoothing techniques for fitting parameter curves to further test and provide the best possible approach to constructing the WHO child growth standards.
Choice of distribution. Five distributions were identified for detailed testing: Box-Cox power exponential (Rigby and Stasinopoulos, 2004a), Box-Cox t (Rigby and Stasinopoulos, 2004b), Box-Cox normal (Cole and Green, 1992), Johnson's SU (Johnson, 1949), and modulus-exponential-normal (Royston and Wright, 1998). The first four distributions were fitted using GAMLSS (Generalized Additive Models for Location, Scale and Shape) software (Stasinopoulos et al., 2004) and the last using the "xriml" module in STATA software (Wright and Royston, 1996). The comparison was done by age group, without considering the smoothing component. The Box-Cox-power-exponential (BCPE) distribution with four parameters (for the median), (coefficient of variation), (Box-Cox transformation power) and (parameter related to kurtosis) was selected for constructing the curves. The BCPE is a flexible distribution that offers the possibility to adjust for kurtosis, thus providing the framework necessary to test if fitting the distribution's fourth moment improves the estimation of extreme percentiles. It simplifies to the normal distribution when =1 and =2, and when `"1 and =2, the distribution is the same as the Box-Cox normal (LMS method's distribution). The BCPE is defined
by a power transformation (or Box-Cox transformation) Y having a shifted and scaled (truncated) power exponential (or Box-Tiao) distribution with parameter (Rigby and Stasinopoulos, 2004a).
8 Methodology
Apart from other theoretical advantages, the BCPE presents as good or better goodness-of-fit than the modulus-exponential-normal or the SU distribution.
Choice of smoothing technique. The expert group recommended two smoothing techniques for comparison: cubic splines and fractional polynomials (Borghi et al., 2006). Using the GAMLSS software, the two techniques were compared for smoothing length/height-for-age, weight-for-age and weight-for-length/height curves. For the fractional polynomials, a function in GAMLSS was used that estimates the best set of powers among {-2, -1, -0.5, 0, 0.5, 1, 2, 3} within the choices of polynomials with the same number of terms. The best fractional polynomial for 1, 2 or 3 terms was fitted for each parameter curve. A number of combinations were tried among the different parameter curves, considering the Akaike Information Criterion (Akaike, 1974), AIC, defined as:
AIC = 2L 2 p,
where L is the maximized likelihood and p is the number of parameters (or the total number of degrees of freedom). According to this criterion, the best model is the one with the smallest AIC value.
The cubic spline smoothing technique offered more flexibility than fractional polynomials in all cases. For the length/height-for-age and weight-for-age standards, a power transformation applied to age prior to fitting was necessary to enhance the goodness of fit by the cubic spline technique.
Choice of method for constructing the curves. In summary, the BCPE method, with curve smoothing by cubic splines, was selected as the approach for constructing the growth curves. This method is included in a broader methodology, the GAMLSS (Rigby and Stasinopoulos, 2005), which offers a general framework that includes a wide range of known methods for constructing growth curves. The GAMLSS allows for modeling the mean (or median) of the growth variable under consideration as well as other parameters of its distribution that determine scale and shape. Various kinds of distributions can be assumed for each growth variable of interest, from normal to skewed and/or kurtotic distributions. Several smoothing terms can be used in generating the curves, including cubic splines, lowess (locally weighted least squares regression), polynomials, power polynomials and fractional polynomials. The simplified notation to describe a particular model within the class of the BCPE method is:
BCPE(x=x, df()=n1, df()=n2, df()=n3, df()=n4),
where df() are the degrees of freedom for the cubic splines smoothing the respective parameter curve and x is age (or transformed age) or length/height. Note that when df()=1, the smoothing function reduces to a constant and when df()=2, it reduces to a linear function.
The GAMLSS software was used to construct the WHO child growth standards. The main selected diagnostic tests and tools are available in this software. To complement and test the software, Dr Huiqi Pan and Professor Tim Cole provided the software LMS Pro, which offers the fitting of growth curves using the LMS method in a user-friendly and interactive way, including some of the available diagnostics for choosing the best set of degrees of freedom for the cubic splines and goodness-of-fit statistics. Wright and Royston's package "xriml", developed in the STATA environment, was used to test the fitting of fractional polynomials (Wright and Royston, 1996).
Diagnostic tests and tools for selecting the best model. The process for selecting the best model to construct each growth standard involved choosing, first, the best model within a class of models and, second, the best model across different classes of models. The set of diagnostic tests and tools was selected based on recommendations from the statistical expert group (Borghi et al., 2006), with additional contributions by Rigby and Stasinopoulos (2004a) and Pan and Cole (2004).
Methodology9
In most cases, before fitting the cubic splines, an age transformation was needed to stretch the age scale for values close to zero. Despite their complexity in terms of shape, even the flexible cubic splines fail to adequately fit early infancy growth with reasonable degrees of freedom. When the degrees of freedom are increased excessively, the function can fit well in infancy but it under-smoothes at older ages. The solution is to expand the age scale when growth velocity is high and to compress it when it is low (Cole et al., 1998). A power transformation applied to age, i.e. f()=age, was a good solution for the considered cases. Therefore, prior to determining the best degrees of freedom for the parameter curves, a search was conducted for the best for the age power transformation. For this, an arbitrary starting model was used to search for the best age-transformation power () based only on the global deviance values over a preset grid of values, since the degrees of freedom remained unchanged. The grid of values ranged from 0.05 to 1 in 0.05 intervals, with the exception of the BMI-for-age standards for children younger than 24 months, for which the value 0.01 also was considered. No length/height transformation was necessary for weight-for-length/height.
Selecting the best model within a class of models
Models were grouped in classes according to the parameters to be modelled. The alternative to modelling parameters was to fix them, e.g. =1 or =2. The criteria used to choose among models within the same class were the AIC and the generalized version of it with penalty equal to 3 (GAIC(3)) as defined in Rigby and Stasinopoulos (2004a):
GAIC (3) = 2L 3 p,
where L is the maximized likelihood and p is the number of parameters (or the total number of degrees of freedom). While the use of the AIC enhances the fitting of local trends, smoother curves are obtained when the model's choice is based on the GAIC(3) criterion. Consistency in the use of these two criteria was attempted across all indicators. For selecting the best combination of df() and df(), both criteria were used in parallel. In cases of disagreement, AIC was used to select df() and GAIC(3) to select df(), overall favouring the options which offered a good compromise between keeping estimates close to the empirical values and producing smooth curves. Only GAIC(3) values were examined to select df() and, whenever needed, df(). In rare cases, other age-specific diagnostic tools were considered for selecting the model with an adequate number of degrees of freedom for the cubic splines fitting the parameter curves. Worm plots (van Buuren and Fredriks, 2001) and Q-test (Royston and Wright, 2000) were used conjointly for this purpose.
Group-specific Q-test statistics resulting in absolute values of z1, z2, z3 or z4 that were larger than 2 were interpreted to indicate a misfit of, respectively, mean, variance, skewness or kurtosis. The overall Q-test statistics combining all groups were based on a Chi-square distribution, which assumes that observations from different groups are independent. In this case, however, given the repeated measurements in the longitudinal study component, the resulting test's p-values could be distorted slightly. To minimize this potential problem, age groups were designed to avoid repeated measurements of the same child within the same age group. The age groups were formed in time intervals (days) to achieve an approximately even sample size distribution across the entire age range of interest, especially in the cross-sectional component, where sample sizes are smaller than in the longitudinal data.
For the longitudinal component, i.e. the first 24 months, time intervals were selected to preserve the longitudinal follow-up structure and avoid having multiple measurements of a given child within one age group. Note that for the longitudinal sample, age ranges were defined to correspond to specific visits, although visits did not always take place at the exact targeted age. For this reason, the constructed age group sample sizes were sometimes slightly different from the designed follow-up
10 Methodology
visit sample sizes. Moreover, cross-sectional observations were added to the longitudinal sample between 18 and 24 months. In the cross-sectional data, it is possible that in a few cases more than one measurement from the same child occurs because of the multiple visits in Brazil and the USA, combined with the lower data density in this component. Similarly, it was impossible to break the sample into independent groups for the weight-for-length/height indicators. For this reason, the Q-test results required a conservative interpretation.
Overall, Q-test results were interpreted with caution and considered simultaneously with results of worm plots (van Buuren and Fredriks, 2001) which do not require any assumption and still offer very specific information about the goodness of fit for each group. The same age grouping was used as defined for the Q-test. Interpretation of results requires careful review of the shapes of the worms formed by a cubic polynomial (the red line in all worm plots) fitted to the points of the detrended Q-Q plots based on z-score values derived from the model being evaluated. A detrended Q-Q plot is presented for each age group. Confidence intervals (95%) are displayed for each of the worms (dotted curves in all worm plots). Table 7 summarizes the interpretation of various worm plot patterns. Flat worms indicate an adequate fit. The Q-test combined with the worm plot patterns provide a robust assessment of a model's goodness of fit, especially in terms of evaluating local fit.
Table 7 Interpretation of various patterns in the worm plota
ShapeMomentIf the wormThen theInterceptMeanpasses above the origin,fitted mean is too small.passes below the origin,fitted mean is too large.SlopeVariancehas a positive slope,fitted variance is too small.has a negative slope,fitted variance is too large.ParabolaSkewnesshas a U-shape,fitted distribution is too skew tothe left.has an inverted U-shape,fitted distribution is too skew tothe right.
S-curve Kurtosis has an S-shape on the left
bent down,
has an S-shape on the left
bent up,
tails of the fitted distribution are too light.
tails of the fitted distribution are too heavy.
Reproduced from van Buuren and Fredriks (2001) with permission from John Wiley & Sons Limited.
Pan and Cole (2004) proposed using a new tool to guide the choice of degrees of freedom for cubic splines fitting each of the parameter curves. They suggested plotting standardized Q-statistics against the number of age groups minus the corresponding degrees of freedom, for each of the L, M and S curves of the LMS method (Cole and Green, 1992). If fitting is adequate, the Q-statistics should be normally distributed with values within the range -2 to 2. This tool provides a global rather than a local test of significance and gives an accurate impression of the underlying goodness of fit because it does not depend on the precise choice of the number of groups. The proposed test is very useful for cross-sectional data where the choice of the number of groups can affect the Q-test results considerably. For example, points that are close in age but in opposite tails of the distribution generate opposing skewness when they fall into separate groups but cancel each other out when they are in the same group. This test was not implemented for the MGRS sample for two reasons. First, the largest number of observations was obtained in the study's longitudinal component, i.e. data were collected frequently at relatively well-defined ages from birth to 24 months. Second, splitting age intervals in a manner that failed to follow the study design, e.g. from birth to one month (which includes
Methodology11
measurements taken at birth, and at 7, 14 and 28 days) would group together four measurements per child, thereby reducing the reliability of the Q-test results.
Selecting the best model across different classes of models
The search for the best model was done in an add-up stepwise form, starting from the simplest class of models comprising the age transformation, if any, and the fitting of the and curves, while keeping fixed =1 and =2 as described in section (a) above. The next step was to fit the curve, fixing only =2 and using the df() and df() selected in the previous step. Once the best model within this class of models was selected, Q-test and worm plot results were evaluated to inform the decision on whether or not to select the more complex model. In a few cases when Q-test and worm plots were not sufficient to assess the improvement offered by the more complex model, comparison of observed and fitted percentiles was used to determine if differences were of clinical significance.
The fit of was considered only when Q-test or worm plots indicated misfit with respect to kurtosis. In this case, a third class of models was considered and comparison of observed against fitted percentiles was done to assess the improvement in the final curves. Among the rare cases where this occurred, fitting the fourth parameter always led to change that was negligible in practical terms. Therefore, all the models fitted had at most 3 non-fixed parameters (, and ).
With df() thus selected (i.e. when was not fixed to value 1), a new iteration was done to re-search for df() and df(). However, none of the additional iterations indicated any need to change either df() or df(). A further iteration was carried out to investigate if it was necessary to change the age-transformation power . This exercise did not lead to any changes in the selected models.
The methodology described above was used for all the indicators. Methodological aspects that are specific to the construction of each of the standards are described hereafter in relevant sections.
As part of the internal validation for each indicator, a detailed examination was made of the differences between empirical and the fitted centiles resulting from the selected model. Comparisons were also made between the observed and expected proportions of children with measurements below selected centiles across age (or length/height for weight-for-length/height) groups. For these two diagnostic tools, evidence of systematic patterns indicative of biases and the magnitude of deviations were examined.
Length/height-for-age, weight-for-age and BMI-for age curves were constructed using all available data (i.e. from birth to 71 months) but final age-based standards were truncated at 60 completed months to avoid the right-edge effect (Borghi et al., 2006). The weight-for-length standards go from 45 to 110 cm and weight-for-height from 65 to 120 cm.
CONSTRUCTION OF THE LENGTH/HEIGHT-FOR-AGE STANDARDS 3.1 Indicator-specific methodology
For the linear growth indicator, the objective was to construct a length-for-age (birth to 2 years) and height-for-age (2 to 5 years) standard using the same model and yet reflect the average difference between recumbent length and standing height. By design, children between 18 and 30 months in the cross-sectional component had both length and height measurements taken. The average difference between the two measurements in this set of 1625 children was 0.73 cm. The results by age group are shown in Table 8.
Table 8 Summary of differences between recumbent length and standing height in a sample of children measured both ways
Age (months)18 to <2121 to <2424 to <2727 to d"3018 to d"30Sample size3343544764611625Mean (cm)a0.750.690.720.770.73St Deviation (cm)a0.610.670.610.610.62
Recumbent length minus standing height.
To fit a single model for the whole age range, 0.7 cm was thus added to the cross-sectional height values. After the model was fitted, the median curve was shifted back downwards by 0.7 cm for ages above two years and the coefficient of variation curve adjusted to the new median values to construct the height-for-age growth curves. The adjusted coefficient of variation (S*) was calculated as follows:
S * =StDev=M S,M *M *
where M and S are, respectively, the fitted median and coefficient of variation values, and M* are the shifted-down median values; StDev is the standard deviation calculated as the median times the coefficient of variation.
The curves were derived directly from a model that used cubic spline fitting functions for the median and coefficient of variation curves. The age transformation used to stretch the x-axis resulted in a large gap between the birth and day 14 measurements, and when the centiles were shrunk back to the original age scale, the cubic spline-fitted curves formed an artificial pattern in this interval. Therefore, keeping the cubic spline-fitted points at days 0 and 14, linear interpolation was applied to derive estimates of the median and the coefficient of variation curves from day 1 to 13 for the final standards.
Although all available data (birth to 71 months) were used when modelling the curves, to minimize the right-edge effect the length/height-for-age and all the other age-based standards extend up to 60 completed months only.
3.2 Length/height-for-age for boys
3.2.1 Sample size
There were 13 551 length/height observations for boys. The longitudinal and cross-sectional sample sizes by visit and age are shown in Tables 9 and 10.
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14 Length/height-for-age, boys
Table 9 Longitudinal sample sizes for length/height-for-age for boys
VisitBirth123456Age02 wk4 wk6 wk2 mo3 mo4 moN893425424424424420419Visit78910111213Age5 mo6 mo7 mo8 mo9 mo10 mo11 moN420424420420416411422Visit14151617181920Age12 mo14 mo16 mo18 mo20 mo22 mo24 moN422419418417422418421
Table 10 Cross-sectional sample sizes for length/height-for-age for boys
Age (mo)<1818 2021 2324 2627 2930 3233 35N3177185238263232259Age (mo)36 3839 4142 4445 4748 5051 5354 56N273255263244245229234Age (mo)57 5960 6263 6566 6869 71>71N2452362212252214
3.2.2 Model selection and results
The model BCPE(x=age, df()=10, df()=6, =1, =2) served as a starting point to construct the length-for-age growth curves. Improvement of the model's fit was investigated by studying changes in global deviance at varying levels of the age-transformation power . Table 11 shows the global deviance for a grid of values. The smallest global deviance corresponds to age-transformation power =0.35.
Table 11 Global deviance (GD) for models within the class BCPE(x=age, df()=10, df()=6, =1, =2) for length/height-for-age for boys
0.050.100.150.200.250.300.350.400.450.50GDa339.9333.7329.1325.6323.0321.3320.8322.2326.2332.60.550.600.650.700.750.800.850.900.951.00GDa340.5347.1349.4345.5337.2331.4340.8383.1479.1648.0
In excess of 65 000
Having chosen the age-transformation power =0.35, the search for the best df() and df() followed, comparing models in which the parameters and had the fixed values 1 and 2, respectively. For this, all possible combinations of df() ranging from 5 to 15 and df() from 2 to 10 were considered. Partial results are presented in Table 12.
Length/height-for-age, boys15
Table 12 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for length/height-for-age for boys
df()df()GDaAICaGAIC(3)aTotal df4338.5364.5377.51395330.1358.1372.1146326.5356.5371.5157324.5356.6372.6168323.1357.1374.1174332.9360.9374.914105324.5354.5369.5156320.8352.8368.8167318.9352.9369.9178317.5353.5371.5184329.8359.8374.815115321.4353.4369.4166317.7351.7368.7177315.8351.8369.8188314.4352.4371.4194327.8359.8375.816125319.4353.4370.4176315.7351.7369.7187313.8351.8370.8198312.4352.4372.4204326.4360.4377.417135317.9353.9371.9186314.2352.2371.2197312.3352.3372.3208311.0353.0374.021
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 65 000.
The best combination of AIC and GAIC(3) corresponds to df()=11 or 12 and df()=6. To select between df()=11 and 12, their respective worm plots (Figures 1 and 5) were compared. Age group labels in the worm plots correspond to those shown in Table 14. The model df()=11 presents evidence of misfit in the median curve for a few age groups (e.g. 14 d, 4 mo) for which corresponding plots have worms shifted down or up (Figure 1). The fit was improved by increasing the df() to 12 (Figure 5), and thus the combination of df()=12 and df()=6 was chosen. Further evaluations of this model were carried out by examining the fit of the and curves and the patterns of the centile residuals (the empirical minus the fitted centiles) across age.
16 Length/height-for-age, boys
-3-11 2 3-3 -11 2 3-3-11 2 340.46 mo52 mo58 mo64 mo70 mo00.-0.420 mo22 mo24 mo28 mo34 mo40 mo
Deviation0 40.40.0.10 mo11 mo12 mo14 mo16 mo18 mo-4 mo5 mo6 mo7 mo8 mo9 mo
40.Birth14 d28 d42 d2 mo3 mo00.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 00. 40.
-0.4 00. 40.
Unit normal quantile
Figure 1 Worm plots of z-scores for candidate model with df()=11 and df()=6 with age transformation age0.35 for length/height-for-age for boys
Model 1: BCPE(x=age0.35, df()=12, df()=6, =1, =2)
The fitted parameter curves show adequate smoothing despite the erratic coefficient of variation in the cross-sectional sample's height (Figure 2). The residual plots of the fitted centiles for the period 0 to 24 months (Figure 3) showed no evidence of bias. For the age range 24 to 71 months, residuals of the fitted centiles showed a non-random pattern for the 50th centile, but were smaller than 0.6 cm up to 60 months where estimated SDs vary from 3.5 to 5 cm (Figure 4).
Table 13 shows the proportions of children with length (or height) below the fitted centiles. Age group labels correspond to the same age intervals provided in Table 14. Overall, there was no evidence of systematic departures from expected patterns suggestive of bias. Overestimates in the median (50th centile) for the age groups 14 d (55%), 2 mo (54%) and 40 mo (56%) were noted. The opposite was observed for the age group 70 mo (46%), i.e. the median was underestimated. The clinical significance of these few observed differences between fitted and observed proportions is likely to be small.
Length/height-for-age, boys17
900.03860 70 80Length Coeff of VariationLength Median (cm)0. 0. 0.032034036500.030024681012141618202224024681012141618202224115Height Coeff of Variation0.044Height Median (cm)95 100 105 1100. 0. 0.038040042900.03685243036424854606672243036424854606672
Age (months)
Figure 2 Fitting of and curves of Model 1 for length/height-for-age for boys (dotted line)
and their respective sample estimates (points with solid line)
The worm plots for Model 1 are shown in Figure 5. The worms fitted to the points (solid red line) do not indicate any upward or downward shifts except in the last age group (70 mo). This implies that, overall, the fit of the median was adequate. In older age groups (40 mo and above), extreme values are noted outside the 95% confidence interval depicted by the dotted curve lines. This may be due to some extreme values that were not considered as data errors or outliers. The shapes of the worms deviate slightly from flat, but remain within bounds of the confidence intervals. For example, the age groups 40 mo, 46 mo and 70 mo present slightly U-shaped worms, indicating residual skewness to the left. There is no evidence of worms with a slope, which would indicate misfit in the variance curve. S-shaped worms indicate a misfit in the curve of the parameter related to kurtosis as is the case in the birth and 58 mo age groups, although here too, the worms are contained within the 95% confidence interval.
18 Length/height-for-age, boys
3rd Centile5th Centile10th Centile60.60.60.20.20.20.-0.2-0.2-0.2(cm)-0.6-0.6-0.6forLength02468121620240246812162024024681216202460.25th Centile60.50th Centile60.75th Centile-Fitted Centile2-0.6-0.20.2-0.6-0.20.2-0.6-0.20.Empirical60.24681216202460.24681216202460.24681216202400090th Centile95th Centile97th Centile20.20.20.-0.2-0.2-0.2-0.6-0.6-0.6024681216202402468121620240246812162024
Age (months)
Figure 3 Centile residuals from fitting Model 1 for length/height-for-age from 0 to 24 months for boys
3rd Centile5th Centile10th Centile51.51.51.50.50.50.-0.5-0.5-0.5(cm)-1.531374349556167-1.531374349556167-1.531374349556167forHeight25252551.25th Centile51.50th Centile51.75th CentileFitted Centile51.5-0.50.51.5-0.50.51.5-0.50.----Empirical51.3137434955616751.3137434955616751.3137434955616725252590th Centile95th Centile97th Centile50.50.50.-0.5-0.5-0.5-1.5-1.5-1.5253137434955616725313743495561672531374349556167
Age (months)
Figure 4 Centile residuals from fitting Model 1 for length/height-for-age from 24 to 71 months for boys
Length/height-for-age, boys19
-3-11 2 3-3 -11 2 3-3-11 2 30.446 mo52 mo58 mo64 mo70 mo0.0-0.420 mo22 mo24 mo28 mo34 mo40 mo
Deviation0.4 0. 0.0410 mo11 mo12 mo14 mo16 mo18 mo-4 mo5 mo6 mo7 mo8 mo9 mo
0.4Birth14 d28 d42 d2 mo3 mo0.0-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 5 Worm plots of z-scores for Model 1 for length/height-for-age for boys
Table 13 Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for boys
ExpectedBirth14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo10.70.50.71.20.21.21.00.50.50.732.02.93.02.64.02.92.62.43.14.655.26.44.44.05.75.04.14.15.55.61011.111.710.39.09.79.38.210.18.610.72525.525.524.624.624.122.924.524.324.622.65048.955.151.852.754.251.950.549.550.649.47574.474.574.074.076.275.074.075.076.678.69088.088.891.189.889.290.290.689.790.791.29594.895.095.194.894.895.294.294.094.794.29797.496.997.096.596.996.795.795.097.196.19999.498.398.898.898.698.697.898.398.898.8
Expected8 mo9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo10.91.01.51.71.21.71.21.41.20.734.73.83.73.23.44.04.63.23.12.656.45.85.74.76.05.55.84.34.83.61010.610.310.19.09.410.211.17.010.49.32522.423.124.023.924.723.525.524.126.922.85052.150.849.950.849.649.450.050.751.149.27575.577.972.672.075.372.975.273.975.674.59091.091.289.491.490.689.392.592.190.890.59596.095.795.895.196.494.195.995.595.695.39797.296.296.897.297.697.996.997.597.397.19999.198.098.898.999.099.598.699.199.299.620
Length/height-for-age, boys
Table 13 Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for boys (continued)
Expected24 mo28 mo34 mo40 mo46 mo52 mo58 mo64 mo70 moOverall11.20.41.31.00.81.20.41.50.71.034.03.12.32.11.73.93.23.42.43.155.24.85.34.43.65.55.74.25.15.01011.510.210.410.79.010.111.59.18.810.02525.323.124.326.722.822.326.325.922.124.35050.948.850.756.050.749.352.452.245.950.97575.571.575.175.674.875.175.375.870.774.89091.289.489.589.791.491.791.188.287.190.29594.995.094.294.595.296.196.094.995.695.19797.696.595.996.297.197.897.496.698.096.99999.598.897.697.798.799.499.499.2100.098.9
Note: Group labels correspond to the age intervals in Table 14.
Length/height-for -age, boys
2122 Length/height-for-age, boys
The Q-test was performed to assess the overall significance of the deviations noted for the birth and 40 mo, 46 mo, 58 mo age groups (Table 14). Absolute values of z3 larger than 2 were observed only in the age groups 40 mo and 46 mo, and for z4 at birth and in age group 58 mo. Nevertheless, the overall tests (p-values shown for each statistic in the last row of the table) do not suggest any significant departures of the fitted model z-scores from normality at the 5% level of significance.
Table 14 Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=12, df()=6, =1, =2)] for length/height-for-age for boys
Age (days)GroupNz1z2z3z40Birth8930.21-0.300.07-2.241 to 1614 d419-0.461.021.290.0817 to 3428 d427-0.210.080.390.2435 to 4942 d4230.010.230.291.2550 to 692 mo424-0.25-0.151.120.8070 to 993 mo4200.11-0.281.091.38100 to 1294 mo4160.750.651.150.72130 to 1595 mo4160.270.231.73-0.07160 to 1896 mo419-0.02-0.620.570.16190 to 2197 mo411-0.36-0.010.160.30220 to 2498 mo424-0.30-0.16-0.740.23250 to 2799 mo398-0.38-0.140.690.91280 to 30910 mo4050.490.18-0.540.12310 to 34911 mo4650.29-0.18-0.83-0.42350 to 37912 mo417-0.34-0.36-1.02-0.41380 to 43914 mo4210.210.37-1.040.13440 to 49916 mo416-0.28-0.02-0.591.51500 to 55918 mo4440.00-0.96-0.151.69560 to 61920 mo521-0.230.09-0.601.81620 to 67922 mo5490.51-0.92-1.050.83680 to 74924 mo593-0.960.04-0.81-0.23750 to 92928 mo4801.020.150.630.11930 to 111934 mo5310.271.520.291.371120 to 130940 mo525-0.521.463.551.821310 to 149946 mo5230.37-0.622.011.471500 to 168952 mo507-0.12-0.72-1.47-0.321690 to 187958 mo494-1.04-0.380.09-2.071880 to 206964 mo475-0.130.460.360.482070 to 224970 mo2951.39-0.25-1.86-1.23Overall Q stats13 5517.7610.0738.5133.73degrees of freedom17.025.529.029.0p-value0.97140.99720.11130.2494
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
To evaluate whether Model 1 could be improved by modelling the parameter that corrects for skewness, a model using the BCPE distribution fixing =2 and modelling the other three parameters was considered. The degrees of freedom of the cubic splines for and were kept as indicated earlier for Model 1, with the same age-transformation power. The best choice of degrees of freedom for the cubic splines to fit the parameter was then sought.
Length/height-for-age, boys23
Table 15 Goodness-of-fit summary for models BCPE(x=age0.35, df()=12, df()=6, df()=?, =2) for length/height-for-age for boys
df()GDaGAIC(3)aTotal df3312.1375.1214307.4373.4225301.4370.4236297.0369.0247294.4369.4258292.7370.726
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 65 000
To assess the goodness of fit of the models considered within this class, only the GAIC(3) values were compared, since this criterion penalizes more than does the AIC for increased degrees of freedom. Table 15 shows the GAIC(3) values for degrees of freedom varying from 3 to 8. In this case df()=6 presented the best fit, so the corresponding model was selected for further evaluation.
Model 2: BCPE(x=age0.35, df()=12, df()=6, df()=6, =2)
Model 2 yielded a GAIC(3) of 65 369.0 compared with the 65 369.7 of Model 1. The results for Model 2 from the same diagnostic tools/tests presented for Model 1 were compared to assess the impact of modelling skewness for specific ages.
The worm plots for the z-scores derived from Model 2 (Figure 6) show very similar results to those that correspond to Model 1 (Figure 5). This indicates that deviations from normal that were observed in z-scores derived from Model 1 are unlikely to be corrected by modelling skewness. The Q-test for Model 2 (Table 16) provides slightly improved results where only one group (40 mo) has residual skewness compared to two groups in Model 1 (Table 14). Nonetheless both sets of results lead to the same conclusion, i.e. neither model's residuals (or z-scores) depart significantly from the normal distribution.
Although some indication of residual kurtosis was observed in two of the 29 age groups after fitting both Models 1 and 2, the overall test results were not significant: Q-test (z4) p-values were 0.25 and 0.26 for models 1 and 2, respectively (Tables 14 and 16).
Table 17 presents the observed proportions of children below specific fitted centiles by age group. Observed proportion values are slightly closer to the expected proportion of children below the centiles for age groups 40 mo, 46 mo and 70 mo, when Model 2 is fitted, i.e. modelling skewness.
24 Length/height-for-age, boys
-3-11 2 3-3 -11 2 3-3-11 2 340.46 mo52 mo58 mo64 mo70 mo00.-0.420 mo22 mo24 mo28 mo34 mo40 mo
Deviation0 40.40.0.10 mo11 mo12 mo14 mo16 mo18 mo-4 mo5 mo6 mo7 mo8 mo9 mo
40.Birth14 d28 d42 d2 mo3 mo00.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 00. 40.
-40. 00. 40.
Unit normal quantile
Figure 6 Worm plots of z-scores for Model 2 for length/height-for-age for boys
The diagnostic tools/tests used to evaluate distinct models supported the selection of the simplest model, i.e. the BCPE distribution with fixed =1 and =2, that corresponds to the normal distribution. Overall statistics like GAIC(3) supported this choice. Considering local goodness of fit, the Q-test indicated minor departures from normality as reflected by the residuals (z-scores) of very few age groups when Model 1 was fitted. The worm plot results similarly indicate misfits for very few age groups. Since those isolated discrepancies or misfits were only partially corrected by modelling the parameter of the distribution (Model 2), it is reasonable to assume that these deviations occurred by chance or for other than biological reasons, and that the simpler model (i.e. Model 1) is adequate.
Model 1 was selected and a new iteration was done using the values of df() and df() equal to 12 and 6, respectively, to re-search the best age-transformation power . The smallest global deviance in this case was for =0.4 (GD=65 315.6), but with only a very minor difference from the model using =0.35 (GD=65 315.7). There was thus no need for updating , and the selected model for constructing the length/height-for-age growth curves for boys remained BCPE(x= age0.35, df()=12, df()=6, =1, =2).
Length/height-for-age, boys25
Table 16 Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=12, df()=6, df()=6, =2)] for length/height-for-age for boys
Age (days)GroupNz1z2z3z40Birth8930.21-0.30-0.20-2.241 to 1614 d419-0.431.000.56-0.0317 to 3428 d427-0.190.10-0.410.3835 to 4942 d4230.020.26-0.671.5350 to 692 mo424-0.25-0.150.240.7670 to 993 mo4200.11-0.290.191.27100 to 1294 mo4160.750.610.400.65130 to 1595 mo4160.260.201.23-0.21160 to 1896 mo419-0.02-0.600.230.10190 to 2197 mo411-0.370.01-0.020.29220 to 2498 mo424-0.30-0.14-0.760.24250 to 2799 mo398-0.38-0.130.820.94280 to 30910 mo4050.490.19-0.300.12310 to 34911 mo4650.30-0.18-0.50-0.48350 to 37912 mo417-0.35-0.39-0.64-0.46380 to 43914 mo4210.220.35-0.540.03440 to 49916 mo416-0.28-0.040.011.56500 to 55918 mo444-0.01-0.950.401.72560 to 61920 mo521-0.220.09-0.081.78620 to 67922 mo5490.53-0.91-0.760.72680 to 74924 mo593-0.930.05-0.70-0.25750 to 92928 mo4801.070.160.350.04930 to 111934 mo5310.301.59-0.701.631120 to 130940 mo525-0.541.342.411.301310 to 149946 mo5230.35-0.671.031.101500 to 168952 mo507-0.13-0.63-1.90-0.181690 to 187958 mo494-1.06-0.340.07-2.061880 to 206964 mo475-0.120.460.840.432070 to 224970 mo2951.42-0.29-1.34-1.65Overall Q stats13 5517.949.8019.9233.53degrees of freedom17.025.523.029.0p-value0.96780.99780.64680.2568
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Figures 7 to 10 show the empirical and fitted centiles derived from the selected model for the length-for-age (0 to 24 months) and height-for-age (24 to 71 months) growth curves. The final standards were constructed as described in detail in section 3.1.
Table 17 Observed proportions of children with measurements below the fitted centiles from Model 2, length/height-for-age for boys
ExpectedBirth14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo10.71.00.71.20.21.41.41.00.50.732.03.13.02.84.02.92.92.63.84.655.26.44.74.56.45.04.14.36.06.11011.112.210.59.59.79.38.710.18.610.72525.525.324.124.323.822.623.624.324.622.45048.955.151.352.253.851.750.249.050.649.47574.474.573.573.375.975.073.675.076.678.69088.089.091.390.389.490.290.989.790.791.29595.395.295.195.095.095.294.294.294.794.29797.696.997.096.597.496.795.995.497.496.49999.498.399.199.198.699.098.398.398.898.8
Expected8 mo9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo10.91.01.21.51.21.71.21.41.20.534.73.53.73.22.93.84.33.22.92.656.45.85.74.75.55.25.84.34.83.61010.610.310.18.89.410.211.17.010.49.32522.423.124.224.324.724.225.524.526.922.85052.151.049.950.850.150.150.551.151.149.47575.577.972.872.375.572.975.574.175.674.59091.091.289.491.490.689.192.591.790.890.59596.095.795.895.196.293.895.995.595.695.19797.296.296.897.297.497.696.997.597.397.19999.198.098.898.999.099.598.699.199.299.626
Length/height-for-age, boys
Table 17 Observed proportions of children with measurements below the fitted centiles from Model 2, length/height-for-age for boys (continued)
Expected24 mo28 mo34 mo40 mo46 mo52 mo58 mo64 mo70 moOverall11.20.41.31.30.81.20.41.30.71.034.03.12.62.11.93.93.23.42.43.255.24.85.54.64.65.55.74.25.15.11011.510.210.410.99.210.311.59.18.510.02525.322.724.125.922.822.326.726.122.424.35050.947.749.955.250.548.952.452.246.950.87575.571.574.875.274.275.175.376.071.174.79091.289.489.589.991.491.791.188.287.190.39594.895.094.494.795.896.396.094.595.295.29797.696.796.296.297.398.097.296.498.097.09999.598.897.797.998.799.499.299.2100.098.9
Note: Group labels correspond to the age intervals in Table 16.
Length/height-for-age, boys
27
97th90th9050th10th3rd80Length (cm)7060FittedEmpirical50
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 7 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: length-for-age for boys from birth to 24 months
28
Length/height-for-age, boys
95th9075th50th25th5th80Length (cm)7060Fitted50Empirical
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 8 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: length-for-age for boys from birth to 24 months
Length/height-for-age, boys
29
97th12090th50th11010thHeight (cm)3rd100
90
Fitted
Empirical
80
24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72
Age (months)
Figure 9 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: height-for-age for boys from 24 to 71 months
30
Length/height-for-age, boys
95th12075th50th11025thHeight (cm)5th10090FittedEmpirical802427303336394245485154576063666972Age (months)
Figure 10 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: height-for-age for boys from 24 to 71 months
Length/height-for-age, boys
3132 Length/height-for-age, boys
3.2.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO length/height-for-age z-score and percentile charts (Figures 11 to
and tables (Tables 18 to 20) for boys. It also provides the z-score comparisons of the WHO versus NCHS (Figure 15) and CDC 2000 (Figure 16) curves.
Charts
9080Length (cm)706050
3
2
1
0
-1
-2
-3
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 11 WHO length-for-age z-scores for boys from birth to 24 months
Length/height-for-age, boys
33
120110Height (cm)1009080
3
2
1
0
-1
-2
-3
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Age (months)
Figure 12 WHO height-for-age z-scores for boys from 24 to 60 months
34
Length/height-for-age, boysLength/height-for-age, boys35
97th85th50th15th3rd
2422months202418birth to16from10 12 14Age (months)age percentiles for boys6 8WHO length-for-42Figure 130
9080706050Length (cm)
120110Height (cm)1009080
97th
85th
50th
15th
3rd
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Age (months)
Figure 14 WHO height-for-age percentiles for boys from 24 to 60 months
36
Length/height-for-age, boys
Tables
Table 18 Length-for-age for boys, age in weeks
Percentiles (length in cm)WeekLMSSD1st3rd5th15th25th50th75th85th95th97th99th0149.88420.037951.893145.546.346.847.948.649.951.251.853.053.454.31151.11520.037231.903046.747.548.049.149.851.152.453.154.254.755.52152.34610.036521.911747.948.849.250.451.152.353.654.355.555.956.83153.39050.036091.926948.949.850.251.452.153.454.755.456.657.057.94154.38810.035701.941749.950.751.252.453.154.455.756.457.658.058.95155.33740.035341.955650.851.752.153.354.055.356.757.458.659.059.96156.23570.035011.968851.752.553.054.254.956.257.658.359.559.960.87157.08510.034701.980952.553.453.855.055.757.158.459.160.360.861.78157.88890.034421.992553.354.154.655.856.557.959.260.061.261.662.59158.65360.034162.003654.054.955.456.657.358.760.060.761.962.463.310159.38720.033922.014454.755.656.157.358.059.460.761.562.763.264.111160.08940.033692.024455.456.356.858.058.760.161.562.263.463.964.812160.76050.033482.034356.056.957.458.759.460.862.162.964.164.665.513161.40130.033292.044056.657.658.059.360.061.462.863.564.865.266.2
Length/height-for-age, boys
37Table 18 Length-for-age for boys, age in weeks (continued)
Z-scores (length in cm)WeekLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0149.88420.037951.893144.246.148.049.951.853.755.61151.11520.037231.903045.447.349.251.153.054.956.82152.34610.036521.911746.648.550.452.354.356.258.13153.39050.036091.926947.649.551.553.455.357.259.24154.38810.035701.941748.650.552.454.456.358.360.25155.33740.035341.955649.551.453.455.357.359.261.26156.23570.035011.968850.352.354.356.258.260.262.17157.08510.034701.980951.153.155.157.159.161.063.08157.88890.034421.992551.953.955.957.959.961.963.99158.65360.034162.003652.654.656.658.760.762.764.710159.38720.033922.014453.355.457.459.461.463.465.411160.08940.033692.024454.056.058.160.162.164.166.212160.76050.033482.034354.756.758.760.862.864.866.913161.40130.033292.044055.357.359.461.463.465.567.5
38
Length/height-for-age, boys
Table 19 Length-for-age for boys, age in years and months
Percentiles (length in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th0:00149.88420.037951.893145.546.346.847.948.649.951.251.853.053.454.30:11154.72440.035571.946550.251.151.552.753.454.756.056.757.958.459.30:22158.42490.034242.000553.854.755.156.457.158.459.860.561.762.263.10:33161.42920.033282.044456.757.658.159.360.161.462.863.564.865.366.20:44163.88600.032572.080859.060.060.561.762.563.965.366.067.367.868.70:55165.90260.032042.111561.061.962.463.764.565.967.368.169.469.970.80:66167.62360.031652.140362.663.664.165.466.267.669.169.871.171.672.60:77169.16450.031392.171164.165.165.666.967.769.270.671.472.773.274.20:88170.59940.031242.205565.566.567.068.369.170.672.172.974.274.775.70:99171.96870.031172.243366.867.768.369.670.572.073.574.375.776.277.20:1010173.28120.031182.284968.069.069.570.971.773.374.875.677.077.678.60:1111174.53880.031252.329369.170.270.772.173.074.576.177.078.478.980.01:012175.74880.031372.376270.271.371.873.374.175.777.478.279.780.281.31:113176.91860.031542.426071.372.472.974.475.376.978.679.480.981.582.61:214178.04970.031742.477372.373.474.075.576.478.079.780.682.182.783.81:315179.14580.031972.530373.374.475.076.577.479.180.981.883.383.985.01:416180.21130.032222.584474.275.476.077.578.580.282.082.984.585.186.21:517181.24870.032502.640675.176.376.978.579.581.283.084.085.686.287.41:618182.25870.032792.697376.077.277.879.580.482.384.185.186.787.388.51:719183.24180.033102.755376.878.178.780.481.483.285.186.187.888.489.71:820184.19960.033422.814077.778.979.681.382.384.286.187.188.889.590.71:921185.13480.033762.874278.479.780.482.283.285.187.188.189.990.591.81:1022186.04770.034102.934279.280.581.283.084.186.088.089.190.991.692.91:1123186.94100.034452.995180.081.382.083.884.986.989.090.091.992.693.92:024187.81610.034793.055180.782.182.884.685.887.889.991.092.893.694.9
Length/height-for-age, boys
39Table 19 Length-for-age for boys, age in years and months (continued)
Z-scores (length in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0:00149.88420.037951.893144.246.148.049.951.853.755.60:11154.72440.035571.946548.950.852.854.756.758.660.60:22158.42490.034242.000552.454.456.458.460.462.464.40:33161.42920.033282.044455.357.359.461.463.565.567.60:44163.88600.032572.080857.659.761.863.966.068.070.10:55165.90260.032042.111559.661.763.865.968.070.172.20:66167.62360.031652.140361.263.365.567.669.871.974.00:77169.16450.031392.171162.764.867.069.271.373.575.70:88170.59940.031242.205564.066.268.470.672.875.077.20:99171.96870.031172.243365.267.569.772.074.276.578.70:1010173.28120.031182.284966.468.771.073.375.677.980.10:1111174.53880.031252.329367.669.972.274.576.979.281.51:012175.74880.031372.376268.671.073.475.778.180.582.91:113176.91860.031542.426069.672.174.576.979.381.884.21:214178.04970.031742.477370.673.175.678.080.583.085.51:315179.14580.031972.530371.674.176.679.181.784.286.71:416180.21130.032222.584472.575.077.680.282.885.488.01:517181.24870.032502.640673.376.078.681.283.986.589.21:618182.25870.032792.697374.276.979.682.385.087.790.41:719183.24180.033102.755375.077.780.583.286.088.891.51:820184.19960.033422.814075.878.681.484.287.089.892.61:921185.13480.033762.874276.579.482.385.188.090.993.81:1022186.04770.034102.934277.280.283.186.089.091.994.91:1123186.94100.034452.995178.081.083.986.989.992.995.92:024187.81610.034793.055178.781.784.887.890.993.997.0
40
Length/height-for-age, boys
Table 20 Height-for age for boys, age in years and months
Percentiles (height in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th2:024187.11610.035073.055180.081.482.183.985.187.189.290.392.192.994.22:125187.97200.035423.116080.782.182.884.785.988.090.191.293.193.895.22:226188.80650.035763.175781.482.883.685.586.788.890.992.194.094.896.22:327189.61970.036103.235382.183.584.386.387.489.691.893.094.995.797.12:428190.41200.036423.292882.884.285.087.088.290.492.693.895.896.698.12:529191.18280.036743.350183.484.985.787.788.991.293.494.796.797.599.02:630191.93270.037043.405284.085.586.388.489.691.994.295.597.598.399.92:731192.66310.037333.459184.686.287.089.190.392.795.096.298.499.2100.72:832193.37530.037613.511885.286.887.689.791.093.495.797.099.2100.0101.52:933194.07110.037873.562585.887.488.290.491.794.196.597.899.9100.8102.42:1034194.75320.038123.612086.488.088.891.092.394.897.298.5100.7101.5103.22:1135195.42360.038363.660486.988.589.491.693.095.497.999.2101.4102.3103.93:036196.08350.038583.706987.589.190.092.293.696.198.699.9102.2103.1104.73:137196.73370.038793.752388.089.790.692.894.296.799.3100.6102.9103.8105.53:238197.37490.039003.797688.590.291.193.494.897.499.9101.3103.6104.5106.23:339198.00730.039193.840989.190.891.794.095.498.0100.6102.0104.3105.2106.93:440198.63100.039373.883189.691.392.294.696.098.6101.3102.7105.0105.9107.73:541199.24590.039543.924290.191.992.895.296.699.2101.9103.3105.7106.6108.43:642199.85150.039713.965190.692.493.395.797.299.9102.5104.0106.4107.3109.13:7431100.44850.039864.003991.192.993.996.397.7100.4103.1104.6107.0108.0109.83:8441101.03740.040024.043591.693.494.496.898.3101.0103.8105.2107.7108.6110.43:9451101.61860.040164.081092.193.994.997.498.9101.6104.4105.8108.3109.3111.13:10461102.19330.040314.119492.694.495.497.999.4102.2105.0106.5109.0109.9111.83:11471102.76250.040454.156793.194.995.998.5100.0102.8105.6107.1109.6110.6112.44:0481103.32730.040594.194193.695.496.499.0100.5103.3106.2107.7110.2111.2113.1
Length/height-for-age, boys
41Table 20 Height-for age for boys, age in years and months (continued)42Percentiles (height in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th4:1491103.88860.040734.231494.095.996.999.5101.0103.9106.7108.3110.8111.8113.74:2501104.44730.040864.267794.596.497.4100.0101.6104.4107.3108.9111.5112.5114.44:3511105.00410.041004.305295.096.997.9100.5102.1105.0107.9109.5112.1113.1115.04:4521105.55960.041134.341795.597.498.4101.1102.6105.6108.5110.1112.7113.7115.74:5531106.11380.041264.378395.997.998.9101.6103.2106.1109.1110.7113.3114.3116.34:6541106.66680.041394.414996.498.499.4102.1103.7106.7109.6111.2113.9115.0116.94:7551107.21880.041524.451796.998.899.9102.6104.2107.2110.2111.8114.5115.6117.64:8561107.76970.041654.488697.399.3100.4103.1104.7107.8110.8112.4115.2116.2118.24:9571108.31980.041774.524597.899.8100.9103.6105.3108.3111.4113.0115.8116.8118.84:10581108.86890.041904.561698.3100.3101.4104.1105.8108.9111.9113.6116.4117.4119.54:11591109.41700.042024.597798.7100.8101.9104.7106.3109.4112.5114.2117.0118.1120.15:0601109.96380.042144.633999.2101.2102.3105.2106.8110.0113.1114.8117.6118.7120.7
Length/height-for-age, boys
Table 20 Height-for-age for boys, age in years and months (continued)
Z-scores (height in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD2:024187.11610.035073.055178.081.084.187.190.293.296.32:125187.97200.035423.116078.681.784.988.091.194.297.32:226188.80650.035763.175779.382.585.688.892.095.298.32:327189.61970.036103.235379.983.186.489.692.996.199.32:428190.41200.036423.292880.583.887.190.493.797.0100.32:529191.18280.036743.350181.184.587.891.294.597.9101.22:630191.93270.037043.405281.785.188.591.995.398.7102.12:731192.66310.037333.459182.385.789.292.796.199.6103.02:832193.37530.037613.511882.886.489.993.496.9100.4103.92:933194.07110.037873.562583.486.990.594.197.6101.2104.82:1034194.75320.038123.612083.987.591.194.898.4102.0105.62:1135195.42360.038363.660484.488.191.895.499.1102.7106.43:036196.08350.038583.706985.088.792.496.199.8103.5107.23:137196.73370.038793.752385.589.293.096.7100.5104.2108.03:238197.37490.039003.797686.089.893.697.4101.2105.0108.83:339198.00730.039193.840986.590.394.298.0101.8105.7109.53:440198.63100.039373.883187.090.994.798.6102.5106.4110.33:541199.24590.039543.924287.591.495.399.2103.2107.1111.03:642199.85150.039713.965188.091.995.999.9103.8107.8111.73:7431100.44850.039864.003988.492.496.4100.4104.5108.5112.53:8441101.03740.040024.043588.993.097.0101.0105.1109.1113.23:9451101.61860.040164.081089.493.597.5101.6105.7109.8113.93:10461102.19330.040314.119489.894.098.1102.2106.3110.4114.63:11471102.76250.040454.156790.394.498.6102.8106.9111.1115.24:0481103.32730.040594.194190.794.999.1103.3107.5111.7115.9
Length/height-for-age, boys
43Table 20 Height-for-age for boys, age in years and months (continued)44Z-scores (height in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD4:1491103.88860.040734.231491.295.499.7103.9108.1112.4116.64:2501104.44730.040864.267791.695.9100.2104.4108.7113.0117.34:3511105.00410.041004.305292.196.4100.7105.0109.3113.6117.94:4521105.55960.041134.341792.596.9101.2105.6109.9114.2118.64:5531106.11380.041264.378393.097.4101.7106.1110.5114.9119.24:6541106.66680.041394.414993.497.8102.3106.7111.1115.5119.94:7551107.21880.041524.451793.998.3102.8107.2111.7116.1120.64:8561107.76970.041654.488694.398.8103.3107.8112.3116.7121.24:9571108.31980.041774.524594.799.3103.8108.3112.8117.4121.94:10581108.86890.041904.561695.299.7104.3108.9113.4118.0122.64:11591109.41700.042024.597795.6100.2104.8109.4114.0118.6123.25:0601109.96380.042144.633996.1100.7105.3110.0114.6119.2123.9
Length/height-for-age, boys
Comparison with NCHS
120
(cm)100Length / Height8060
3
2
1
0
-1
-2
-3
WHO
NCHS
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 15 Comparison of WHO with NCHS length/height-for-age z-scores for boys
Length/height-for-age, boys
45Comparison with CDC 2000
1203210(cm)100-1-2-3Length / Height8060
WHOCDC 2000400246812162024283236404448525660Age (months)
Figure 16 Comparison of WHO with CDC 2000 length/height-for-age z-scores for boys
46
Length/height-for-age, boysLength/height-for-age, girls47
3.3 Length/height-for-age for girls
The choice of the model to construct the length/height-for-age standards for girls followed the steps described for the corresponding standards for boys. In principle, unless a clear inadequacy is detected, models used for constructing the standards for both sexes should belong to the same class.
3.3.1 Sample size
There were 13 783 length/height observations for girls. The longitudinal and cross-sectional sample sizes by visit and age are presented in Tables 21 and 22.
Table 21 Longitudinal sample sizes for length/height-for-age for girls
VisitBirth123456Age02 wk4 wk6 wk2 mo3 mo4 moN842449448447447449447Visit78910111213Age5 mo6 mo7 mo8 mo9 mo10 mo11 moN450448448445449446445Visit14151617181920Age12 mo14 mo16 mo18 mo20 mo22 mo24 moN451451444449444438449
Table 22 Cross-sectional sample sizes for length/height-for-age for girls
Age (mo)<1818 2021 2324 2627 2930 3233 35N2160171244219238231Age (mo)36 3839 4142 4445 4748 5051 5354 56N229241254219231208240Age (mo)57 5960 6263 6566 6869 71>71N2422232052302100
3.3.2 Model selection and results
Using the model BCPE(x=age, df()=10, df()=6, =1, =2) as the starting point, the best age-transformation power () was sought. For girls, although the minimum global deviance corresponded to =0.30, its performance was similar to the model with =0.35 (Table 23) used for constructing the same standards for boys. Thus, =0.35 was selected as the age-transformation power and a search followed for the best combination of degrees of freedom for the cubic splines to fit the BCPE distribution parameter curves.
48 Length/height-for-age, girls
Table 23 Global deviance (GD) for models within the class BCPE(x=age, df()=10, df()=6, =1, =2) for length/height-for-age for girls
0.050.100.150.200.250.300.350.400.450.50GDa299.5296.2294.1292.9292.2292.1292.8294.7298.4303.80.550.600.650.700.750.800.850.900.951.00GDa310.0314.8316.2312.6305.7300.9308.3341.4416.1547.2
In excess of 67 000.
The search for the best combination of degrees of freedom for the cubic splines to fit the and parameter curves started from the simplest class of models using the BCPE distribution and fixing =1, =2, and =0.35. Table 24 shows various combinations that were considered. The best combination of AIC and GAIC(3) pointed to the model with df()=10 and df()=5. The properties of this model were evaluated using the same set of diagnostic tools used for length/height-for-age for boys.
Table 24 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for length/height-for-age for girls
df()df()GDaAICaGAIC(3)aTotal df3319.6341.6352.61184306.8330.8342.8125303.7329.7342.7136302.3330.3344.3147301.6331.6346.6153313.0337.0349.01294300.1326.1339.1135297.0325.0339.0146295.6325.6340.6157294.9326.9342.9163310.2336.3349.313104297.3325.3339.3145294.1324.1339.1156292.8324.8340.8167292.0326.0343.0173308.7336.8350.814114295.8325.8340.8155292.6324.6340.6166291.2325.2342.2177290.5326.5344.5183307.7337.7352.7154294.7326.7342.716125291.5325.5342.5176290.2326.2344.2187289.5327.5346.419
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 67 000.
Length/height-for-age, girls49
Model 1: BCPE(x=age0.35, df()=10, df()=5, =1, =2)
The two fitted parameter curves, i.e. the median and coefficient of variation appear to be adequately smoothed (Figure 17). Some evidence of a trend to underestimate extreme (3rd and 97th) centiles is shown in the distribution of the fitted centile residuals between birth and 24 months (Figure 18). Fitted centile residuals for the age interval 24 to 71 months showed mild systematic underestimations only for the 5th centile curve (Figure 19). The average bias for this centile curve was around 0.5 cm (SD estimates vary approximately from 3.2 to 5.5 cm across this age range). In this age interval, the proportions of children in the sample that are below the fitted 5th centile vary from 3.8% to 6%, but no clear pattern emerges to indicate bias. Overall, the distribution of the proportions below each of the fitted centiles does not indicate any bias (Table 25).
900. 0.036038Length Median (cm)60 70 80Length Coeff of Variation0.0345002468101214161820222402468101214161820222490 100 110Height Coeff of Variation0.046Height Median (cm)0. 0. 0.0400420440.038243036424854606672243036424854606672
Age (months)
Figure 17 Fitting of the and curves of Model 1 for length/height-for-age for girls (dotted line) and their respective sample estimates (points with solid line)
50 Length/height-for-age, girls
3rd Centile5th Centile10th Centile40.40.40.00.00.00.(cm)-0.4-0.4-0.4forLength02468121620240246812162024024681216202440.25th Centile40.50th Centile40.75th CentileCentile00.00.00.Fitted-0.4-0.4-0.4-40.40.40.Empirical24681216202424681216202424681216202400090th Centile95th Centile97th Centile00.00.00.-0.4-0.4-0.4024681216202402468121620240246812162024
Age (months)
Figure 18 Centile residuals from fitting Model 1 for length/height-for-age from 0 to 24 months for girls
3rd Centile5th Centile10th Centile51.51.51.50.50.50.-0.5-0.5-0.5(cm)-1.531374349556167-1.531374349556167-1.531374349556167forHeight25252551.25th Centile51.50th Centile51.75th CentileFitted Centile51.5-0.50.51.5-0.50.51.5-0.50.----Empirical51.3137434955616751.3137434955616751.3137434955616725252590th Centile95th Centile97th Centile50.50.50.-0.5-0.5-0.5-1.5-1.5-1.5253137434955616725313743495561672531374349556167
Age (months)
Figure 19 Centile residuals from fitting Model 1 for length/height-for-age from 24 to 71 months for girls
Length/height-for-age, girls51
-3-11 2 3-3 -11 2 3-3-11 2 30.446 mo52 mo58 mo64 mo70 mo0.0-0.420 mo22 mo24 mo28 mo34 mo40 mo
Deviation0.4 0. 0.0410 mo11 mo12 mo14 mo16 mo18 mo-4 mo5 mo6 mo7 mo8 mo9 mo
0.4Birth14 d28 d42 d2 mo3 mo0.0-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 20 Worm plots of z-scores for Model 1 for length/height-for-age for girls
Figure 20 shows the worm plots for Model 1. For a few age groups, the shapes of the worms depart slightly from the flat shape but are still constrained within the 95% confidence intervals. For example, groups 52 mo and 64 mo indicate slight overestimation of the median (worms pass below origin). There was some indication of residual skewness in a few age groups, i.e. those with U-shaped worms (2, 5, 20 and 22 mo), but only one age group (52 mo) had an S-shaped worm, suggesting residual kurtosis. Results of the Q-test presented in Table 26 show that the misfits in terms of median and skewness were not significant, since the corresponding z1 and z3 absolute values were all below 2. The only evidence of residual kurtosis was in age group 52 mo (z4=2.36). However, the Q-test results for the z-scores derived from the selected model applied across all age groups bore evidence of the model's overall adequacy (p-values corresponding to overall statistics were all greater than 0.40). More complex modelling (e.g. fitting parameter ) was therefore not pursued.
A new iteration was done to re-search for the best with df()=10 and df()=5. This exercise did not result in any notable changes to the previous findings. The model BCPE(x= age0.35, df()=10, df()=5, =1, =2) was chosen to construct the length/height-for-age growth curves for girls. Figures 21 to 24 show the empirical and fitted centiles derived from the selected model for the length-for-age (0 to 24 months) and height-for-age (24 to 71 months) growth curves. The final standards were constructed as described in detail in section 3.1.
Table 25 Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for girls
ExpectedBirth14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo11.32.00.70.50.20.20.20.70.50.732.64.02.92.71.82.52.51.82.93.054.45.14.75.05.25.45.64.55.45.3109.512.111.39.710.311.210.39.711.09.62524.928.026.424.528.124.825.523.624.825.95048.351.050.050.250.650.847.950.050.249.37574.574.573.875.075.573.274.074.376.675.29089.889.589.389.989.090.689.089.492.391.19595.094.094.493.994.693.794.494.695.794.79797.196.296.496.296.296.696.696.696.497.59998.999.198.999.198.798.498.798.698.698.4
Expected8 mo9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo10.90.91.10.61.10.70.91.30.70.933.43.82.72.72.62.93.43.02.92.056.45.75.44.84.65.45.64.74.63.71010.510.610.18.910.210.511.49.59.29.22523.623.825.123.924.724.124.425.225.925.45049.349.549.349.751.250.252.750.451.050.67576.475.877.474.875.575.274.775.876.077.29091.490.390.690.990.589.788.889.690.189.99595.994.394.694.694.793.893.994.394.594.39796.896.897.396.796.795.896.996.495.896.39999.198.099.199.099.398.998.798.998.298.5
52
Length/height-for-age, girls
Table 25 Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for girls (continued)
Expected24 mo28 mo34 mo40 mo46 mo52 mo58 mo64 mo70 moOverall10.80.91.40.61.11.50.41.71.00.932.52.33.72.23.43.82.22.42.02.855.23.86.04.14.05.34.24.23.94.91010.97.911.710.68.310.08.79.411.410.12525.826.426.126.923.724.921.825.026.725.25049.851.152.853.147.556.546.053.346.950.37575.972.375.475.376.378.774.677.871.775.39090.390.090.889.088.391.588.791.089.390.09594.593.894.394.793.494.295.296.294.194.59796.596.695.596.995.896.897.297.996.196.69998.598.998.498.899.298.598.899.199.098.8
Note: Group labels correspond to the age intervals in Table 26.
Length/height-for -age, girls
5354 Length/height-for-age, girls
Table 26 Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=10, df()=5, =1, =2)] for length/height-for-age for girls
Age (days)GroupNz1z2z3z40Birth8420.42-0.36-0.850.261 to 1614 d447-1.021.12-0.24-0.8817 to 3428 d450-0.300.330.72-0.9035 to 4942 d444-0.01-0.100.56-0.5450 to 692 mo4450.08-0.121.74-0.6370 to 993 mo447-0.010.071.21-1.22100 to 1294 mo4470.670.501.24-0.62130 to 1595 mo4440.750.051.720.14160 to 1896 mo444-0.27-0.541.140.75190 to 2197 mo436-0.03-0.330.860.25220 to 2498 mo440-0.56-0.45-0.220.06250 to 2799 mo4420.110.430.050.70280 to 30910 mo446-0.24-0.410.08-0.23310 to 34911 mo4810.23-0.62-0.020.05350 to 37912 mo453-0.12-0.150.40-0.34380 to 43914 mo4480.220.240.75-0.14440 to 49916 mo446-0.240.380.62-0.50500 to 55918 mo4720.06-0.290.77-0.20560 to 61920 mo545-0.090.081.76-0.27620 to 67922 mo5430.320.041.970.52680 to 74924 mo598-0.09-0.361.180.13750 to 92928 mo4700.60-0.350.77-1.02930 to 111934 mo487-0.831.320.930.181120 to 130940 mo490-0.580.221.19-0.751310 to 149946 mo4721.24-0.100.450.251500 to 168952 mo469-1.300.471.982.361690 to 187958 mo5041.23-0.780.570.081880 to 206964 mo424-1.16-0.67-0.160.992070 to 219170 mo3070.940.940.070.61Overall Q stats13 78311.457.6530.0914.81degrees of freedom19.026.029.029.0p-value0.90780.99980.40950.9865
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
97th9090th50th8010th3rdLength (cm)7060
Fitted
Empirical
50
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 21 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: length-for-age for girls from birth to 24 months
Length/height-for -age, girls
55
9095th75th50th25th805thLength (cm)7060
Fitted
Empirical
50
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 22 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: length-for-age for girls from birth to 24 months
56
Length/height-for-age, girls
97th12090th50th11010thHeight(cm)1003rd90Fitted80Empirical2427303336394245485154576063666972Age (months)
Figure 23 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: height-for-age for girls from 24 to 71 months
Length/height-for-age, girls
57
12095th75th50th11025thHeight (cm)5th10090Fitted80Empirical2427303336394245485154576063666972Age (months)
Figure 24 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: height-for-age for girls from 24 to 71 months
58
Length/height-for-age, girlsLength/height-for-age, girls59
3.3.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO length/height-for-age z-score and percentile charts (Figures 25 to
and tables (Tables 27 to 29) for girls. It also provides the z-score comparisons of the WHO versus NCHS (Figure 29) and CDC 2000 (Figure 30) curves.
Charts
390210-180-2Length (cm)-3706050
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 25 WHO length-for-age z-scores for girls from birth to 24 months
60
Length/height-for-age, girls
120110Height (cm)1009080
3
2
1
0
-1
-2
-3
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Age (months)
Figure 26 WHO height-for-age z-scores for girls from 24 to 60 months
Length/height-for -age, girls
6162 Length/height-for-age, girls
97th85th50th15th3rd
2420 2224 months18birth to16from10 12 14Age (months)age percentiles for girls6 8WHO length-for-42Figure 270
9080706050Length (cm)
120
110Height (cm)10090
80
97th
85th
50th
15th
3rd
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Age (months)
Figure 28 WHO height-for-age percentiles for girls from 24 to 60 months
Length/height-for -age, girls
63Tables64Table 27 Length-for-age for girls, age in weeksPercentiles (length in cm)WeekLMSSD1st3rd5th15th25th50th75th85th95th97th99th0149.14770.037901.862744.845.646.147.247.949.150.451.152.252.753.51150.32980.037421.883345.946.847.248.449.150.351.652.353.453.954.72151.51200.036941.902947.147.948.449.550.251.552.853.554.655.155.93152.46950.036691.925148.048.849.350.551.252.553.854.555.656.156.94153.38090.036471.946848.949.750.251.452.153.454.755.456.657.057.95154.24540.036271.967549.750.551.052.252.954.255.656.357.557.958.86155.06420.036091.987350.451.351.853.053.755.156.457.158.358.859.77155.84060.035932.006451.252.152.553.854.555.857.257.959.159.660.58156.57670.035782.024351.952.853.254.555.256.657.958.759.960.461.39157.27610.035642.041352.553.453.955.255.957.358.759.460.661.162.010157.94360.035522.058253.254.154.655.856.657.959.360.161.361.862.711158.58160.035402.073853.854.755.256.457.258.660.060.762.062.563.412159.19220.035302.089554.355.355.857.057.859.260.661.462.663.164.113159.77730.035202.104254.955.856.357.658.459.861.262.063.263.764.7
Length/height-for-age, girls
Table 27 Length-for-age for girls, age in weeks (continued)
Z-scores (length in cm)WeekLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0149.14770.037901.862743.645.447.349.151.052.954.71150.32980.037421.883344.746.648.450.352.254.156.02151.51200.036941.902945.847.749.651.553.455.357.23152.46950.036691.925146.748.650.552.554.456.358.24153.38090.036471.946847.549.551.453.455.357.359.25154.24540.036271.967548.350.352.354.256.258.260.16155.06420.036091.987349.151.153.155.157.159.061.07155.84060.035932.006449.851.853.855.857.859.961.98156.57670.035782.024350.552.554.656.658.660.662.69157.27610.035642.041351.253.255.257.359.361.463.410157.94360.035522.058251.853.855.957.960.062.164.111158.58160.035402.073852.454.456.558.660.762.764.812159.19220.035302.089552.955.057.159.261.363.465.513159.77730.035202.104253.555.657.759.861.964.066.1
Length/height-for-age, girls
65Table 28 Length-for-age for girls, age in years and months
Percentiles (length in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th0:00149.14770.037901.862744.845.646.147.247.949.150.451.152.252.753.50:11153.68720.036401.954249.150.050.551.752.453.755.055.756.957.458.20:22157.06730.035682.036252.353.253.755.055.757.158.459.260.460.961.80:33159.80290.035202.105154.955.856.357.658.459.861.262.063.363.864.70:44162.08990.034862.164557.158.058.559.860.662.163.564.365.766.267.10:55164.03010.034632.217458.959.960.461.762.564.065.566.367.768.269.20:66165.73110.034482.266460.561.562.063.464.265.767.368.169.570.071.00:77167.28730.034412.315461.962.963.564.965.767.368.869.771.171.672.70:88168.74980.034402.365063.264.364.966.367.268.770.371.272.673.274.30:99170.14350.034442.415764.565.666.267.668.570.171.872.674.174.775.80:1010171.48180.034522.467665.766.867.468.969.871.573.174.075.576.177.20:1111172.77100.034642.520866.968.068.670.271.172.874.575.476.977.578.61:012174.01500.034792.575068.069.269.871.372.374.075.876.778.378.980.01:113175.21760.034962.629669.170.370.972.573.475.277.077.979.580.281.31:214176.38170.035142.684170.171.372.073.674.676.478.279.280.881.482.61:315177.50990.035342.739271.172.473.074.775.777.579.480.382.082.783.91:416178.60550.035552.794472.173.374.075.776.778.680.581.583.283.985.11:517179.67100.035762.849073.074.375.076.777.779.781.682.684.485.086.31:618180.70790.035982.903974.075.275.977.778.780.782.783.785.586.287.51:719181.71820.036202.958274.876.276.978.779.781.783.784.886.687.388.61:820182.70360.036433.012975.777.077.779.680.782.784.785.887.788.489.71:921183.66540.036663.067276.577.978.680.581.683.785.786.888.789.490.81:1022184.60400.036883.120277.378.779.581.482.584.686.787.889.790.591.91:1123185.52020.037113.173778.179.680.382.283.485.587.788.890.791.592.92:024186.41530.037343.226778.980.381.183.184.286.488.689.891.792.593.9
66
Length/height-for-age, girls
Table 28 Length-for-age for girls, age in years and months (continued)
Z-scores (length in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0:00149.14770.037901.862743.645.447.349.151.052.954.70:11153.68720.036401.954247.849.851.753.755.657.659.50:22157.06730.035682.036251.053.055.057.159.161.163.20:33159.80290.035202.105153.555.657.759.861.964.066.10:44162.08990.034862.164555.657.859.962.164.366.468.60:55164.03010.034632.217457.459.661.864.066.268.570.70:66165.73110.034482.266458.961.263.565.768.070.372.50:77167.28730.034412.315460.362.765.067.369.671.974.20:88168.74980.034402.365061.764.066.468.771.173.575.80:99170.14350.034442.415762.965.367.770.172.675.077.40:1010171.48180.034522.467664.166.569.071.573.976.478.90:1111172.77100.034642.520865.267.770.372.875.377.880.31:012174.01500.034792.575066.368.971.474.076.679.281.71:113175.21760.034962.629667.370.072.675.277.880.583.11:214176.38170.035142.684168.371.073.776.479.181.784.41:315177.50990.035342.739269.372.074.877.580.283.085.71:416178.60550.035552.794470.273.075.878.681.484.287.01:517179.67100.035762.849071.174.076.879.782.585.488.21:618180.70790.035982.903972.074.977.880.783.686.589.41:719181.71820.036202.958272.875.878.881.784.787.690.61:820182.70360.036433.012973.776.779.782.785.788.791.71:921183.66540.036663.067274.577.580.683.786.789.892.91:1022184.60400.036883.120275.278.481.584.687.790.894.01:1123185.52020.037113.173776.079.282.385.588.791.995.02:024186.41530.037343.226776.780.083.286.489.692.996.1
Length/height-for -age, girls
67Table 29 Height-for-age for girls, age in years and months
Percentiles (height in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th2:024185.71530.037643.226778.279.680.482.483.585.787.989.191.091.893.22:125186.59040.037863.278379.080.481.283.284.486.688.890.092.092.894.22:226187.44620.038083.330079.781.282.084.085.287.489.790.992.993.795.22:327188.28300.038303.381280.481.982.784.886.088.390.691.893.894.696.12:428189.10040.038513.431381.182.683.585.586.889.191.492.794.795.697.12:529189.89910.038723.480981.883.484.286.387.689.992.293.595.696.498.02:630190.67970.038933.530282.584.084.987.088.390.793.194.396.597.398.92:731191.44300.039133.578283.184.785.687.789.091.493.995.297.398.299.82:832192.19060.039333.625983.885.486.288.489.792.294.695.998.299.0100.62:933192.92390.039523.672484.486.086.989.190.492.995.496.799.099.8101.52:1034193.64440.039713.718685.086.787.589.891.193.696.297.599.8100.6102.32:1135194.35330.039893.763885.687.388.290.591.894.496.998.3100.5101.4103.13:036195.05150.040063.807886.287.988.891.192.595.197.699.0101.3102.2103.93:137195.73990.040243.852686.888.589.491.793.195.798.399.7102.1103.0104.73:238196.41870.040413.896387.489.190.092.493.896.499.0100.5102.8103.7105.53:339197.08850.040573.938987.989.790.693.094.497.199.7101.2103.6104.5106.33:440197.74930.040733.981388.590.391.293.695.197.7100.4101.9104.3105.2107.03:541198.40150.040894.023689.090.891.894.295.798.4101.1102.6105.0106.0107.83:642199.04480.041054.065889.691.492.494.896.399.0101.8103.3105.7106.7108.53:743199.67950.041204.106890.192.092.995.496.999.7102.4103.9106.4107.4109.23:8441100.30580.041354.147690.792.593.596.097.5100.3103.1104.6107.1108.1110.03:9451100.92380.041504.188391.293.094.096.698.1100.9103.7105.3107.8108.8110.73:10461101.53370.041644.227991.793.694.697.298.7101.5104.4105.9108.5109.5111.43:11471102.13600.041794.268392.294.195.197.799.3102.1105.0106.6109.2110.2112.14:0481102.73120.041934.307592.794.695.698.399.8102.7105.6107.2109.8110.8112.8
68
Length/height-for-age, girls
Table 29 Height-for age for girls, age in years and months (continued)
Percentiles (height in cm)Year: MonthMonthLMSSD1st3rd5th15th25th50th75th85th95th97th99th4:1491103.31970.042064.345693.295.196.298.8100.4103.3106.3107.8110.5111.5113.44:2501103.90210.042204.384793.795.796.799.4100.9103.9106.9108.4111.1112.1114.14:3511104.47860.042334.422694.296.297.299.9101.5104.5107.5109.1111.8112.8114.84:4521105.04940.042464.460494.796.797.7100.4102.0105.0108.1109.7112.4113.4115.44:5531105.61480.042594.498195.297.298.2101.0102.6105.6108.6110.3113.0114.1116.14:6541106.17480.042724.535895.697.698.7101.5103.1106.2109.2110.9113.6114.7116.74:7551106.72950.042854.573496.198.199.2102.0103.6106.7109.8111.5114.3115.3117.44:8561107.27880.042984.610896.698.699.7102.5104.2107.3110.4112.1114.9116.0118.04:9571107.82270.043104.647297.099.1100.2103.0104.7107.8111.0112.6115.5116.6118.64:10581108.36130.043224.683497.599.6100.7103.5105.2108.4111.5113.2116.1117.2119.34:11591108.89480.043344.719597.9100.0101.1104.0105.7108.9112.1113.8116.7117.8119.95:0601109.42330.043474.756698.4100.5101.6104.5106.2109.4112.6114.4117.2118.4120.5
Length/height-for-age, girls
69Table 29 Height-for-age for girls, age in years and months (continued)
Z-scores (height in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD2:024185.71530.037643.226776.079.382.585.788.992.295.42:125186.59040.037863.278376.880.083.386.689.993.196.42:226187.44620.038083.330077.580.884.187.490.894.197.42:327188.28300.038303.381278.181.584.988.391.795.098.42:428189.10040.038513.431378.882.285.789.192.596.099.42:529189.89910.038723.480979.582.986.489.993.496.9100.32:630190.67970.038933.530280.183.687.190.794.297.7101.32:731191.44300.039133.578280.784.387.991.495.098.6102.22:832192.19060.039333.625981.384.988.692.295.899.4103.12:933192.92390.039523.672481.985.689.392.996.6100.3103.92:1034193.64440.039713.718682.586.289.993.697.4101.1104.82:1135194.35330.039893.763883.186.890.694.498.1101.9105.63:036195.05150.040063.807883.687.491.295.198.9102.7106.53:137195.73990.040243.852684.288.091.995.799.6103.4107.33:238196.41870.040413.896384.788.692.596.4100.3104.2108.13:339197.08850.040573.938985.389.293.197.1101.0105.0108.93:440197.74930.040733.981385.889.893.897.7101.7105.7109.73:541198.40150.040894.023686.390.494.498.4102.4106.4110.53:642199.04480.041054.065886.890.995.099.0103.1107.2111.23:743199.67950.041204.106887.491.595.699.7103.8107.9112.03:8441100.30580.041354.147687.992.096.2100.3104.5108.6112.73:9451100.92380.041504.188388.492.596.7100.9105.1109.3113.53:10461101.53370.041644.227988.993.197.3101.5105.8110.0114.23:11471102.13600.041794.268389.393.697.9102.1106.4110.7114.94:0481102.73120.041934.307589.894.198.4102.7107.0111.3115.7
70
Length/height-for-age, girls
Table 29 Height-for-age for girls, age in years and months (continued)
Z-scores (height in cm)Year: MonthMonthLMSSD-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD4:1491103.31970.042064.345690.394.699.0103.3107.7112.0116.44:2501103.90210.042204.384790.795.199.5103.9108.3112.7117.14:3511104.47860.042334.422691.295.6100.1104.5108.9113.3117.74:4521105.04940.042464.460491.796.1100.6105.0109.5114.0118.44:5531105.61480.042594.498192.196.6101.1105.6110.1114.6119.14:6541106.17480.042724.535892.697.1101.6106.2110.7115.2119.84:7551106.72950.042854.573493.097.6102.2106.7111.3115.9120.44:8561107.27880.042984.610893.498.1102.7107.3111.9116.5121.14:9571107.82270.043104.647293.998.5103.2107.8112.5117.1121.84:10581108.36130.043224.683494.399.0103.7108.4113.0117.7122.44:11591108.89480.043344.719594.799.5104.2108.9113.6118.3123.15:0601109.42330.043474.756695.299.9104.7109.4114.2118.9123.7
Length/height-for-age, girls
71Comparison with NCHS
1203210(cm)100-1-2-3Length / Height8060
WHO
NCHS
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 29 Comparison of WHO with NCHS length/height-for-age z-scores for girls
72
Length/height-for-age, girls
Comparison with CDC 2000
1203210(cm)100-1-2-3Length / Height8060WHOCDC 2000400246812162024283236404448525660Age (months)
Figure 30 Comparison of WHO with CDC 2000 length/height-for-age z-scores for girls
Length/height-for-age, girls
7374 Length/height-for-age, boys & girls
3.4 Comparisons between boys and girls
This section presents the length/height-for-age z-score comparisons between boys and girls for WHO standards (Figure 31), and NCHS (Figure 32) and CDC 2000 (Figure 33) references.
3.4.1 WHO
1203210(cm)100-1-2-3Length / Height8060
Boys
Girls
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 31 Comparison of boys' and girls' WHO length/height-for-age z-scores
Length/height-for-age, boys & girls
753.4.2 NCHS
1203210(cm)100-1-2-3Length / Height8060
Boys
Girls
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 32 Comparison of boys' and girls' NCHS length/height-for-age z-scores
76
Length/height-for-age, boys & girls
3.4.3 CDC 2000
1203210(cm)100-1-2-3/ Height80Length60
Boys40Girls0246812162024283236404448525660Age (months)
Figure 33 Comparison of boys' and girls' CDC 2000 length/height-for-age z-scores
Length/height-for -age, boys & girls
77
CONSTRUCTION OF THE WEIGHT-FOR-AGE STANDARDS 4.1 Indicator-specific methodology
Similar steps to those described to select the best model for the length/height-for-age growth curves were followed to select the best model to construct the weight-for-age growth standards. The diagnostic tools applied to evaluate and compare candidate models were also similar. The weights of the longitudinal and cross-sectional samples were merged without any adjustments. To correct for right-edge effect, all data up to 71 months were used for modelling the weight-for-age growth curves but the standards were afterwards truncated at 60 completed months (Borghi et al., 2006).
4.2 Weight-for-age for boys
4.2.1 Sample size
There were a total of 13 797 weight observations for boys. The longitudinal and cross-sectional sample sizes by visit and age are presented in Tables 30 and 31. In addition to the 20 home visits at which length was assessed in the longitudinal study, weight was also measured on day 7, except in Brazil (de Onis et al., 2004b).
Table 30 Longitudinal sample sizes for weight-for-age for boys
VisitBirth7 d123456Age01 wk2 wk4 wk6 wk2 mo3 mo4 moN890391424423422423419411Visit7891011121314Age5 mo6 mo7 mo8 mo9 mo10 mo11 mo12 moN413417415415410407418417Visit151617181920Age14 mo16 mo18 mo20 mo22 mo24 moN416420416424420423
Table 31 Cross-sectional sample sizes for weight-for-age for boys
Age (mo)<1818 2021 2324 2627 2930 3233 35N3178186238261223256Age (mo)36 3839 4142 4445 4748 5051 5354 56N268249255238237221229Age (mo)57 5960 6263 6566 6869 71>71N2412282152182154
4.2.2 Model selection and results
To construct the weight-for-age growth curves, the model BCPE(x=age, df()=9, df()=4, df()=4, =2) was used as a starting point to search for the best value of the age-transformation power by examining changes in global deviance. Table 32 shows the global deviance for values of from 0 to 1. The smallest global deviance corresponded to the age-transformation power =0.35.
- 79 -
80 Weight-for-age, boys
Table 32 Global deviance (GD) for models within the class BCPE(x=age, df()=9, df()=4, df()=4, =2) for weight-for-age for boys
0.050.100.150.200.250.300.350.400.450.50GDa664.7658.0655.2648.1643.0639.1636.2636.3642.5658.40.550.600.650.700.750.800.850.900.951.00GDa685.3720.1755.1782.0795.3795.3789.3790.6816.5887.4
In excess of 41 000.
The search for the best df() and df() followed, fixing =0.35, =1 and =2. All possible combinations with df() values ranging from 7 to 15 and df() from 2 to 10 were considered and partial results are presented in Table 33. No fitted model minimized both AIC and GAIC(3) simultaneously. Models with df()=11 or 12 and df()=7 or 8 provided either the smallest AIC or the smallest GAIC(3). The model resulting in the smoothest and curves, i.e. df()=11 and df()=7, was selected for further evaluation.
Table 33 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for weight-for-age for boys
df()df()GDaAICaGAIC(3)aTotal df5891.8919.8933.8146885.2915.2930.21597880.6912.6928.6168877.7911.7928.7179875.9911.9929.9185885.6915.6930.615106878.9910.9926.9167874.4908.4925.4178871.6907.6925.6189869.9907.9926.9195881.4913.4929.416116874.8908.8925.8177870.3906.3924.3188867.6905.6924.6199866.0906.0926.0205878.4912.4929.417126871.8907.8925.8187867.4905.4924.4198864.7904.7924.7209863.1905.1926.1215876.2912.2930.2186869.6907.6926.619137865.2905.2925.2208862.6904.6925.6219861.0905.0927.022
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 41 000.
Weight-for-age, boys81
Model 1: BCPE(x=age0.35, df()=11, df()=7, =1, =2)
For this model, both the worm plots (Figure 34) and the Q-test results (Table 34) indicated good model fit of the and curves but pointed to the need to adjust for skewness. The worms presented a U-shape in most age groups, indicating residual skewness. This finding was confirmed by the Q-test results (Table 34), which show various groups with absolute values of z3 higher than 2. Only one age group presented an absolute value of z4 higher than 2, indicating residual kurtosis. The overall test also rejected the hypotheses of no skewness (p-value < 0.01).
-3-11 2 3-3-11 2 3-3-11 2 340.40 mo46 mo52 mo58 mo64 mo70 mo00.-0.418 mo20 mo22 mo24 mo28 mo34 mo
Deviation0 40.40.0.9 mo10 mo11 mo12 mo14 mo16 mo-3 mo4 mo5 mo6 mo7 mo8 mo
40.Birth7 d14 d28 d42 d2 mo00.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 34 Worm plots of z-scores for Model 1 for weight-for-age for boys
82 Weight-for-age, boys
Table 34 Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=11, df()=7, =1, =2)] for weight-for-age for boys
Age (days)GroupNz1z2z3z40Birth8900.32-0.724.12-0.181 to 117 d3910.321.662.630.8712 to 1614 d418-1.680.821.99-0.1117 to 3428 d426-0.04-0.011.620.2435 to 4942 d4210.30-0.531.351.0350 to 692 mo4230.140.351.541.2870 to 993 mo4190.47-0.372.261.66100 to 1294 mo408-0.09-0.732.31-0.15130 to 1595 mo4100.55-0.602.630.74160 to 1896 mo411-0.31-1.031.82-0.26190 to 2197 mo4060.171.053.171.81220 to 2498 mo4200.430.452.971.27250 to 2799 mo392-0.86-0.611.970.14280 to 30910 mo4000.761.092.66-0.16310 to 34911 mo461-0.21-0.082.63-0.23350 to 37912 mo412-0.10-0.162.720.28380 to 43914 mo4180.09-0.012.35-0.76440 to 49916 mo418-0.170.333.501.68500 to 55918 mo4420.17-0.414.101.83560 to 61920 mo526-0.180.483.941.13620 to 67922 mo552-0.380.042.81-0.37680 to 74924 mo594-1.17-0.972.28-0.90750 to 92928 mo4771.750.291.99-0.57930 to 111934 mo5211.110.423.570.601120 to 130940 mo512-1.760.343.21-0.351310 to 149946 mo5080.13-0.884.172.291500 to 168952 mo489-0.08-0.033.970.191690 to 187958 mo484-1.17-0.323.470.601880 to 206964 mo4610.200.532.30-1.942070 to 224970 mo2871.970.113.090.12Overall Q stats13 79719.6312.32249.8831.24degrees of freedom19.026.030.030.0p-value0.41700.9892< 0.010.4035
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
The next step involved fitting the parameter for skewness using the BCPE distribution with fixed parameter =2 and keeping the degrees of freedom for the and curves selected for Model 1. Table 35 shows the GAIC(3) values for various degrees of freedom for the curve.
Weight-for-age, boys83
Table 35 Goodness-of-fit summary for models BCPE(x=age0.35, df()=11, df()=7, df()=?, =2) for weight-for-age for boys
df()GDaGAIC(3)aTotal df1616.7673.7192610.2670.2203608.3671.3214605.1671.1225603.1672.2236602.2674.2247601.5676.525
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 41 000.
The smallest GAIC(3) value corresponded to df()=2 and the model BCPE(x=age0.35, df()=11, df()=7, df()=2, =2) was further evaluated.
Model 2: BCPE(x= age0.35, df()=11, df()=7, df()=2, =2)
Figure 35 shows the fitting of the parameters , and for Model 2 with their respective sample estimates, that is, the median for and Box-Cox transform power for . It should be noted that the sample estimate for the parameter is no longer the coefficient of variation when the distribution departs significantly from the normal distribution. In this case, the best estimator of is the sample standard deviation of the Box-Cox transformed data (Cole and Green, 1992).
Figures 36 and 37 show the distribution of the empirical minus fitted centile differences for the longitudinal and cross-sectional samples, respectively. For the longitudinal data, although there is some evidence of systematic overestimation in the 50th centile between 16 and 24 months, the average bias is less than 50 g (Figure 36) compared to SD values varying from 400 to 1800 g in this age range. For the cross-sectional component (Figure 37), underestimation in the 50th centile is noted between ages 25 and 35 months with an average bias of around 200 g relative to SD values varying from 1100 to 3700 g in this age range.
The worm plots for this model (Figure 38) were significantly improved compared to those of Model 1 (Figure 34). The U-shaped worms flattened out significantly (Figure 38), indicating that the residual skewness associated with Model 1 had been corrected. The median curve remained underestimated in only one age group (70 mo). Various groups' worms present slight S-shapes, e.g. ages 0 to 2 months and group 64 mo, but all are contained within the 95% confidence interval.
84 Weight-for-age, boys
20Weight0.15MedianofWeight(kg)1015of Box-CoxTransformed0. 0.0.1213145St Dev0.11
06142230394857660614223039485766Age (months)Age (months)51.Box-Cox Transform Power5 0-0.50.1.-1.5
0 6 14 22 30 39 48 57 66
Age (months)
Figure 35 Fitting of the , , and curves of Model 2 for weight-for-age for boys from 0 to 71 months (dotted line) and their respective sample estimates (points with solid line)
Weight-for-age, boys85
3rd Centile5th Centile10th Centile0.150.150.150.050.050.05-0.05-0.05-0.05(kg)-0.15246812162024-0.15246812162024-0.15246812162024forWeight0000.1525th Centile0.1550th Centile0.1575th CentileEmpirical-FittedCentile0.-0.15 -0.05 0.05152468121620240.-0.15 -0.05 0.05152468121620240.-0.15 -0.05 0.051524681216202400090th Centile95th Centile97th Centile0.050.050.05-0.05-0.05-0.05-0.15-0.15-0.15024681216202402468121620240246812162024
Age (months)
Figure 36 Centile residuals from fitting Model 2 for weight-for-age from 0 to 24 months for boys
3rd Centile5th Centile10th Centile1.01.01.00.50.50.50.00.00.0(kg)-1.031374349556167-1.031374349556167-1.031374349556167CentileforWeight2525250.0.51.0025th Centile0.0.51.0050th Centile0.0.51.0075th CentileFitted-1.0-1.0-1.0-1.01.01.0Empirical31374349556167313743495561673137434955616725252590th Centile95th Centile97th Centile0.50.50.50.00.00.0-1.0-1.0-1.0253137434955616725313743495561672531374349556167
Age (months)
Figure 37 Centile residuals from fitting Model 2 for weight-for-age from 24 to 71 months for boys
86 Weight-for-age, boys
-3-11 2 3-3-11 2 3-3-11 2 340.40 mo46 mo52 mo58 mo64 mo70 mo00.-0.418 mo20 mo22 mo24 mo28 mo34 mo
Deviation0 40.40.0.9 mo10 mo11 mo12 mo14 mo16 mo-3 mo4 mo5 mo6 mo7 mo8 mo
40.Birth7 d14 d28 d42 d2 mo00.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 38 Worm plots of z-scores for Model 2 for weight-for-age for boys
The Q-test results from Model 2 are shown in Table 36. There were no absolute values larger than 2 for the statistics z1, z2 or z3. Only one value of z4 (group 64 mo) suggested residual kurtosis. Considering this, there was no justification in increasing the complexity of the model by adjusting for kurtosis (modelling ). The overall Q-test p-values were all non-significant, indicating an adequate fit of the boys' weight-for-age curves.
Table 37 presents observed percentages with weights below the fitted centiles. As expected, age groups above 24 months presented larger differences compared to the age range younger than 24 months, yet there was no detectable pattern of a systematic bias.
Weight-for-age, boys87
Table 36 Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=11, df()=7, df()=2, =2)] for weight-for-age for boys
Age (days)GroupNz1z2z3z40Birth8900.22-0.741.21-1.591 to 117 d3910.551.520.14-0.6212 to 1614 d418-1.551.04-0.42-1.1717 to 3428 d426-0.010.01-1.050.6135 to 4942 d4210.31-0.49-1.611.9850 to 692 mo4230.080.42-1.491.9170 to 993 mo4190.41-0.45-0.461.16100 to 1294 mo408-0.16-0.760.22-0.69130 to 1595 mo4100.50-0.720.370.03160 to 1896 mo411-0.29-0.90-0.30-0.57190 to 2197 mo4060.110.960.510.85220 to 2498 mo4200.440.360.420.44250 to 2799 mo392-0.80-0.38-0.33-0.01280 to 30910 mo4000.730.980.41-0.76310 to 34911 mo461-0.17-0.020.28-0.95350 to 37912 mo412-0.06-0.140.38-0.33380 to 43914 mo4180.110.050.16-1.52440 to 49916 mo418-0.180.270.730.62500 to 55918 mo4420.21-0.641.460.17560 to 61920 mo526-0.230.361.01-0.32620 to 67922 mo552-0.410.16-0.03-1.38680 to 74924 mo594-1.13-0.63-0.59-1.90750 to 92928 mo4771.750.17-0.85-1.09930 to 111934 mo5211.140.140.24-0.241120 to 130940 mo512-1.830.67-0.01-1.271310 to 149946 mo5080.21-1.040.280.501500 to 168952 mo489-0.08-0.200.64-1.091690 to 187958 mo484-1.17-0.04-0.33-0.661880 to 206964 mo4610.130.82-1.07-2.132070 to 224970 mo2872.00-0.390.25-1.11Overall Q stats13 79719.5112.1015.6935.75degrees of freedom19.026.028.030.0p-value0.42480.99060.97010.2164
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
A new iteration was performed using df()=2 to re-search for df() and df() but, as before, no combination of df() and df() was found for which both AIC and GAIC(3) were simultaneously minimized. For example, AIC values were smallest for df() 11 to 15, and df() 7 to 9, while GAIC(3) values were smallest for df() 11 or 12, and df() 7 or 8. Since the previously selected model still provided better GAIC(3) with fixed df()=2, there was no need to change Model 2. A new search for the best value of was carried out using the selected model. The lowest global deviance values were associated with 0.30 or 0.35, precluding the necessity to update the selected model. In conclusion, the model selected for constructing the weight-for-age growth curves for boys was BCPE(x=age0.35, df()=11, df()=7, df()=2, =2) that adjusts only for skewness, and thus reduces in essence to the LMS method. The fitted centile curves and empirical centiles are shown in Figures 39 to 42.
Table 37 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-age for boys88ExpectedBirth7 d14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo10.40.81.41.41.21.71.21.20.50.71.032.63.83.32.61.72.82.42.22.41.53.454.75.97.74.54.55.05.04.44.14.96.21011.09.512.710.39.59.510.39.810.210.511.12525.727.429.925.824.523.923.224.323.426.022.75048.147.351.950.548.549.648.952.550.751.651.27572.871.675.473.973.974.974.275.274.175.474.99090.687.790.789.091.489.890.790.789.590.388.99595.194.496.495.595.294.895.795.195.196.195.19796.797.498.697.797.997.497.497.597.398.396.89999.199.099.599.399.098.898.899.099.099.398.3Expected8 mo9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo24 mo11.00.51.00.91.00.21.00.50.80.91.033.63.33.03.02.42.63.11.83.23.33.755.55.95.05.24.95.74.13.84.95.15.11010.211.710.310.48.710.89.89.011.010.310.82523.824.724.525.626.225.125.824.725.527.227.15048.653.350.551.450.050.051.250.751.550.750.37574.375.873.874.073.573.475.674.975.573.975.69090.590.687.589.890.388.890.491.489.490.991.69594.895.293.394.494.795.595.595.094.594.496.59796.496.796.597.697.196.996.996.496.697.197.69998.399.598.598.999.399.599.098.999.299.399.7boysage,-for-Weight
Table 37 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-age for boys (continued)
Expected28 mo34 mo40 mo46 mo52 mo58 mo64 mo70 moOverall10.60.60.80.60.60.41.50.30.833.41.73.92.63.14.13.71.72.955.24.07.24.34.77.25.23.15.1108.410.211.59.48.411.210.28.410.22524.323.628.925.026.625.026.523.025.45045.347.653.548.851.151.249.044.950.07571.774.177.075.274.477.973.370.074.49088.190.290.291.790.090.588.988.290.09593.992.994.795.594.395.594.492.794.99796.695.497.997.297.396.997.295.897.19999.898.899.498.699.099.299.699.099.1
Note: Group labels correspond to the age intervals in Table 36.
Weight-for-age, boys
8990 Weight-for-age, boys
97th90th50th10th3rd24for boysageFittedEmpirical10 12 14 16 18 20 22Age (months)centile curves and empirical values: weight-for-frombirthto24months8smoothed697th490th,210th, 50th,03rd,1614121086439FigureWeight (kg)
Weight-for-age, boys91
95th75th50th25th5th24for boysageFittedEmpirical10 12 14 16 18 20 22Age (months)centile curves and empirical values: weight-for-frombirthto24months8smoothed695th475th,225th, 50th,05th,1614121086440FigureWeight (kg)
97th
25
90th
2050thWeight (kg)10th153rd
Fitted10Empirical2427303336394245485154576063666972Age (months)
Figure 41 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for boys from 24 to 71 months
92
Weight-for-age, boys
2595th75th(kg)2050thWeight25th155th
Fitted10Empirical2427303336394245485154576063666972Age (months)
Figure 42 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for boys from 24 to 71 months
Weight-for-age, boys
9394 Weight-for-age, boys
4.2.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO weight-for-age z-score and percentile charts (Figures 43 and 44) and tables (Tables 38 and 39) for boys. It also provides the z-score comparisons of the WHO versus NCHS (Figure 45) and CDC 2000 (Figure 46) curves.
Charts
3252120(Kg)0-1Weight15-2-310
5
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 43 WHO weight-for-age z-scores for boys from birth to 60 months
Weight-for-age, boys
95
97th85th2050th15th(kg)15Weight3rd10
5
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 44 WHO weight-for-age percentiles for boys from birth to 60 months
96
Weight-for-age, boys
Tables
Table 38 Weight-for-age for boys, age in weeks
Percentiles (weight in kg)WeekLMS1st3rd5th15th25th50th75th85th95th97th99th00.34873.34640.146022.32.52.62.93.03.33.73.94.24.34.610.27763.48790.144832.42.62.73.03.23.53.84.04.44.54.820.25813.75290.141422.72.83.03.23.43.84.14.34.74.95.130.24424.06030.138072.93.13.23.53.74.14.54.75.15.25.540.23314.36710.134973.23.43.53.84.04.44.85.05.45.65.950.22374.65900.132153.43.63.74.14.34.75.15.35.85.96.360.21554.93030.129603.63.84.04.34.54.95.45.66.16.36.670.20815.18170.127293.84.14.24.54.85.25.65.96.46.56.980.20145.41490.125204.04.34.44.75.05.45.96.26.66.87.290.19525.63190.123304.24.44.64.95.25.66.16.46.97.17.4100.18945.83460.121574.44.64.85.15.45.86.36.67.17.37.7110.18406.02420.120014.54.84.95.35.66.06.56.87.37.57.9120.17896.20190.118604.74.95.15.55.76.26.77.07.57.78.1130.17406.36900.117324.85.15.25.65.96.46.97.27.77.98.3
Weight-for-age, boys
97Table 38 Weight-for-age for boys, age in weeks (continued)
Z-scores (weight in kg)WeekLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD00.34873.34640.146022.12.52.93.33.94.45.010.27763.48790.144832.22.63.03.54.04.65.320.25813.75290.141422.42.83.23.84.34.95.630.24424.06030.138072.63.13.54.14.75.36.040.23314.36710.134972.93.33.84.45.05.76.450.22374.65900.132153.13.54.14.75.36.06.860.21554.93030.129603.33.84.34.95.66.37.270.20815.18170.127293.54.04.65.25.96.67.580.20145.41490.125203.74.24.85.46.16.97.890.19525.63190.123303.84.45.05.66.47.28.0100.18945.83460.121574.04.55.25.86.67.48.3110.18406.02420.120014.24.75.36.06.87.68.5120.17896.20190.118604.34.95.56.27.07.88.8130.17406.36900.117324.45.05.76.47.28.09.0
98
Weight-for-age, boys
Table 39 Weight-for-age for boys, age in years and months
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th0:000.34873.34640.146022.32.52.62.93.03.33.73.94.24.34.60:110.22974.47090.133953.23.43.63.94.14.54.95.15.55.76.00:220.19705.56750.123854.14.44.54.95.15.66.06.36.87.07.40:330.17386.37620.117274.85.15.25.65.96.46.97.27.77.98.30:440.15537.00230.113165.45.65.86.26.57.07.67.98.48.69.10:550.13957.51050.110805.86.16.26.77.07.58.18.49.09.29.70:660.12577.93400.109586.16.46.67.17.47.98.58.99.59.710.20:770.11348.29700.109026.46.76.97.47.78.38.99.39.910.210.70:880.10218.61510.108826.77.07.27.78.08.69.39.610.310.511.10:990.09178.90140.108816.97.27.47.98.38.99.610.010.610.911.40:10100.08209.16490.108917.17.57.78.28.59.29.910.310.911.211.80:11110.07309.41220.109067.37.77.98.48.79.410.110.511.211.512.11:0120.06449.64790.109257.57.88.18.69.09.610.410.811.511.812.41:1130.05639.87490.109497.68.08.28.89.29.910.611.111.812.112.71:2140.048710.09530.109767.88.28.49.09.410.110.911.312.112.413.01:3150.041310.31080.110078.08.48.69.29.610.311.111.612.312.713.31:4160.034310.52280.110418.18.58.89.49.810.511.311.812.612.913.61:5170.027510.73190.110798.38.78.99.610.010.711.612.012.913.213.91:6180.021110.93850.111198.48.99.19.710.110.911.812.313.113.514.21:7190.014811.14300.111648.69.09.39.910.311.112.012.513.413.714.41:8200.008711.34620.112118.79.29.410.110.511.312.212.713.614.014.71:9210.002911.54860.112618.99.39.610.310.711.512.513.013.914.315.01:1022-0.002811.75040.113149.09.59.810.510.911.812.713.214.214.515.31:1123-0.008311.95140.113699.29.79.910.611.112.012.913.414.414.815.62: 024-0.013712.15150.114269.39.810.110.811.312.213.113.714.715.115.9
Weight-for-age, boys
99Table 39 Weight-for-age for boys, age in years and months (continued)
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th2: 125-0.018912.35020.114859.510.010.211.011.412.413.313.914.915.316.12: 226-0.024012.54660.115449.610.110.411.111.612.513.614.115.215.616.42: 327-0.028912.74010.116049.710.210.511.311.812.713.814.415.415.916.72: 428-0.033712.93030.116649.910.410.711.512.012.914.014.615.716.117.02: 529-0.038513.11690.1172310.010.510.811.612.113.114.214.815.916.417.32: 630-0.043113.30000.1178110.110.711.011.812.313.314.415.016.216.617.52: 731-0.047613.47980.1183910.310.811.111.912.413.514.615.216.416.917.82: 832-0.052013.65670.1189610.410.911.212.112.613.714.815.516.617.118.02: 933-0.056413.83090.1195310.511.111.412.212.813.815.015.716.917.318.32:1034-0.060614.00310.1200810.611.211.512.412.914.015.215.917.117.618.62:1135-0.064814.17360.1206210.711.311.612.513.114.215.416.117.317.818.83: 036-0.068914.34290.1211610.811.411.812.713.214.315.616.317.518.019.13: 137-0.072914.51130.1216811.011.611.912.813.414.515.816.517.818.319.33: 238-0.076914.67910.1222011.111.712.012.913.514.715.916.718.018.519.63: 339-0.080814.84660.1227111.211.812.213.113.714.816.116.918.218.719.83: 440-0.084615.01400.1232211.311.912.313.213.815.016.317.118.419.020.13: 541-0.088315.18130.1237311.412.112.413.414.015.216.517.318.619.220.33: 642-0.092015.34860.1242511.512.212.513.514.115.316.717.518.919.420.63: 743-0.095715.51580.1247811.712.312.713.614.315.516.917.719.119.720.83: 844-0.099315.68280.1253111.812.412.813.814.415.717.117.919.319.921.13: 945-0.102815.84970.1258611.912.512.913.914.615.817.318.119.520.121.33:1046-0.106316.01630.1264312.012.713.014.114.716.017.418.319.820.421.63:1147-0.109716.18270.1270012.112.813.214.214.916.217.618.520.020.621.94: 048-0.113116.34890.1275912.212.913.314.315.016.317.818.720.220.922.1
100
Weight-for-age, boys
Table 39 Weight-for-age for boys, age in years and months (continued)
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th4: 149-0.116516.51500.1281912.313.013.414.515.216.518.018.920.421.122.44: 250-0.119816.68110.1288012.413.113.514.615.316.718.219.120.721.322.64: 351-0.123016.84710.1294312.513.313.714.715.416.818.419.320.921.622.94: 452-0.126217.01320.1300512.613.413.814.915.617.018.619.521.121.823.24: 553-0.129417.17920.1306912.713.513.915.015.717.218.819.721.422.123.44: 654-0.132517.34520.1313312.913.614.015.215.917.319.019.921.622.323.74: 755-0.135617.51110.1319713.013.714.115.316.017.519.220.121.822.524.04: 856-0.138717.67680.1326113.113.814.315.416.217.719.320.322.122.824.24: 957-0.141717.84220.1332513.213.914.415.616.317.819.520.522.323.024.54:1058-0.144718.00730.1338913.314.114.515.716.518.019.720.722.523.324.84:1159-0.147718.17220.1345313.414.214.615.816.618.219.920.922.823.525.05: 060-0.150618.33660.1351713.514.314.716.016.718.320.121.123.023.825.3
Weight-for-age, boys
101Table 39 Weight-for-age for boys, age in years and months (continued)
Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0:000.34873.34640.146022.12.52.93.33.94.45.00:110.22974.47090.133952.93.43.94.55.15.86.60:220.19705.56750.123853.84.34.95.66.37.18.00:330.17386.37620.117274.45.05.76.47.28.09.00:440.15537.00230.113164.95.66.27.07.88.79.70:550.13957.51050.110805.36.06.77.58.49.310.40:660.12577.93400.109585.76.47.17.98.89.810.90:770.11348.29700.109025.96.77.48.39.210.311.40:880.10218.61510.108826.26.97.78.69.610.711.90:990.09178.90140.108816.47.18.08.99.911.012.30:10100.08209.16490.108916.67.48.29.210.211.412.70:11110.07309.41220.109066.87.68.49.410.511.713.01:0120.06449.64790.109256.97.78.69.610.812.013.31:1130.05639.87490.109497.17.98.89.911.012.313.71:2140.048710.09530.109767.28.19.010.111.312.614.01:3150.041310.31080.110077.48.39.210.311.512.814.31:4160.034310.52280.110417.58.49.410.511.713.114.61:5170.027510.73190.110797.78.69.610.712.013.414.91:6180.021110.93850.111197.88.89.810.912.213.715.31:7190.014811.14300.111648.08.910.011.112.513.915.61:8200.008711.34620.112118.19.110.111.312.714.215.91:9210.002911.54860.112618.29.210.311.512.914.516.21:1022-0.002811.75040.113148.49.410.511.813.214.716.51:1123-0.008311.95140.113698.59.510.712.013.415.016.82: 024-0.013712.15150.114268.69.710.812.213.615.317.1
102
Weight-for-age, boys
Table 39 Weight-for-age for boys, age in years and months (continued)
Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD2: 125-0.018912.35020.114858.89.811.012.413.915.517.52: 226-0.024012.54660.115448.910.011.212.514.115.817.82: 327-0.028912.74010.116049.010.111.312.714.316.118.12: 428-0.033712.93030.116649.110.211.512.914.516.318.42: 529-0.038513.11690.117239.210.411.713.114.816.618.72: 630-0.043113.30000.117819.410.511.813.315.016.919.02: 731-0.047613.47980.118399.510.712.013.515.217.119.32: 832-0.052013.65670.118969.610.812.113.715.417.419.62: 933-0.056413.83090.119539.710.912.313.815.617.619.92:1034-0.060614.00310.120089.811.012.414.015.817.820.22:1135-0.064814.17360.120629.911.212.614.216.018.120.43: 036-0.068914.34290.1211610.011.312.714.316.218.320.73: 137-0.072914.51130.1216810.111.412.914.516.418.621.03: 238-0.076914.67910.1222010.211.513.014.716.618.821.33: 339-0.080814.84660.1227110.311.613.114.816.819.021.63: 440-0.084615.01400.1232210.411.813.315.017.019.321.93: 541-0.088315.18130.1237310.511.913.415.217.219.522.13: 642-0.092015.34860.1242510.612.013.615.317.419.722.43: 743-0.095715.51580.1247810.712.113.715.517.620.022.73: 844-0.099315.68280.1253110.812.213.815.717.820.223.03: 945-0.102815.84970.1258610.912.414.015.818.020.523.33:1046-0.106316.01630.1264311.012.514.116.018.220.723.63:1147-0.109716.18270.1270011.112.614.316.218.420.923.94: 048-0.113116.34890.1275911.212.714.416.318.621.224.2
Weight-for-age, boys
103Table 39 Weight-for-age for boys, age in years and months (continued)104Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD4: 149-0.116516.51500.1281911.312.814.516.518.821.424.54: 250-0.119816.68110.1288011.412.914.716.719.021.724.84: 351-0.123016.84710.1294311.513.114.816.819.221.925.14: 452-0.126217.01320.1300511.613.215.017.019.422.225.44: 553-0.129417.17920.1306911.713.315.117.219.622.425.74: 654-0.132517.34520.1313311.813.415.217.319.822.726.04: 755-0.135617.51110.1319711.913.515.417.520.022.926.34: 856-0.138717.67680.1326112.013.615.517.720.223.226.64: 957-0.141717.84220.1332512.113.715.617.820.423.426.94:1058-0.144718.00730.1338912.213.815.818.020.623.727.24:1159-0.147718.17220.1345312.314.015.918.220.823.927.65: 060-0.150618.33660.1351712.414.116.018.321.024.227.9
Weight-for-age, boys
Comparison with NCHS
3252120(Kg)0-1Weight15-2-310
5WHONCHS0246812162024283236404448525660Age (months)
Figure 45 Comparison of WHO with NCHS weight-for-age z-scores for boys
Weight-for-age, boys
105Comparison with CDC 2000
302520Weight (Kg)15105
3
2
1
0
-1
-2
-3
WHO
CDC 2000
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 46 Comparison of WHO with CDC 2000 weight-for-age z-scores for boys
106
Weight-for-age, boysWeight-for-age, girls107
4.3 Weight-for-age for girls
Steps similar to those described in the preceding sections were followed to select the best model to fit the weight-for-age growth standard for girls.
4.3.1 Sample size
The data for constructing this standard combined weights from the longitudinal and cross-sectional samples without any adjustments. There were a total of 14 056 weight measurements for girls. The longitudinal and cross-sectional sample sizes by visit and age are presented in Tables 40 and 41.
Table 40 Longitudinal sample sizes for weight-for-age for girls
VisitBirth7 d123456Age01 wk2 wk4 wk6 wk2 mo3 mo4 moN838395449448447447446444Visit7891011121314Age5 mo6 mo7 mo8 mo9 mo10 mo11 mo12 moN447445444440446444444449Visit151617181920Age14 mo16 mo18 mo20 mo22 mo24 moN450445447445439449
Table 41 Cross-sectional sample sizes for weight-for-age for girls
Age (mo)<1818 2021 2324 2627 2930 3233 35N2163170240214229225Age (mo)36 3839 4142 4445 4748 5051 5354 56N224236250209225201231Age (mo)57 5960 6263 6566 6869 71>71N2412172052252010
4.3.2 Model selection and results
The initial step in the modelling process was to search for the best age power transformation using the same starting model as that used for boys. Table 42 shows the values of global deviance for a grid of possible powers from 0 to 1. The smallest global deviance value was associated with =0.4, but =0.35 the power used in constructing the same standard for boys yielded very similar global deviance. Therefore, in the interest of homogeneity between boys and girls, =0.35 was selected for the age transformation.
108 Weight-for-age, girls
Table 42 Global deviance (GD) for models within the class BCPE(x=age, df()=9, df()=4, df()=4, =2) for weight-for-age for girls
0.050.100.150.200.250.300.350.400.450.50GDa694.5681.2673.6665.2660.0656.7654.4654.0657.5667.30.550.600.650.700.750.800.850.900.951.00GDa684.8708.2732.5751.1759.6757.0747.7740.4747.3783.1
In excess of 42 000.
Using =0.35, optimal values for df() and df() were sought by fixing =1 and =2. All possible combinations of df() values from 10 to 15 and df() from 2 to 10 were considered. Partial results are presented in Table 43. There was no combination df() and df() that simultaneously minimized AIC and GAIC(3). The smallest values of AIC corresponded to df() 11 to 13 and df() 8 to 10, while the smallest values of GAIC(3) corresponded to df()=11 and df() 7 or 8. Among these, the model that produced the smoothest curves, i.e. with df()=11 and df()=7, was selected, since it presented the smallest number of degrees of freedom. This model was further evaluated.
Table 43 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for weight-for-age for girls
df()df()GDaAICaGAIC(3)aTotal df61110.01140.01155.01571105.11137.11153.116981101.91135.91152.91791099.61135.61153.618101097.81135.81154.81961105.91137.91153.91671101.01135.01152.0171081097.81133.81151.81891095.51133.51152.519101093.71133.71153.72061103.21137.21154.21771098.31134.31152.3181181095.01133.11152.11991092.81132.81152.820101091.01133.01154.02161101.11137.11155.11871096.21134.21153.2191281092.91132.91152.92091090.61132.61153.621101088.91132.91154.92261099.31137.31156.31971094.41134.41154.4201381091.11133.11154.12191088.81132.81154.822101087.01133.11156.123
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 42 000.
Weight-for-age, girls109
Model 1: BCPE(x=age0.35, df()=11, df()=7, =1, =2)
Table 44 shows the Q-test results for this model. As noted in constructing the weight-for-age standards for boys, this class of models was inadequate, i.e. strong evidence was observed of residual skewness in almost all age groups (absolute values of z3 larger than 2). Only one group out of 30 had an absolute value of z2 larger than 2, indicating misfit of the variance, while residual kurtosis was indicated in five age groups (absolute values of z4 larger than 2). It was clear that the parameter should be modelled to adjust for skewness. Consequently, the optimal df() was sought using df()=11 and df()=7 selected for the previous model, and fixing =2. Table 45 summarizes the resulting goodness-of-fit statistics from this step.
Table 44 Q-test for z-scores from Model 1 [BCPE(x=age0.35, df()=11, df()=7, =1, =2)] for weight-for-age for girls
Age (days)GroupNz1z2z3z40Birth8380.29-0.744.681.861 to 117 d3960.062.502.021.2012 to 1614 d446-1.400.291.840.8317 to 3428 d4500.24-0.582.100.9235 to 4942 d4440.45-0.532.731.6250 to 692 mo4450.08-0.522.700.4970 to 993 mo444-0.07-0.083.170.58100 to 1294 mo444-0.010.212.870.75130 to 1595 mo4410.310.293.241.34160 to 1896 mo4410.05-0.692.41-0.15190 to 2197 mo4320.32-0.322.830.91220 to 2498 mo435-0.25-0.663.210.44250 to 2799 mo4390.630.633.651.28280 to 30910 mo444-0.47-0.524.041.78310 to 34911 mo4800.290.654.821.80350 to 37912 mo451-0.240.364.281.43380 to 43914 mo447-0.090.834.982.27440 to 49916 mo447-0.43-0.044.632.01500 to 55918 mo469-0.01-0.524.271.83560 to 61920 mo5490.630.545.111.93620 to 67922 mo545-0.52-0.395.152.50680 to 74924 mo596-0.720.755.813.63750 to 92928 mo4591.55-0.513.69-0.94930 to 111934 mo475-0.84-0.571.92-2.491120 to 130940 mo4800.34-0.943.060.171310 to 149946 mo456-0.200.563.24-0.421500 to 168952 mo453-1.82-0.233.590.691690 to 187958 mo4961.120.625.331.691880 to 206964 mo4180.18-0.224.700.742070 to 219170 mo2960.860.284.312.00Overall Q stats14 05613.3114.46442.6173.99degrees of freedom19.026.030.030.0p-value0.82200.9665< 0.01< 0.01
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
110 Weight-for-age, girls
Table 45 Goodness-of-fit summary for models BCPE(x=age0.35, df()=11, df()=7, df()=?, =2) for weight-for-age for girls
df()GDaGAIC(3)aTotal df2640.5700.5203634.6697.6214628.5694.5225623.6692.6236620.8692.8247619.2694.225
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 42 000
The best df() was 5, according to the criterion GAIC(3), and this model was further evaluated.
Model 2: BCPE(x=age0.35, df()=11, df()=7, df()=5, =2)
With df()=5 the curve seemed under-smoothed. If this number of degrees of freedom were used, it would probably result in the outer centile curves depicting a wiggly pattern not expected for this indicator, especially when compared to the boys' curve for the same parameter. When the degrees of freedom were reduced to df()=3, the shape of the curve seemed more adequate (Figure 47). For reasons that remain unclear, weight data for girls are more irregular than for boys, especially in the age range corresponding to the cross-sectional component.
40.
20.
00.
-0.4 -0.2
df(v)=5
df(v)=4
df(v)=3
0 10 20 30 40 50 60
Age (months)
Figure 47 Cubic splines fitted for the curve with varying numbers of degrees of freedom
Weight-for-age, girls111
The Q-test results for Model 2 are presented in Table 46. The adjustment for skewness corrected the kurtosis in all groups with residual kurtosis noted in Model 1 (Table 44) except for two groups (28 mo and 34 mo). The overall Q-test p-values for kurtosis became non-significant. The indication of variance misfit observed at 7 days for the previous model remained when fitting Model 2 (absolute value of z2 larger than 2).
Table 46 Q-test for z-scores from Model 2 [BCPE(x=age0.35, df()=11, df()=7, df()=5, =2)] for weight-for-age for girls
Age (days)GroupNz1z2z3z40Birth8380.18-0.810.800.631 to 117 d3960.292.57-0.540.8012 to 1614 d446-1.300.51-0.610.7117 to 3428 d4500.20-0.61-0.431.2035 to 4942 d4440.37-0.640.031.4050 to 692 mo4450.01-0.570.200.2870 to 993 mo444-0.08-0.160.57-0.48100 to 1294 mo444-0.030.24-0.13-0.05130 to 1595 mo4410.270.230.00-0.11160 to 1896 mo4410.04-0.53-0.58-1.08190 to 2197 mo4320.28-0.23-0.56-0.52220 to 2498 mo435-0.23-0.53-0.09-0.94250 to 2799 mo4390.580.56-0.15-0.27280 to 30910 mo444-0.39-0.400.000.51310 to 34911 mo4800.310.440.630.24350 to 37912 mo451-0.200.430.20-0.25380 to 43914 mo447-0.090.690.69-0.01440 to 49916 mo447-0.380.010.52-0.68500 to 55918 mo4690.07-0.41-0.08-0.28560 to 61920 mo5490.600.290.66-0.95620 to 67922 mo545-0.48-0.370.430.11680 to 74924 mo596-0.840.730.340.72750 to 92928 mo4591.59-0.940.55-2.59930 to 111934 mo475-0.92-0.08-1.30-2.531120 to 130940 mo4800.39-0.99-0.72-0.871310 to 149946 mo456-0.240.64-0.42-1.881500 to 168952 mo453-1.800.38-0.72-0.281690 to 187958 mo4961.160.130.74-0.271880 to 206964 mo4180.21-0.240.38-0.032070 to 219170 mo2960.790.17-0.110.39Overall Q stats14 05613.1214.168.3927.74degrees of freedom19.026.025.030.0p-value0.83210.97090.99920.5840
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
112 Weight-for-age, girls
Model 3: BCPE((x=age0.35, df()=11, df()=7, df()=3, =2)
The Q-test results for Model 3 are shown in Table 47. Compared to Model 2 (Table 46), there was no significant loss in goodness of fit when using the smoother fitting function for the parameter .
Table 47 Q-test for z-scores from Model 3 [BCPE(x=age0.35, df()=11, df()=7, df()=3, =2)] for weight-for-age for girls
Age (days)GroupNz1z2z3z40Birth8380.21-0.821.630.741 to 117 d3960.342.57-1.070.8612 to 1614 d446-1.270.57-1.270.8317 to 3428 d4500.19-0.60-1.121.4535 to 4942 d4440.35-0.65-0.601.5150 to 692 mo4450.00-0.58-0.260.3770 to 993 mo444-0.09-0.170.30-0.52100 to 1294 mo444-0.030.24-0.28-0.05130 to 1595 mo4410.270.23-0.04-0.11160 to 1896 mo4410.04-0.54-0.52-1.08190 to 2197 mo4320.28-0.23-0.41-0.51220 to 2498 mo435-0.23-0.540.12-0.91250 to 2799 mo4390.580.570.14-0.24280 to 30910 mo444-0.40-0.410.370.50310 to 34911 mo4800.310.461.060.27350 to 37912 mo451-0.200.420.63-0.19380 to 43914 mo447-0.090.711.160.12440 to 49916 mo447-0.380.010.94-0.51500 to 55918 mo4690.07-0.410.33-0.19560 to 61920 mo5490.610.311.03-0.81620 to 67922 mo545-0.48-0.380.740.17680 to 74924 mo596-0.830.710.590.78750 to 92928 mo4591.59-0.960.58-2.61930 to 111934 mo475-0.93-0.07-1.45-2.471120 to 130940 mo4800.38-1.00-1.03-0.831310 to 149946 mo456-0.270.64-0.75-1.871500 to 168952 mo453-1.820.43-1.06-0.191690 to 187958 mo4961.150.090.48-0.281880 to 206964 mo4180.23-0.240.240.012070 to 219170 mo2960.820.18-0.140.39Overall Q stats14 05613.2114.4219.2228.40degrees of freedom19.026.027.030.0p-value0.82760.96700.86190.5491
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
As was the case for Models 1 and 2, the value of z2 for age group 7 days was higher than 2, pointing to variance misfit in an age interval of likely postnatal physiological adaptation. The same two age groups (28 mo and 34 mo) as observed for Model 2 indicated residual kurtosis.
Figure 48 shows the fit of the parameter curves for the full age range (0 to 71 months) using Model 3.
Weight-for-age, girls113
Median of Weight (kg)10 15 20of Box-Cox Transformed Weight0. 0. 0. 0.131415165St Dev0.1206142230394857660614223039485766Age (months)Age (months)1.5Box-Cox Transform Power-0.5 0. 1.50-1.5
0 6 14 22 30 39 48 57 66
Age (months)
Figure 48 Fitting of the , , and curves of Model 3 for weight-for-age for girls from 0 to 71 months (dotted line) and their respective sample estimates (points with solid line)
Figures 49 and 50 present the distribution of the centile residuals for Model 3. The residuals around the median were very small, about 40 g from 0 to 24 months (Figure 49), and although there were more positive than negative points, their magnitude was of likely minor clinical significance. The 3rd centile had a clear pattern of positive residuals from 12 to 24 months, but no other centiles presented any clear pattern suggestive of bias. Overall, the patterns of residuals from 24 to 71 months showed no evidence of bias (Figure 50). As expected, outer centiles presented more unstable patterns, especially above 60 months.
Figure 51 presents worm plots for z-scores derived from Model 3 based on age groups as defined in Table 47. As expected, for a few age groups the worms indicated a misfit of the parameters: the age group 7 days presented a worm with a positive slope (indicating misfit of the variance) and the groups 28 mo and 34 mo presented S-shaped worms (indicating residual kurtosis). These findings were similar to those from the Q-test (Table 47).
Table 48 compares observed and expected proportions of children below each fitted centile. Results generally indicated no systematic pattern suggestive of bias or inadequacy of the fitted model.
114 Weight-for-age, girls
3rd Centile5th Centile10th Centile30.30.30.10.10.10.-0.1-0.1-0.1(kg)-0.3246812162024-0.3246812162024-0.3246812162024forWeight00030.25th Centile30.50th Centile30.75th CentileFitted Centile-0.3 -0.1 0.1-0.3 -0.1 0.1-0.3 -0.1 0.1-0.30.30.3Empirical24681216202424681216202424681216202400090th Centile95th Centile97th Centile0.10.10.1-0.1-0.1-0.1-0.3-0.3-0.3024681216202402468121620240246812162024
Age (months)
Figure 49 Centile residuals from fitting Model 3 for weight-for-age from 0 to 24 months for girls
3rd Centile5th Centile10th Centile1.51.51.50.50.50.5-0.5-0.5-0.5(kg)-1.531374349556167-1.531374349556167-1.531374349556167forWeight25252551.25th Centile51.50th Centile51.75th CentileFitted Centile5-1.5-0.50.5-1.5-0.50.5-1.5-0.50.-51.51.51.Empirical31374349556167313743495561673137434955616725252590th Centile95th Centile97th Centile50.50.50.-0.5-0.5-0.5-1.5-1.5-1.5253137434955616725313743495561672531374349556167
Age (months)
Figure 50 Centile residuals from fitting Model 3 for weight-for-age from 24 to 71 months for girls
Weight-for-age, girls115
-3-11 2 3-3-11 2 3-3-11 2 30.440 mo46 mo52 mo58 mo64 mo70 mo0.0-0.418 mo20 mo22 mo24 mo28 mo34 mo
Deviation0.4 0. 0.049 mo10 mo11 mo12 mo14 mo16 mo-3 mo4 mo5 mo6 mo7 mo8 mo
0.4Birth7 d14 d28 d42 d2 mo0.0-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 00. 40.
-0.4 00. 40.
Unit normal quantile
Figure 51 Worm plots of z-scores for Model 3 for weight-for-age for girls
The model was updated using df()=3, and one more iteration was performed to re-search for the best df() and df(). Results of AIC and GAIC(3) led to the same combination df()=11 and df()=7. The best value was then sought using the selected combination of degrees of freedom, i.e. df()=11, df()=7 and df()=3. In this new iteration, the smallest values of global deviance were yielded by values between 0.25 and 0.30 (42 633.3 and 42 633.6, respectively). Yet differences in overall
goodness of fit between those and the model using =0.35 (global deviance equal to 42 634.6) were very small. Thus, the model BCPE(x=age0.35, df()=11, df()=7, df()=3, =2) was selected for
constructing the weight-for-age growth curves for girls. The fitted centile curves and empirical centiles are shown in Figures 52 to 55.
Table 48 Observed proportions of children with measurements below the fitted centiles from Model 3, weight-for-age for girls116ExpectedBirth7 d14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo10.61.51.60.91.10.70.90.70.90.90.932.35.65.82.72.52.72.73.83.22.93.553.78.37.24.44.55.25.25.95.45.04.9108.012.111.29.68.310.19.910.410.210.010.92524.525.025.322.423.223.425.024.523.124.923.85050.848.051.848.947.750.650.249.847.649.747.77577.471.776.975.675.974.874.375.773.774.875.59091.688.991.991.190.391.090.589.990.289.690.59594.694.995.194.994.894.295.394.494.895.795.89796.596.096.296.796.896.996.896.497.197.797.59998.799.099.199.698.699.198.999.598.999.399.1Expected8 mo9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo24 mo10.70.70.91.00.40.70.40.40.20.61.232.82.72.72.72.73.12.52.82.62.64.455.35.04.54.25.55.45.65.84.75.36.91010.69.89.09.012.012.112.111.910.910.110.92525.725.325.926.324.225.325.724.124.025.726.85049.047.449.848.547.951.051.049.949.251.050.57574.974.976.874.676.775.475.875.973.277.177.09091.590.491.290.289.489.090.491.788.590.590.89594.593.895.794.494.594.294.995.394.995.095.59796.895.797.195.495.896.697.196.896.096.996.89999.399.199.197.998.797.898.998.598.798.998.7girlsage,-for-Weight
Table 48 Observed proportions of children with measurements below the fitted centiles from Model 3, weight-for-age for girls (continued)
Expected28 mo34 mo40 mo46 mo52 mo58 mo64 mo70 moOverall10.01.30.80.91.50.60.71.00.831.54.02.74.23.83.02.63.03.153.36.34.46.66.44.63.35.75.2108.510.98.812.511.98.19.110.110.22523.326.923.527.627.223.026.123.324.95046.049.748.147.852.148.648.845.949.37572.174.973.375.778.173.275.176.075.39086.790.391.089.789.887.388.888.990.19593.995.496.394.795.194.093.593.994.89796.998.397.196.598.096.096.295.396.79999.6100.099.499.699.699.099.898.699.0
Note: Group labels correspond to the age intervals in Table 47.
Weight-for-age, girls
117118 Weight-for-age, girls
97th90th50th10th3rd24for girlsageFittedEmpirical8 10 12 14 16 18 20 22Age (months)smoothed centile curves and empirical values: weight-for-frombirthto24months697th490th,210th, 50th,03rd,141210864252FigureWeight (kg)
Weight-for-age, girls119
95th75th50th25th5th24for girlsageFittedEmpirical10 12 14 16 18 20 22Age (months)centile curves and empirical values: weight-for-frombirthto24months8smoothed695th475th,225th, 50th,05th,141210864253FigureWeight (kg)
97th2590th(kg)2050thWeight10th153rd
10FittedEmpirical
24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72
Age (months)
Figure 54 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for girls from 24 to 71 months
120
Weight-for-age, girls
2595th75th(kg)2050thWeight25th155th
10FittedEmpirical
24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72
Age (months)
Figure 55 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for girls from 24 to 71 months
Weight-for-age, girls
121122 Weight-for-age, girls
4.3.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO weight-for-age z-score and percentile charts (Figures 56 and 57) and tables (Tables 49 and 50) for girls. It also provides the z-score comparisons of the WHO versus NCHS (Figure 58) and CDC 2000 (Figure 59) curves.
Charts
302520Weight (Kg)15105
3
2
1
0
-1
-2
-3
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 56 WHO weight-for-age z-scores for girls from birth to 60 months
Weight-for-age, girls
123124 Weight-for-age, girls
97th85th50th15th3rd6052 56months48to 6044birth40from28 32 36Age (months)percentiles for girls24age16 20weight-for-12WHO8572 4 6Figure0252015105Weight (kg)
Tables
Table 49 Weight-for-age for girls, age in weeks
Percentiles (weight in kg)WeekLMS1st3rd5th15th25th50th75th85th95th97th99th00.38093.23220.141712.32.42.52.82.93.23.63.74.04.24.410.26713.33880.146002.32.52.62.93.03.33.73.94.24.44.620.23043.56930.143392.52.72.83.13.23.63.94.14.54.64.930.20243.83520.140602.72.93.03.33.53.84.24.44.85.05.340.17894.09870.138052.93.13.33.53.74.14.54.75.15.35.650.15824.34760.135833.13.33.53.84.04.34.85.05.45.65.960.13954.57930.133923.33.53.74.04.24.65.05.35.75.96.270.12244.79500.132283.53.73.84.24.44.85.25.55.96.16.580.10654.99590.130873.73.94.04.44.65.05.55.76.26.46.790.09185.18420.129663.84.14.24.54.75.25.75.96.46.67.0100.07795.36180.128614.04.24.34.74.95.45.86.16.66.87.2110.06485.52950.127704.14.34.54.85.15.56.06.36.87.07.4120.05255.68830.126914.24.54.65.05.25.76.26.57.07.27.6130.04075.83930.126224.34.64.75.15.45.86.46.77.27.47.8
Weight-for-age, girls
125Table 49 Weight-for-age for girls, age in weeks (continued)
Z-scores (weight in kg)WeekLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD00.38093.23220.141712.02.42.83.23.74.24.810.26713.33880.146002.12.52.93.33.94.45.120.23043.56930.143392.32.73.13.64.14.75.430.20243.83520.140602.52.93.33.84.45.05.740.17894.09870.138052.73.13.64.14.75.46.150.15824.34760.135832.93.33.84.35.05.76.560.13954.57930.133923.03.54.04.65.26.06.870.12244.79500.132283.23.74.24.85.56.27.180.10654.99590.130873.33.84.45.05.76.57.390.09185.18420.129663.54.04.65.25.96.77.6100.07795.36180.128613.64.14.75.46.16.97.8110.06485.52950.127703.84.34.95.56.37.18.1120.05255.68830.126913.94.45.05.76.57.38.3130.04075.83930.126224.04.55.15.86.67.58.5
126
Weight-for-age, girls
Table 50 Weight-for-age for girls, age in years and months
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th0:000.38093.23220.141712.32.42.52.82.93.23.63.74.04.24.40:110.17144.18730.137243.03.23.33.63.84.24.64.85.25.45.70:220.09625.12820.130003.84.04.14.54.75.15.65.96.36.56.90:330.04025.84580.126194.44.64.75.15.45.86.46.77.27.47.80: 44-0.00506.42370.124024.85.15.25.65.96.47.07.37.98.18.60: 55-0.04306.89850.122745.25.55.66.16.46.97.57.88.48.79.20: 66-0.07567.29700.122045.55.86.06.46.77.37.98.38.99.29.70: 77-0.10397.64220.121785.86.16.36.77.07.68.38.79.49.610.20: 88-0.12887.94870.121816.06.36.57.07.37.98.69.09.710.010.60: 99-0.15078.22540.121996.26.66.87.37.68.28.99.310.110.411.00:1010-0.17008.48000.122236.46.87.07.57.88.59.29.610.410.711.30:1111-0.18728.71920.122476.67.07.27.78.08.79.59.910.711.011.71: 012-0.20248.94810.122686.87.17.37.98.28.99.710.211.011.312.01: 113-0.21589.16990.122836.97.37.58.18.49.210.010.411.311.612.31: 214-0.22789.38700.122947.17.57.78.38.69.410.210.711.511.912.61: 315-0.23849.60080.122997.37.77.98.58.89.610.410.911.812.212.91: 416-0.24789.81240.123037.47.88.18.79.09.810.711.212.112.513.21: 517-0.256210.02260.123067.68.08.28.89.210.010.911.412.312.713.51: 618-0.263710.23150.123097.88.28.49.09.410.211.111.612.613.013.81: 719-0.270310.43930.123157.98.38.69.29.610.411.411.912.913.314.11: 820-0.276210.64640.123238.18.58.79.49.810.611.612.113.113.514.41: 921-0.281510.85340.123358.28.78.99.610.010.911.812.413.413.814.61:1022-0.286211.06080.123508.48.89.19.810.211.112.012.613.614.114.91:1123-0.290311.26880.123698.59.09.29.910.411.312.312.813.914.315.22: 024-0.294111.47750.123908.79.29.410.110.611.512.513.114.214.615.5
Weight-for-age, girls
127Table 50 Weight-for-age for girls, age in years and months (continued)
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th2: 125-0.297511.68640.124148.99.39.610.310.811.712.713.314.414.915.82: 226-0.300511.89470.124419.09.59.810.510.911.912.913.614.715.216.12: 327-0.303212.10150.124729.29.69.910.711.112.113.213.815.015.416.42: 428-0.305712.30590.125069.39.810.110.811.312.313.414.015.215.716.72: 529-0.308012.50730.125459.510.010.211.011.512.513.614.315.516.017.02: 630-0.310112.70550.125879.610.110.411.211.712.713.814.515.716.217.32: 731-0.312012.90060.126339.710.310.511.311.912.914.114.716.016.517.62: 832-0.313813.09300.126839.910.410.711.512.013.114.315.016.216.817.82: 933-0.315513.28370.1273710.010.510.811.712.213.314.515.216.517.018.12:1034-0.317113.47310.1279410.110.711.011.812.413.514.715.416.817.318.42:1135-0.318613.66180.1285510.310.811.112.012.513.714.915.717.017.618.73: 036-0.320113.85030.1291910.411.011.312.112.713.915.115.917.317.819.03: 137-0.321614.03850.1298810.511.111.412.312.914.015.316.117.518.119.33: 238-0.323014.22650.1305910.611.211.612.513.014.215.616.317.818.419.63: 339-0.324314.41400.1313510.811.411.712.613.214.415.816.618.018.619.93: 440-0.325714.60100.1321310.911.511.812.813.414.616.016.818.318.920.23: 541-0.327014.78730.1329311.011.612.012.913.514.816.217.018.619.220.53: 642-0.328314.97270.1337611.111.812.113.113.715.016.417.318.819.520.83: 743-0.329615.15730.1346011.311.912.213.213.915.216.617.519.119.721.13: 844-0.330915.34100.1354511.412.012.413.414.015.316.817.719.320.021.43: 945-0.332215.52400.1363011.512.112.513.514.215.517.017.919.620.321.73:1046-0.333515.70640.1371611.612.312.613.714.315.717.318.219.920.622.03:1147-0.334815.88820.1380011.712.412.813.814.515.917.518.420.120.822.34: 048-0.336116.06970.1388411.812.512.914.014.716.117.718.620.421.122.6
128
Weight-for-age, girls
Table 50 Weight-for-age for girls, age in years and months (continued)
Percentiles (weight in kg)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th4: 149-0.337416.25110.1396811.912.613.014.114.816.317.918.920.621.422.94: 250-0.338716.43220.1405112.112.813.214.315.016.418.119.120.921.723.24: 351-0.340016.61330.1413212.212.913.314.415.116.618.319.321.222.023.54: 452-0.341416.79420.1421312.313.013.414.515.316.818.519.521.422.223.94: 553-0.342716.97480.1429312.413.113.514.715.417.018.719.821.722.524.24: 654-0.344017.15510.1437112.513.213.714.815.617.218.920.022.022.824.54: 755-0.345317.33470.1444812.613.413.815.015.817.319.120.222.223.124.84: 856-0.346617.51360.1452512.713.513.915.115.917.519.320.422.523.325.14: 957-0.347917.69160.1460012.813.614.015.316.117.719.620.722.723.625.44:1058-0.349217.86860.1467512.913.714.215.416.217.919.820.923.023.925.74:1159-0.350518.04450.1474813.113.814.315.516.418.020.021.123.324.226.05: 060-0.351818.21930.1482113.214.014.415.716.518.220.221.323.524.426.3
Weight-for-age, girls
129Table 50 Weight-for-age for girls, age in years and months (continued)
Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0:000.38093.23220.141712.02.42.83.23.74.24.80:110.17144.18730.137242.73.23.64.24.85.56.20:220.09625.12820.130003.43.94.55.15.86.67.50:330.04025.84580.126194.04.55.25.86.67.58.50: 44-0.00506.42370.124024.45.05.76.47.38.29.30: 55-0.04306.89850.122744.85.46.16.97.88.810.00: 66-0.07567.29700.122045.15.76.57.38.29.310.60: 77-0.10397.64220.121785.36.06.87.68.69.811.10: 88-0.12887.94870.121815.66.37.07.99.010.211.60: 99-0.15078.22540.121995.86.57.38.29.310.512.00:1010-0.17008.48000.122235.96.77.58.59.610.912.40:1111-0.18728.71920.122476.16.97.78.79.911.212.81: 012-0.20248.94810.122686.37.07.98.910.111.513.11: 113-0.21589.16990.122836.47.28.19.210.411.813.51: 214-0.22789.38700.122946.67.48.39.410.612.113.81: 315-0.23849.60080.122996.77.68.59.610.912.414.11: 416-0.24789.81240.123036.97.78.79.811.112.614.51: 517-0.256210.02260.123067.07.98.910.011.412.914.81: 618-0.263710.23150.123097.28.19.110.211.613.215.11: 719-0.270310.43930.123157.38.29.210.411.813.515.41: 820-0.276210.64640.123237.58.49.410.612.113.715.71: 921-0.281510.85340.123357.68.69.610.912.314.016.01:1022-0.286211.06080.123507.88.79.811.112.514.316.41:1123-0.290311.26880.123697.98.910.011.312.814.616.72: 024-0.294111.47750.123908.19.010.211.513.014.817.0
130
Weight-for-age, girls
Table 50 Weight-for-age for girls, age in years and months (continued)
Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD2: 125-0.297511.68640.124148.29.210.311.713.315.117.32: 226-0.300511.89470.124418.49.410.511.913.515.417.72: 327-0.303212.10150.124728.59.510.712.113.715.718.02: 428-0.305712.30590.125068.69.710.912.314.016.018.32: 529-0.308012.50730.125458.89.811.112.514.216.218.72: 630-0.310112.70550.125878.910.011.212.714.416.519.02: 731-0.312012.90060.126339.010.111.412.914.716.819.32: 832-0.313813.09300.126839.110.311.613.114.917.119.62: 933-0.315513.28370.127379.310.411.713.315.117.320.02:1034-0.317113.47310.127949.410.511.913.515.417.620.32:1135-0.318613.66180.128559.510.712.013.715.617.920.63: 036-0.320113.85030.129199.610.812.213.915.818.120.93: 137-0.321614.03850.129889.710.912.414.016.018.421.33: 238-0.323014.22650.130599.811.112.514.216.318.721.63: 339-0.324314.41400.131359.911.212.714.416.519.022.03: 440-0.325714.60100.1321310.111.312.814.616.719.222.33: 541-0.327014.78730.1329310.211.513.014.816.919.522.73: 642-0.328314.97270.1337610.311.613.115.017.219.823.03: 743-0.329615.15730.1346010.411.713.315.217.420.123.43: 844-0.330915.34100.1354510.511.813.415.317.620.423.73: 945-0.332215.52400.1363010.612.013.615.517.820.724.13:1046-0.333515.70640.1371610.712.113.715.718.120.924.53:1147-0.334815.88820.1380010.812.213.915.918.321.224.84: 048-0.336116.06970.1388410.912.314.016.118.521.525.2
Weight-for-age, girls
131Table 50 Weight-for-age for girls, age in years and months (continued)132Z-scores (weight in kg)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD4: 149-0.337416.25110.1396811.012.414.216.318.821.825.54: 250-0.338716.43220.1405111.112.614.316.419.022.125.94: 351-0.340016.61330.1413211.212.714.516.619.222.426.34: 452-0.341416.79420.1421311.312.814.616.819.422.626.64: 553-0.342716.97480.1429311.412.914.817.019.722.927.04: 654-0.344017.15510.1437111.513.014.917.219.923.227.44: 755-0.345317.33470.1444811.613.215.117.320.123.527.74: 856-0.346617.51360.1452511.713.315.217.520.323.828.14: 957-0.347917.69160.1460011.813.415.317.720.624.128.54:1058-0.349217.86860.1467511.913.515.517.920.824.428.84:1159-0.350518.04450.1474812.013.615.618.021.024.629.25: 060-0.351818.21930.1482112.113.715.818.221.224.929.5
Weight-for-age, girls
Comparison with NCHS
302520Weight (Kg)15105
3
2
1
0
-1
-2
-3
WHO
NCHS
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 58 Comparison of WHO with NCHS weight-for-age z-scores for girls
Weight-for-age, girls
133Comparison with CDC 2000
3025(Kg)20Weight15105
3
2
1
0
-1
-2
-3
WHO
CDC 2000
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 59 Comparison of WHO with CDC 2000 weight-for-age z-scores for girls
134
Weight-for-age, girlsWeight-for-age, boys & girls135
4.4 Comparisons between boys and girls
This section presents the weight-for-age z-score comparisons between boys and girls for WHO standards (Figure 60), and for NCHS (Figure 61) and CDC 2000 (Figure 62) references.
4.4.1 WHO
302520Weight (Kg)15105
3
2
1
0
-1
-2
-3
Boys
Girls
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 60 Comparison of boys' and girls' WHO weight-for-age z-scores
136
Weight-for-age, boys & girls
4.4.2 NCHS
25322010(Kg)-115-2Weight-310
5
Boys
Girls
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 61 Comparison of boys' and girls' NCHS weight-for-age z-scores
Weight-for-age, boys & girls
137
4.4.3 CDC 2000
303252(Kg)2010Weight15-2-1-3105BoysGirls0246812162024283236404448525660Age (months)
Figure 62 Comparison of boys' and girls' CDC 2000 weight-for-age z-scores
138
Weight-for-age, boys & girlsCONSTRUCTION OF THE WEIGHT-FOR-LENGTH AND WEIGHT-FOR-HEIGHT STANDARDS
5.1 Indicator-specific methodology
The construction of the weight-for-length (45 to 110 cm) and weight-for-height (65 to 120 cm) standards followed a procedure similar to that applied to constructing the length/height-for-age standards (see section 3.1). To fit a single model, 0.7 cm was added to the cross-sectional height values. This was the average difference found between length and height in 1625 children aged 18 to 30 months measured for both length and height. After the model was fitted, the weight-for-length centile curves in the length interval 65.7 to 120.7 cm were shifted back by 0.7 cm to derive the weight-for-height standards corresponding to the height range 65 cm to 120 cm.
There was an important distinction between age versus length/height as the x-axis variable. Although the study was designed to give a relatively constant number of observations per age group, this was not the case for length/height. Therefore, in contrast to the square tail of the uniform age distribution there was a light upper tail for the height distribution. The age-based indicator curves were constructed using all available data (0 to 71 months) but the resulting standards were truncated at 60 completed months to avoid the right-edge effect (Borghi et al., 2006). The construction of the weight-for-height standards followed this precedent by using the full range of available heights independently of age. The decision about where to set the upper limit for the weight-for-height standards was influenced by the need to accommodate the tallest children at age 60 months. The upper limit was set at 120 cm, approximately the +2 SD boys' height-for-age at 60 months. Few children in the MGRS sample were taller than 120 cm (91 boys and 72 girls) and the distribution of their heights distorted the trajectory of the median and other centiles because the sample was small and the observed weight values were clustered at the upper tail. Thus, observations with height values >120 cm were assigned a model weight=0 to avoid distorting the trajectory at the upper end of the height range. It was considered a sensible precaution to exclude height values above 120 cm from the modelling but retain them for the diagnostic tests and other types of assessment. The lower limit of the weight-for-length standards (45 cm) was chosen to cover up to approximately -2 SD girls' length at birth.
5.2 Weight-for-length/height for boys
5.2.1 Sample size
There were 13 362 observations with both weight and length/height measurements. The longitudinal and cross-sectional samples were merged (after converting cross-sectional height values to length by adding 0.7 cm) and sample sizes by length interval are presented in Table 51.
Table 51 Sample sizes for boys' weight-for-length/height by lengtha interval
LengthNLengthNLengthNLengthN(cm)(cm)(cm)(cm)<45263 to <6538383 to <85528103 to <10525845 to <476165 to <6747285 to <87486105 to <10729647 to <4923467 to <6950187 to <89452107 to <10926749 to <5145369 to <7157389 to <91340109 to <11124051 to <5348071 to <7362791 to <93276111 to <11322753 to <5543173 to <7557293 to <95270113 to <11519855 to <5740575 to <7751595 to <97247115 to <11715157 to <5936377 to <7941797 to <99258117 to <11910059 to <6129279 to <8146499 to <101276119 to <1216561 to <6333981 to <83467101 to <103292e"12184
Height values were converted to length before merging the data (length=height+0.7).
139 -
140 Weight-for-length/height, boys
5.2.2 Model selection and results
There was no indication that a length/height transformation similar to that described for age was required for constructing the weight-for-length/height standards (i.e. global deviance values did not vary over the grid of values 0 to 1). Initial steps used the simplest model, i.e. the BCPE distribution with fixed =1 and =2 (the normal distribution). A search procedure for the best combination of df() and df() was carried out. Table 52 summarizes the goodness-of-fit statistics for various combinations of df() and df().
The models with df()=13 or 14 and df()=6 resulted in the best fit. Because the median curve with df()=13 was slightly wiggly, the model with df()=12 was fitted to assess if improvement in smoothing would compensate for the loss in goodness of fit. The resulting difference in the trajectory of the median curve was negligible. Other models with progressively lower degrees of freedom for the
curve were tested until significant smoothing was visible, but this was accompanied by significant losses in goodness of fit. Therefore, the original model with df()=13 and df()=6 was adopted for further evaluation. The fact that the weight-for-length/height indicator combines different velocities for the two measurements involved (weight and length/height) at different ages likely explains the slight wiggle observed in the WHO standards and other references (CDC 2000 (Kuczmarski et al., 2002) and Swiss (Prader et al., 1989)).
Table 52 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for weight-for-length/height for boys
df()df()GDaAICaGAIC(3)aTotal df41102.81132.81147.81551096.91128.91144.9161161093.31127.31144.31771091.31127.31145.31881090.11128.11147.11941097.51129.51145.51651091.61125.61142.6171261088.01124.01142.01871085.91123.91142.91981084.71124.71144.72041093.81127.81144.81751087.81123.81141.8181361084.21122.21141.21971082.11122.11142.12081080.81122.81143.82141090.91126.91144.91851085.01123.01142.0191461081.31121.31141.32071079.21121.21142.22181077.91121.91143.92241088.61126.61145.61951082.71122.71142.7201561079.01121.01142.02171076.91120.91142.92281075.61121.61144.623
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 30 000.
Weight-for-length/height, boys141
Model 1: BCPE(x=length (or height+0.7), df()=13, df()=6, =1, =2)
Figure 63 shows the worm plots of the z-scores derived from Model 1. Intervals correspond to the length/height groups defined in Table 53. The worm plots were all U-shaped, indicating poor model fit due to skewness. Table 53 presents Q-test results of the z-scores from the same model. Almost all the length (or height+0.7) intervals presented absolute values of z3 larger than 2, confirming skewness in the data. No misfit was noted for the median or the variance (values of z1 and z2 within interval -2 to 2).
-3-11 2 3-3 -11 2 3-3 -11 2 340.100-104104-108108-112112-116116-13000.-0.484-8686-8888-9090-9292-9696-100
Deviation0 40.40.0.72-7474-7676-7878-8080-8282-84-60-6262-6464-6666-6868-7070-72
40.44-5050-5252-5454-5656-5858-6000.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 00. 40.
-0.4 00. 40.
Unit normal quantile
Figure 63 Worm plots of z-scores for Model 1 for weight-for-length/height for boys
Keeping df() and df() as specified in Model 1, the next step was to search for the best degrees of freedom for the parameter . Table 54 presents goodness-of-fit values for different degrees of freedom for the curve.
The best GAIC(3) was associated with df()=1. It is worth noting that there is a difference between a model with =1 where the parameter is fixed at value 1, and a model with df()=1 where a constant is estimated by the maximum pseudo-likelihood method across the whole length/height range to define the parameter curve. In the latter, the parameter estimation contributes one degree of freedom to the total, while in the former case does not add to the model's total degrees of freedom.
142 Weight-for-length/height, boys
Table 53 Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7), df()=13, df()=6, =1, =2)] for weight-for-length/height for boys
Length (cm)Nz1z2z3z444 to <50513-0.43-0.373.701.3450 to <524840.550.732.691.1752 to <54452-1.39-0.532.741.1454 to <564090.290.371.800.1056 to <583970.870.971.970.4258 to <60321-0.43-1.652.951.4660 to <623311.20-0.502.460.4762 to <64350-0.570.953.471.0064 to <664140.35-0.142.531.0866 to <684770.37-0.492.18-0.4268 to <70566-0.95-0.651.12-0.4970 to <725850.08-0.163.181.5472 to <746040.670.452.951.1074 to <76527-0.61-0.324.39-0.2376 to <784650.52-0.392.09-0.1378 to <804420.531.643.961.1680 to <82468-0.100.654.331.6482 to <84508-1.850.843.921.6284 to <86531-0.440.924.941.5186 to <884691.10-1.872.680.3488 to <903801.19-0.573.050.5890 to <92308-0.480.151.85-1.2992 to <965190.87-0.520.22-0.0496 to <100531-1.26-0.222.24-1.40100 to <1045510.600.071.96-0.62104 to <1085650.230.482.99-0.52108 to <112490-1.58-1.293.671.20112 to <1163850.481.453.23-1.03116 to 1303201.36-1.022.950.30Overall Q stats13 36221.5020.93261.7029.50degrees of freedom16.025.529.029.0p-value0.15980.7214< 0.010.4394
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 54 Goodness-of-fit summaryfor models BCPE(x=length (or height+0.7), df()=13,df()=6, df()=?, =2) for weight-for-length/height for boysdf()GDaGAIC(3)aTotal df1835.1895.1202834.5897.6213833.2899.2224830.4899.4235826.9898.9246823.8898.825
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 30 000.
Weight-for-length/height, boys143
Model 2: BCPE(x=length (or height+0.7), df()=13, df()=6, df()=1, =2)
The fitted curves of the parameters , and seemed adequate when compared to the empirical values (Figure 64). The distribution of the residuals from the fitted centile curves across length (or height+0.7) intervals (Figure 65) were investigated further to assess the fitted model's performance. The largest residuals were associated with the 97th centile in the two tallest groups. For all other centiles and length/height groups, the pattern of residuals indicated that the model's fit was most adequate.
Weight (kg)15 20Transformed Weight0. 0.090095Medianof5 10Dev ofBox-Cox0.0.080085St60801001206080100120Length (or Height + 0.7) (cm)Length (or Height + 0.7) (cm)Power0.5-1.0 -0.5 0.0Box-Cox Transform6080100120Length (or Height + 0.7) (cm)
Figure 64 Fitting of the , , and curves of Model 2 for weight-for-length/height for boys (dotted line) and their respective sample estimates (points with solid line)
144 Weight-for-length/height, boys
3rd Centile5th Centile10th Centile40.40.40.00.00.00.(kg)-0.4-0.4-0.4forWeight40.8010040.8010040.8010060606025th Centile50th Centile75th CentileCentile00.00.00.Fitted-0.4-0.4-0.4-Empirical60801006080100608010090th Centile95th Centile97th Centile40.40.40.00.00.00.-0.4-0.4-0.4608010060801006080100Length (or Height+0.7) (cm)
Figure 65 Centile residuals from fitting Model 2 for weight-for-length/height for boys
According to the Q-test results in Table 55, only three groups had residual skewness, i.e. with an absolute value of z3 larger than 2, and one group had residual kurtosis as indicated by the absolute value of z4 larger than 2. Worm plots for this model reflect departures from normality of the derived z - scores in the same groups indicated by the Q-test results (Figure 66). In addition, worms with non-flat shapes were noted in other groups but within their 95% confidence intervals. The worm for group 86 to 88 cm presented a steep slope, indicating misfit of the variance. The overall Q-test for kurtosis was not significant and since only one out of 29 length/height groups presented evidence of remaining kurtosis, increasing the model's complexity to include the modelling of the parameter was unwarranted.
Weight-for-length/height, boys145
Table 55 Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7), df()=13, df()=6, df()=1, =2)] for weight-for-length/height for boys
Length (cm)Nz1z2z3z444 to <50513-0.41-0.380.320.7050 to <524840.610.71-0.891.2252 to <54452-1.29-0.31-0.410.4554 to <564090.270.45-1.070.1756 to <583970.750.93-0.930.2658 to <60321-0.39-1.720.460.8860 to <623311.19-0.750.18-0.4462 to <64350-0.660.791.00-0.0564 to <664140.33-0.20-0.310.3166 to <684770.34-0.49-0.46-0.8868 to <70566-1.00-0.18-1.85-0.5170 to <725850.05-0.15-0.280.5072 to <746040.630.46-0.520.1774 to <76527-0.56-0.492.03-1.9676 to <784650.63-0.24-0.66-0.4878 to <804420.571.421.090.0880 to <824680.040.491.48-0.0582 to <84508-1.791.100.740.2784 to <86531-0.460.692.13-0.3286 to <884691.15-1.960.15-0.6788 to <903801.11-0.840.76-0.6490 to <92308-0.620.25-0.09-1.1792 to <965190.80-0.25-2.740.6696 to <100531-1.30-0.08-0.30-1.91100 to <1045510.610.05-0.91-1.19104 to <1085650.240.390.02-1.06108 to <112490-1.46-1.120.660.09112 to <1163850.401.300.91-2.08116 to 1303201.43-1.180.53-0.14Overall Q stats13 36220.9619.9431.9922.08degrees of freedom16.025.528.029.0p-value0.18010.77300.27490.8170
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 56 shows the percentage of children below the fitted centiles. Discrepancies between observed and expected proportions were small (except for the last group) and without any systematic pattern.
The foregoing considerations led to selection of the model BCPE(x=length (or height+0.7), df()=13, df()=6, df()=1, =2) for constructing the weight-for-length/height growth curves for boys. One more iteration was done using df()=1 to re-search for the best values of df() and df() for constructing the weight-for-length/height standards. The alternative model with df()=15 and df()=6 presented AIC= 30 873.8 and GAIC(3)=30 895.8 compared with Model 2's AIC=30 875.1 and GAIC(3)=30 895.1. In sum, since the performances of the two models were very similar, the decision was to retain Model 2.
146 Weight-for-length/height, boys
-3-11 2 3-3 -11 2 3-3-11 2 340.100-104104-108108-112112-116116-13000.-0.484-8686-8888-9090-9292-9696-100
Deviation0 40.40.0.72-7474-7676-7878-8080-8282-84-60-6262-6464-6666-6868-7070-72
40.44-5050-5252-5454-5656-5858-6000.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 66 Worm plots of z-scores for Model 2 for weight-for-length/height for boys
To derive the weight-for-height standards in the range 65 to 120 cm, the weight-for-length centile curves in the length interval 65.7 to 120.7 cm were shifted back by 0.7 cm for the reason explained previously (see also section 5.1). Figures 67 and 68 present fitted centile curves plotted against empirical weight-for-length values derived from the longitudinal component. Similarly, Figures 69 and 70 present plots of fitted centiles against empirical weight-for-height values derived from the cross-sectional component.
Table 56 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for boys
Expected44 to <5050 to <5252 to <5454 to <5656 to <5858 to <6060 to <6262 to <6464 to <6666 to <6810.81.21.31.51.50.30.31.11.00.432.52.93.33.73.32.82.73.43.13.654.74.86.05.45.54.74.56.34.65.51010.78.511.310.011.19.07.610.99.710.72524.025.823.924.223.221.822.425.723.423.55052.247.953.549.646.952.348.951.449.849.97576.473.877.973.672.577.972.576.674.673.69090.889.591.889.589.991.988.890.690.190.49594.594.095.694.695.096.395.594.395.295.09797.196.997.197.195.798.197.994.997.196.99998.898.899.199.398.599.198.898.098.699.8
Expected68 to <7070 to <7272 to <7474 to <7676 to <7878 to <8080 to <8282 to <8484 to <8686 to <8811.21.41.20.20.61.40.61.00.60.234.13.12.82.12.82.52.44.52.31.556.95.55.84.24.74.54.76.94.93.81011.711.511.19.99.910.612.211.810.07.92524.723.923.027.323.426.226.527.828.623.55048.948.047.752.448.450.749.853.352.246.57577.976.674.374.673.571.975.677.076.373.69091.089.990.990.190.889.190.891.390.490.89595.495.095.094.795.392.594.494.994.095.59797.996.296.496.897.295.795.996.595.397.29999.698.898.399.199.197.797.998.898.799.4
Weight-for-length/height, boys
147
Table 56 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for boys (continued)
Expected88 to <9090 to <9292 to <9696 to <100100 to <104104 to <108108 to <112112 to <116116 to 130Overall10.51.31.70.90.70.70.60.80.60.931.12.33.73.43.63.03.53.11.63.053.74.95.05.86.44.85.36.02.85.2108.711.010.211.710.511.311.010.66.910.42523.426.922.227.723.625.524.525.220.624.75047.952.646.853.548.849.452.751.249.750.17573.775.073.275.573.173.679.071.973.874.99089.588.690.990.289.589.492.487.088.490.29595.395.595.695.595.394.095.593.594.494.99797.197.196.997.796.696.597.395.395.996.79998.7100.099.699.498.799.199.098.299.198.9
Note: Group labels correspond to the length (or height+0.7) intervals in Table 55.
148
Weight-for-length/height, boysWeight-for-length/height, boys149
97th90th50th10th3rd90length for boysFittedEmpirical80empirical values: weight-for-70Length (cm)centile curves and60smoothed5010th, 50th, 90th, 97th3rd,141210864267FigureWeight (kg)
150 Weight-for-length/height, boys
95th75th50th25th5th90length for boysFittedEmpirical80empirical values: weight-for-70Length (cm)centile curves and60smoothed5025th, 50th, 75th, 95th5th,141210864268FigureWeight (kg)
Weight-for-length/height, boys151
97th90th50th10th3rd120height for boysFittedEmpirical110empirical values: weight-for-100Height (cm)centile curves and9097th smoothed803rd, 10th, 50th, 90th,2520151069FigureWeight (kg)
152 Weight-for-length/height, boys
95th75th50th25th5th120height for boysFittedEmpirical110empirical values: weight-for-100Height (cm)centile curves and9095th smoothed805th, 25th, 50th, 75th,2520151070FigureWeight (kg)
Weight-for-length/height, boys153
5.2.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO weight-for-length and weight-for-height z-score and percentile charts (Figures 71 to 74) and tables (Tables 57 and 58) for boys. It also provides the z-score comparisons of the WHO versus NCHS (Figures 75 and 76) and CDC 2000 (Figures 77 and 78) curves.
Charts
322010-1(kg)15-2-3Weight10
5
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 71 WHO weight-for-length z-scores for boys from 45 to 110 cm
154
Weight-for-length/height, boysWeight-for-length/height, boys155
3210-1-2-3120115120 cm110105from 65 to100boys90 95Height (cm)height z-scores for80 85WHO weight-for-757270Figure6530252015105Weight (kg)
156 Weight-for-length/height, boys
97th85th50th15th3rd110105cm1001109545 to90boys from85for70 75 80Length (cm)for-length percentiles65weight-60WHO557350Figure452015105Weight (kg)
Weight-for-length/height, boys157
97th85th50th15th3rd120115cm110to 120105from 65100for boys90 95Height (cm)height percentiles85-for-75 80WHO weight70Figure 746525201510Weight (kg)
Tables
Table 57 Weight-for-length for boys
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th45.0-0.35212.44100.091822.02.12.12.22.32.42.62.72.92.93.045.5-0.35212.52440.091532.12.12.22.32.42.52.72.82.93.03.146.0-0.35212.60770.091242.12.22.32.42.52.62.82.93.03.13.346.5-0.35212.69130.090942.22.32.32.52.52.72.93.03.13.23.447.0-0.35212.77550.090652.32.42.42.52.62.83.03.13.23.33.547.5-0.35212.86090.090362.32.42.52.62.72.93.03.13.33.43.648.0-0.35212.94800.090072.42.52.62.72.82.93.13.23.43.53.748.5-0.35213.03770.089772.52.62.62.82.93.03.23.33.53.63.849.0-0.35213.13080.089482.62.72.72.92.93.13.33.43.63.73.949.5-0.35213.22760.089192.62.72.82.93.03.23.43.53.83.84.050.0-0.35213.32780.088902.72.82.93.03.13.33.53.73.94.04.150.5-0.35213.43110.088612.82.93.03.13.23.43.63.84.04.14.251.0-0.35213.53760.088312.93.03.13.23.33.53.83.94.14.24.451.5-0.35213.64770.088013.03.13.23.33.43.63.94.04.24.34.552.0-0.35213.76200.087713.13.23.33.43.53.84.04.14.44.54.652.5-0.35213.88140.087413.23.33.43.63.73.94.14.34.54.64.853.0-0.35214.00600.087113.33.43.53.73.84.04.34.44.64.74.953.5-0.35214.13540.086813.43.53.63.83.94.14.44.54.84.95.154.0-0.35214.26930.086513.53.63.73.94.04.34.54.74.95.05.354.5-0.35214.40660.086213.63.83.84.04.24.44.74.85.15.25.455.0-0.35214.54670.085923.73.94.04.24.34.54.85.05.35.45.655.5-0.35214.68920.085633.94.04.14.34.44.75.05.15.45.55.856.0-0.35214.83380.085354.04.14.24.44.64.85.15.35.65.75.956.5-0.35214.97960.085074.14.34.34.64.75.05.35.45.75.96.1158
Weight-for-length/height, boys
Table 57 Weight-for-length for boys (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th57.0-0.35215.12590.084814.24.44.54.74.85.15.45.65.96.06.357.5-0.35215.27210.084554.44.54.64.85.05.35.65.86.16.26.558.0-0.35215.41800.084304.54.64.75.05.15.45.75.96.26.46.658.5-0.35215.56320.084064.64.84.95.15.35.65.96.16.46.56.859.0-0.35215.70740.083834.74.95.05.25.45.76.06.26.66.77.059.5-0.35215.85010.083624.85.05.15.45.55.96.26.46.76.97.260.0-0.35215.99070.083425.05.15.25.55.76.06.36.56.97.07.360.5-0.35216.12840.083245.15.35.45.65.86.16.56.77.17.27.561.0-0.35216.26320.083085.25.45.55.85.96.36.66.87.27.47.761.5-0.35216.39540.082925.35.55.65.96.16.46.87.07.47.57.862.0-0.35216.52510.082795.45.65.76.06.26.56.97.17.57.78.062.5-0.35216.65270.082665.55.75.86.16.36.77.07.37.67.88.163.0-0.35216.77860.082555.65.85.96.26.46.87.27.47.88.08.363.5-0.35216.90280.082455.75.96.06.36.56.97.37.57.98.18.464.0-0.35217.02550.082365.86.06.26.56.67.07.47.78.18.28.664.5-0.35217.14670.082295.96.16.36.66.87.17.67.88.28.48.765.0-0.35217.26660.082236.06.36.46.76.97.37.77.98.38.58.965.5-0.35217.38540.082186.16.46.56.87.07.47.88.18.58.79.066.0-0.35217.50340.082156.26.56.66.97.17.57.98.28.68.89.166.5-0.35217.62060.082136.36.66.77.07.27.68.18.38.88.99.367.0-0.35217.73700.082126.46.76.87.17.37.78.28.48.99.19.467.5-0.35217.85260.082126.56.86.97.27.47.98.38.69.09.29.668.0-0.35217.96740.082146.66.97.07.37.58.08.48.79.29.39.768.5-0.35218.08160.082166.77.07.17.47.78.18.58.89.39.59.869.0-0.35218.19550.082196.87.17.27.57.88.28.78.99.49.610.069.5-0.35218.30920.082246.97.17.37.67.98.38.89.19.59.710.170.0-0.35218.42270.082297.07.27.47.78.08.48.99.29.79.910.370.5-0.35218.53580.082357.17.37.57.88.18.59.09.39.810.010.471.0-0.35218.64800.082417.27.47.68.08.28.69.19.49.910.110.571.5-0.35218.75940.082487.37.57.78.18.38.89.39.610.110.310.7
Weight-for-length/height, boys
159Table 57 Weight-for-length for boys (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th72.0-0.35218.86970.082547.47.67.88.28.48.99.49.710.210.410.872.5-0.35218.97880.082627.57.77.98.38.59.09.59.810.310.511.073.0-0.35219.08650.082697.57.88.08.48.69.19.69.910.410.711.173.5-0.35219.19270.082767.67.98.08.48.79.29.710.010.610.811.274.0-0.35219.29740.082837.78.08.18.58.89.39.810.110.710.911.474.5-0.35219.40100.082897.88.18.28.68.99.49.910.310.811.011.575.0-0.35219.50320.082957.98.28.38.79.09.510.110.410.911.211.675.5-0.35219.60410.083018.08.28.48.89.19.610.210.511.011.311.776.0-0.35219.70330.083078.08.38.58.99.29.710.310.611.211.411.976.5-0.35219.80070.083118.18.48.69.09.39.810.410.711.311.512.077.0-0.35219.89630.083148.28.58.79.19.49.910.510.811.411.612.177.5-0.35219.99020.083178.38.68.79.29.510.010.610.911.511.712.278.0-0.352110.08270.083188.48.78.89.39.510.110.711.011.611.812.378.5-0.352110.17410.083188.48.78.99.39.610.210.811.111.712.012.479.0-0.352110.26490.083168.58.89.09.49.710.310.911.211.812.112.579.5-0.352110.35580.083138.68.99.19.59.810.411.011.311.912.212.780.0-0.352110.44750.083088.79.09.19.69.910.411.111.412.012.312.880.5-0.352110.54050.083018.79.19.29.710.010.511.211.512.112.412.981.0-0.352110.63520.082938.89.19.39.810.110.611.311.612.212.513.081.5-0.352110.73220.082848.99.29.49.910.210.711.411.712.312.613.182.0-0.352110.83210.082739.09.39.510.010.210.811.511.812.512.713.282.5-0.352110.93500.082609.19.49.610.110.310.911.611.912.612.813.383.0-0.352111.04150.082469.29.59.710.110.411.011.712.012.713.013.583.5-0.352111.15160.082319.39.69.810.310.611.211.812.212.813.113.684.0-0.352111.26510.082159.49.79.910.410.711.311.912.312.913.213.784.5-0.352111.38170.081989.59.810.010.510.811.412.012.413.113.313.985.0-0.352111.50070.081819.69.910.110.610.911.512.212.513.213.514.085.5-0.352111.62180.081639.710.010.210.711.011.612.312.713.313.614.186.0-0.352111.74440.081459.810.110.310.811.111.712.412.813.513.714.386.5-0.352111.86780.081289.910.210.410.911.211.912.512.913.613.914.4
160
Weight-for-length/height, boys
Table 57 Weight-for-length for boys (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th87.0-0.352111.99160.0811110.010.310.511.011.412.012.713.113.714.014.687.5-0.352112.11520.0809610.110.410.611.211.512.112.813.213.914.214.788.0-0.352112.23820.0808210.210.610.711.311.612.212.913.314.014.314.988.5-0.352112.36030.0806910.310.710.911.411.712.413.113.514.214.415.089.0-0.352112.48150.0805810.410.811.011.511.812.513.213.614.314.615.289.5-0.352112.60170.0804810.510.911.111.611.912.613.313.714.414.715.390.0-0.352112.72090.0804110.611.011.211.712.112.713.413.814.614.915.490.5-0.352112.83920.0803410.711.111.311.812.212.813.614.014.715.015.691.0-0.352112.95690.0803010.811.211.411.912.313.013.714.114.815.115.791.5-0.352113.07420.0802610.911.311.512.012.413.113.814.215.015.315.992.0-0.352113.19100.0802511.011.411.612.212.513.213.914.415.115.416.092.5-0.352113.30750.0802511.111.511.712.312.613.314.114.515.215.516.193.0-0.352113.42390.0802611.211.611.812.412.713.414.214.615.415.716.393.5-0.352113.54040.0802911.311.711.912.512.813.514.314.715.515.816.494.0-0.352113.65720.0803411.411.812.012.612.913.714.414.915.616.016.694.5-0.352113.77460.0804011.511.912.112.713.113.814.515.015.816.116.795.0-0.352113.89280.0804711.612.012.212.813.213.914.715.115.916.216.995.5-0.352114.01200.0805611.712.112.312.913.314.014.815.316.016.417.096.0-0.352114.13250.0806711.812.212.413.013.414.114.915.416.216.517.296.5-0.352114.25440.0807811.912.312.513.113.514.315.115.516.316.717.397.0-0.352114.37820.0809212.012.412.613.213.614.415.215.716.516.817.597.5-0.352114.50380.0810612.112.512.713.413.714.515.315.816.617.017.698.0-0.352114.63160.0812212.212.612.813.513.914.615.515.916.817.117.898.5-0.352114.76140.0813912.312.713.013.614.014.815.616.116.917.318.099.0-0.352114.89340.0815712.412.813.113.714.114.915.716.217.117.418.199.5-0.352115.02750.0817712.512.913.213.814.215.015.916.417.217.618.3100.0-0.352115.16370.0819812.613.013.313.914.415.216.016.517.417.818.5100.5-0.352115.30180.0822012.713.213.414.114.515.316.216.717.617.918.7101.0-0.352115.44190.0824312.813.313.514.214.615.416.316.817.718.118.8101.5-0.352115.58380.0826712.913.413.614.314.715.616.517.017.918.319.0
Weight-for-length/height, boys
161Table 57 Weight-for-length for boys (continued)162Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th102.0-0.352115.72760.0829213.013.513.814.514.915.716.617.218.118.519.2102.5-0.352115.87320.0831713.213.613.914.615.015.916.817.318.318.619.4103.0-0.352116.02060.0834313.313.814.014.715.216.017.017.518.418.819.6103.5-0.352116.16970.0837013.413.914.114.815.316.217.117.718.619.019.8104.0-0.352116.32040.0839713.514.014.315.015.416.317.317.818.819.220.0104.5-0.352116.47280.0842513.614.114.415.115.616.517.418.019.019.420.2105.0-0.352116.62680.0845313.714.214.515.315.716.617.618.219.219.620.4105.5-0.352116.78260.0848113.914.414.615.415.916.817.818.419.419.820.6106.0-0.352116.94010.0851014.014.514.815.516.016.918.018.519.620.020.8106.5-0.352117.09950.0853914.114.614.915.716.217.118.118.719.720.221.0107.0-0.352117.26070.0856814.214.815.015.816.317.318.318.919.920.421.2107.5-0.352117.42370.0859914.414.915.216.016.517.418.519.120.120.621.4108.0-0.352117.58850.0862914.515.015.316.116.617.618.719.320.320.821.7108.5-0.352117.75530.0866014.615.215.516.316.817.818.819.520.521.021.9109.0-0.352117.92420.0869114.715.315.616.416.917.919.019.620.821.222.1109.5-0.352118.09540.0872314.915.415.716.617.118.119.219.821.021.422.3110.0-0.352118.26890.0875515.015.615.916.717.218.319.420.021.221.622.6
Weight-for-length/height, boys
Table 57 Weight-for-length for boys (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD45.0-0.35212.44100.091821.92.02.22.42.73.03.345.5-0.35212.52440.091531.92.12.32.52.83.13.446.0-0.35212.60770.091242.02.22.42.62.93.13.546.5-0.35212.69130.090942.12.32.52.73.03.23.647.0-0.35212.77550.090652.12.32.52.83.03.33.747.5-0.35212.86090.090362.22.42.62.93.13.43.848.0-0.35212.94800.090072.32.52.72.93.23.63.948.5-0.35213.03770.089772.32.62.83.03.33.74.049.0-0.35213.13080.089482.42.62.93.13.43.84.249.5-0.35213.22760.089192.52.73.03.23.53.94.350.0-0.35213.32780.088902.62.83.03.33.64.04.450.5-0.35213.43110.088612.72.93.13.43.84.14.551.0-0.35213.53760.088312.73.03.23.53.94.24.751.5-0.35213.64770.088012.83.13.33.64.04.44.852.0-0.35213.76200.087712.93.23.53.84.14.55.052.5-0.35213.88140.087413.03.33.63.94.24.65.153.0-0.35214.00600.087113.13.43.74.04.44.85.353.5-0.35214.13540.086813.23.53.84.14.54.95.454.0-0.35214.26930.086513.33.63.94.34.75.15.654.5-0.35214.40660.086213.43.74.04.44.85.35.855.0-0.35214.54670.085923.63.84.24.55.05.46.055.5-0.35214.68920.085633.74.04.34.75.15.66.156.0-0.35214.83380.085353.84.14.44.85.35.86.356.5-0.35214.97960.085073.94.24.65.05.45.96.557.0-0.35215.12590.084814.04.34.75.15.66.16.757.5-0.35215.27210.084554.14.54.95.35.76.36.958.0-0.35215.41800.084304.34.65.05.45.96.47.158.5-0.35215.56320.084064.44.75.15.66.16.67.259.0-0.35215.70740.083834.54.85.35.76.26.87.459.5-0.35215.85010.083624.65.05.45.96.47.07.6
Weight-for-length/height, boys
163Table 57 Weight-for-length for boys (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD60.0-0.35215.99070.083424.75.15.56.06.57.17.860.5-0.35216.12840.083244.85.25.66.16.77.38.061.0-0.35216.26320.083084.95.35.86.36.87.48.161.5-0.35216.39540.082925.05.45.96.47.07.68.362.0-0.35216.52510.082795.15.66.06.57.17.78.562.5-0.35216.65270.082665.25.76.16.77.27.98.663.0-0.35216.77860.082555.35.86.26.87.48.08.863.5-0.35216.90280.082455.45.96.46.97.58.28.964.0-0.35217.02550.082365.56.06.57.07.68.39.164.5-0.35217.14670.082295.66.16.67.17.88.59.365.0-0.35217.26660.082235.76.26.77.37.98.69.465.5-0.35217.38540.082185.86.36.87.48.08.79.666.0-0.35217.50340.082155.96.46.97.58.28.99.766.5-0.35217.62060.082136.06.57.07.68.39.09.967.0-0.35217.73700.082126.16.67.17.78.49.210.067.5-0.35217.85260.082126.26.77.27.98.59.310.268.0-0.35217.96740.082146.36.87.38.08.79.410.368.5-0.35218.08160.082166.46.97.58.18.89.610.569.0-0.35218.19550.082196.57.07.68.28.99.710.669.5-0.35218.30920.082246.67.17.78.39.09.810.870.0-0.35218.42270.082296.67.27.88.49.210.010.970.5-0.35218.53580.082356.77.37.98.59.310.111.171.0-0.35218.64800.082416.87.48.08.69.410.211.271.5-0.35218.75940.082486.97.58.18.89.510.411.372.0-0.35218.86970.082547.07.68.28.99.610.511.572.5-0.35218.97880.082627.17.68.39.09.810.611.673.0-0.35219.08650.082697.27.78.49.19.910.811.873.5-0.35219.19270.082767.27.88.59.210.010.911.974.0-0.35219.29740.082837.37.98.69.310.111.012.174.5-0.35219.40100.082897.48.08.79.410.211.212.2164
Weight-for-length/height, boys
Table 57 Weight-for-length for boys (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD75.0-0.35219.50320.082957.58.18.89.510.311.312.375.5-0.35219.60410.083017.68.28.89.610.411.412.576.0-0.35219.70330.083077.68.38.99.710.611.512.676.5-0.35219.80070.083117.78.39.09.810.711.612.777.0-0.35219.89630.083147.88.49.19.910.811.712.877.5-0.35219.99020.083177.98.59.210.010.911.913.078.0-0.352110.08270.083187.98.69.310.111.012.013.178.5-0.352110.17410.083188.08.79.410.211.112.113.279.0-0.352110.26490.083168.18.79.510.311.212.213.379.5-0.352110.35580.083138.28.89.510.411.312.313.480.0-0.352110.44750.083088.28.99.610.411.412.413.680.5-0.352110.54050.083018.39.09.710.511.512.513.781.0-0.352110.63520.082938.49.19.810.611.612.613.881.5-0.352110.73220.082848.59.19.910.711.712.713.982.0-0.352110.83210.082738.59.210.010.811.812.814.082.5-0.352110.93500.082608.69.310.110.911.913.014.283.0-0.352111.04150.082468.79.410.211.012.013.114.383.5-0.352111.15160.082318.89.510.311.212.113.214.484.0-0.352111.26510.082158.99.610.411.312.213.314.684.5-0.352111.38170.081989.09.710.511.412.413.514.785.0-0.352111.50070.081819.19.810.611.512.513.614.985.5-0.352111.62180.081639.29.910.711.612.613.715.086.0-0.352111.74440.081459.310.010.811.712.813.915.286.5-0.352111.86780.081289.410.111.011.912.914.015.387.0-0.352111.99160.081119.510.211.112.013.014.215.587.5-0.352112.11520.080969.610.411.212.113.214.315.688.0-0.352112.23820.080829.710.511.312.213.314.515.888.5-0.352112.36030.080699.810.611.412.413.414.615.989.0-0.352112.48150.080589.910.711.512.513.514.716.189.5-0.352112.60170.0804810.010.811.612.613.714.916.2
Weight-for-length/height, boys
165Table 57 Weight-for-length for boys (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD90.0-0.352112.72090.0804110.110.911.812.713.815.016.490.5-0.352112.83920.0803410.211.011.912.813.915.116.591.0-0.352112.95690.0803010.311.112.013.014.115.316.791.5-0.352113.07420.0802610.411.212.113.114.215.416.892.0-0.352113.19100.0802510.511.312.213.214.315.617.092.5-0.352113.30750.0802510.611.412.313.314.415.717.193.0-0.352113.42390.0802610.711.512.413.414.615.817.393.5-0.352113.54040.0802910.711.612.513.514.716.017.494.0-0.352113.65720.0803410.811.712.613.714.816.117.694.5-0.352113.77460.0804010.911.812.713.814.916.317.795.0-0.352113.89280.0804711.011.912.813.915.116.417.995.5-0.352114.01200.0805611.112.012.914.015.216.518.096.0-0.352114.13250.0806711.212.113.114.115.316.718.296.5-0.352114.25440.0807811.312.213.214.315.516.818.497.0-0.352114.37820.0809211.412.313.314.415.617.018.597.5-0.352114.50380.0810611.512.413.414.515.717.118.798.0-0.352114.63160.0812211.612.513.514.615.917.318.998.5-0.352114.76140.0813911.712.613.614.816.017.519.199.0-0.352114.89340.0815711.812.713.714.916.217.619.299.5-0.352115.02750.0817711.912.813.915.016.317.819.4100.0-0.352115.16370.0819812.012.914.015.216.518.019.6100.5-0.352115.30180.0822012.113.014.115.316.618.119.8101.0-0.352115.44190.0824312.213.214.215.416.818.320.0101.5-0.352115.58380.0826712.313.314.415.616.918.520.2102.0-0.352115.72760.0829212.413.414.515.717.118.720.4102.5-0.352115.87320.0831712.513.514.615.917.318.820.6103.0-0.352116.02060.0834312.613.614.816.017.419.020.8103.5-0.352116.16970.0837012.713.714.916.217.619.221.0104.0-0.352116.32040.0839712.813.915.016.317.819.421.2104.5-0.352116.47280.0842512.914.015.216.517.919.621.5166
Weight-for-length/height, boys
Table 57 Weight-for-length for boys (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD105.0-0.352116.62680.0845313.014.115.316.618.119.821.7105.5-0.352116.78260.0848113.214.215.416.818.320.021.9106.0-0.352116.94010.0851013.314.415.616.918.520.222.1106.5-0.352117.09950.0853913.414.515.717.118.620.422.4107.0-0.352117.26070.0856813.514.615.917.318.820.622.6107.5-0.352117.42370.0859913.614.716.017.419.020.822.8108.0-0.352117.58850.0862913.714.916.217.619.221.023.1108.5-0.352117.75530.0866013.815.016.317.819.421.223.3109.0-0.352117.92420.0869114.015.116.517.919.621.423.6109.5-0.352118.09540.0872314.115.316.618.119.821.723.8110.0-0.352118.26890.0875514.215.416.818.320.021.924.1
Weight-for-length/height, boys
167Table 58 Weight-for-height for boys
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th65.0-0.35217.43270.082176.26.46.56.87.07.47.98.18.58.79.165.5-0.35217.55040.082146.36.56.66.97.17.68.08.28.78.99.266.0-0.35217.66730.082126.46.66.77.17.37.78.18.48.89.09.366.5-0.35217.78340.082126.56.76.87.27.47.88.28.58.99.19.567.0-0.35217.89860.082136.66.86.97.37.57.98.48.69.19.39.667.5-0.35218.01320.082146.76.97.07.47.68.08.58.79.29.49.868.0-0.35218.12720.082176.87.07.17.57.78.18.68.99.39.59.968.5-0.35218.24100.082216.87.17.27.67.88.28.79.09.59.710.069.0-0.35218.35470.082266.97.27.37.77.98.48.89.19.69.810.269.5-0.35218.46800.082317.07.37.47.88.08.59.09.29.79.910.370.0-0.35218.58080.082377.17.47.57.98.18.69.19.49.910.110.570.5-0.35218.69270.082437.27.57.68.08.28.79.29.510.010.210.671.0-0.35218.80360.082507.37.67.78.18.38.89.39.610.110.310.771.5-0.35218.91350.082577.47.77.88.28.48.99.49.710.210.510.972.0-0.35219.02210.082647.57.87.98.38.59.09.59.810.410.611.072.5-0.35219.12920.082727.67.88.08.48.69.19.710.010.510.711.173.0-0.35219.23470.082787.77.98.18.58.79.29.810.110.610.811.373.5-0.35219.33900.082857.88.08.28.68.89.39.910.210.711.011.474.0-0.35219.44200.082927.88.18.38.78.99.410.010.310.911.111.574.5-0.35219.54380.082987.98.28.48.89.09.510.110.411.011.211.775.0-0.35219.64400.083038.08.38.48.99.19.610.210.511.111.311.875.5-0.35219.74250.083088.18.48.59.09.29.710.310.611.211.411.976.0-0.35219.83920.083128.28.58.69.09.39.810.410.711.311.612.076.5-0.35219.93410.083158.28.58.79.19.49.910.510.811.411.712.177.0-0.352110.02740.083178.38.68.89.29.510.010.610.911.511.812.377.5-0.352110.11940.083188.48.78.99.39.610.110.711.011.611.912.478.0-0.352110.21050.083178.58.88.99.49.710.210.811.111.712.012.578.5-0.352110.30120.083158.58.89.09.59.710.310.911.211.912.112.679.0-0.352110.39230.083118.68.99.19.59.810.411.011.312.012.212.779.5-0.352110.48450.083058.79.09.29.69.910.511.111.412.112.312.8168
Weight-for-length/height, boys
Table 58 Weight-for-height for boys (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th80.0-0.352110.57810.082988.89.19.39.710.010.611.211.512.212.412.980.5-0.352110.67370.082908.99.29.39.810.110.711.311.612.312.513.081.0-0.352110.77180.082798.99.39.49.910.210.811.411.812.412.613.181.5-0.352110.87280.082689.09.39.510.010.310.911.511.912.512.813.382.0-0.352110.97720.082559.19.49.610.110.411.011.612.012.612.913.482.5-0.352111.08510.082419.29.59.710.210.511.111.712.112.713.013.583.0-0.352111.19660.082259.39.69.810.310.611.211.812.212.913.113.683.5-0.352111.31140.082099.49.79.910.410.711.312.012.313.013.313.884.0-0.352111.42900.081919.59.810.010.510.811.412.112.513.113.413.984.5-0.352111.54900.081749.69.910.110.610.911.512.212.613.313.514.185.0-0.352111.67070.081569.710.110.210.711.111.712.312.713.413.714.285.5-0.352111.79370.081389.810.210.310.911.211.812.512.813.513.814.386.0-0.352111.91730.081219.910.310.511.011.311.912.613.013.713.914.586.5-0.352112.04110.0810510.010.410.611.111.412.012.713.113.814.114.687.0-0.352112.16450.0809010.110.510.711.211.512.212.913.213.914.214.887.5-0.352112.28710.0807610.210.610.811.311.612.313.013.414.114.414.988.0-0.352112.40890.0806410.310.710.911.411.812.413.113.514.214.515.188.5-0.352112.52980.0805410.510.811.011.511.912.513.213.614.414.615.289.0-0.352112.64950.0804510.610.911.111.712.012.613.413.814.514.815.489.5-0.352112.76830.0803810.711.011.211.812.112.813.513.914.614.915.590.0-0.352112.88640.0803210.811.111.311.912.212.913.614.014.815.115.690.5-0.352113.00380.0802810.911.211.412.012.313.013.714.114.915.215.891.0-0.352113.12090.0802511.011.311.512.112.413.113.914.315.015.315.991.5-0.352113.23760.0802411.011.411.612.212.513.214.014.415.215.516.192.0-0.352113.35410.0802511.111.511.712.312.713.414.114.515.315.616.292.5-0.352113.47050.0802711.211.611.812.412.813.514.214.715.415.716.393.0-0.352113.58700.0803111.311.711.912.512.913.614.414.815.615.916.593.5-0.352113.70410.0803611.411.812.012.613.013.714.514.915.716.016.694.0-0.352113.82170.0804311.511.912.112.713.113.814.615.015.816.116.894.5-0.352113.94030.0805111.612.012.212.813.213.914.715.216.016.316.9
Weight-for-length/height, boys
169
Table 58 Weight-for-height for boys (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th95.0-0.352114.06000.0806011.712.112.412.913.314.114.915.316.116.417.195.5-0.352114.18110.0807111.812.212.513.113.414.215.015.416.216.617.296.0-0.352114.30370.0808311.912.312.613.213.614.315.115.616.416.717.496.5-0.352114.42820.0809712.012.412.713.313.714.415.215.716.516.917.597.0-0.352114.55470.0811212.112.512.813.413.814.615.415.916.717.017.797.5-0.352114.68320.0812912.212.712.913.513.914.715.516.016.817.217.998.0-0.352114.81400.0814612.312.813.013.614.014.815.716.117.017.318.098.5-0.352114.94680.0816512.412.913.113.814.214.915.816.317.217.518.299.0-0.352115.08180.0818512.513.013.213.914.315.115.916.417.317.718.499.5-0.352115.21870.0820612.713.113.314.014.415.216.116.617.517.818.5100.0-0.352115.35760.0822912.813.213.514.114.515.416.216.717.618.018.7100.5-0.352115.49850.0825212.913.313.614.214.715.516.416.917.818.218.9101.0-0.352115.64120.0827713.013.413.714.414.815.616.517.118.018.419.1101.5-0.352115.78570.0830213.113.613.814.514.915.816.717.218.218.519.3102.0-0.352115.93200.0832813.213.713.914.615.115.916.917.418.318.719.5102.5-0.352116.08010.0835413.313.814.114.815.216.117.017.618.518.919.7103.0-0.352116.22980.0838113.413.914.214.915.316.217.217.718.719.119.9103.5-0.352116.38120.0840813.614.014.315.015.516.417.317.918.919.320.1104.0-0.352116.53420.0843613.714.214.415.215.616.517.518.119.119.520.3104.5-0.352116.68890.0846413.814.314.615.315.816.717.718.219.219.720.5105.0-0.352116.84540.0849313.914.414.715.415.916.817.818.419.419.920.7105.5-0.352117.00360.0852114.014.514.815.616.117.018.018.619.620.120.9106.0-0.352117.16370.0855114.214.715.015.716.217.218.218.819.820.321.1106.5-0.352117.32560.0858014.314.815.115.916.417.318.419.020.020.521.3107.0-0.352117.48940.0861114.414.915.216.016.517.518.519.120.220.721.5107.5-0.352117.65500.0864114.515.115.416.216.717.718.719.320.420.921.7108.0-0.352117.82260.0867314.715.215.516.316.817.818.919.520.621.122.0108.5-0.352117.99240.0870414.815.315.616.517.018.019.119.720.821.322.2109.0-0.352118.16450.0873614.915.515.816.617.118.219.319.921.121.522.4109.5-0.352118.33900.0876815.115.615.916.817.318.319.520.121.321.722.7170
Weight-for-length/height, boys
Table 58 Weight-for-height for boys (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th110.0-0.352118.51580.0880015.215.816.116.917.518.519.720.321.522.022.9110.5-0.352118.69480.0883215.315.916.217.117.618.719.920.521.722.223.1111.0-0.352118.87590.0886415.516.116.417.217.818.920.120.721.922.423.4111.5-0.352119.05900.0889615.616.216.517.418.019.120.320.922.122.623.6112.0-0.352119.24390.0892815.716.316.717.618.119.220.521.122.422.923.9112.5-0.352119.43040.0896015.916.516.817.718.319.420.721.422.623.124.1113.0-0.352119.61850.0899116.016.617.017.918.519.620.921.622.823.424.4113.5-0.352119.80810.0902216.216.817.118.118.719.821.121.823.123.624.6114.0-0.352119.99900.0905416.317.017.318.218.820.021.322.023.323.824.9114.5-0.352120.19120.0908516.517.117.518.419.020.221.522.223.524.125.2115.0-0.352120.38460.0911616.617.317.618.619.220.421.722.423.824.325.4115.5-0.352120.57890.0914716.817.417.818.719.420.621.922.724.024.625.7116.0-0.352120.77410.0917716.917.617.918.919.520.822.122.924.324.825.9116.5-0.352120.97000.0920817.117.718.119.119.721.022.323.124.525.126.2117.0-0.352121.16660.0923917.217.918.319.319.921.222.523.324.725.326.5117.5-0.352121.36360.0927017.418.018.419.420.121.422.823.625.025.626.7118.0-0.352121.56110.0930017.518.218.619.620.321.623.023.825.225.827.0118.5-0.352121.75880.0933117.718.418.719.820.421.823.224.025.526.127.3119.0-0.352121.95680.0936217.818.518.920.020.622.023.424.225.726.327.5119.5-0.352122.15490.0939317.918.719.120.120.822.223.624.526.026.627.8120.0-0.352122.35300.0942418.118.819.220.321.022.423.824.726.226.828.1
Weight-for-length/height, boys
171Table 58 Weight-for-height for boys (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD65.0-0.35217.43270.082175.96.36.97.48.18.89.665.5-0.35217.55040.082146.06.47.07.68.28.99.866.0-0.35217.66730.082126.16.57.17.78.39.19.966.5-0.35217.78340.082126.16.67.27.88.59.210.167.0-0.35217.89860.082136.26.77.37.98.69.410.267.5-0.35218.01320.082146.36.87.48.08.79.510.468.0-0.35218.12720.082176.46.97.58.18.89.610.568.5-0.35218.24100.082216.57.07.68.29.09.810.769.0-0.35218.35470.082266.67.17.78.49.19.910.869.5-0.35218.46800.082316.77.27.88.59.210.011.070.0-0.35218.58080.082376.87.37.98.69.310.211.170.5-0.35218.69270.082436.97.48.08.79.510.311.371.0-0.35218.80360.082506.97.58.18.89.610.411.471.5-0.35218.91350.082577.07.68.28.99.710.611.672.0-0.35219.02210.082647.17.78.39.09.810.711.772.5-0.35219.12920.082727.27.88.49.19.910.811.873.0-0.35219.23470.082787.37.98.59.210.011.012.073.5-0.35219.33900.082857.47.98.69.310.211.112.174.0-0.35219.44200.082927.48.08.79.410.311.212.274.5-0.35219.54380.082987.58.18.89.510.411.312.475.0-0.35219.64400.083037.68.28.99.610.511.412.575.5-0.35219.74250.083087.78.39.09.710.611.612.676.0-0.35219.83920.083127.78.49.19.810.711.712.876.5-0.35219.93410.083157.88.59.29.910.811.812.977.0-0.352110.02740.083177.98.59.210.010.911.913.077.5-0.352110.11940.083188.08.69.310.111.012.013.178.0-0.352110.21050.083178.08.79.410.211.112.113.378.5-0.352110.30120.083158.18.89.510.311.212.213.479.0-0.352110.39230.083118.28.89.610.411.312.313.579.5-0.352110.48450.083058.38.99.710.511.412.413.6172
Weight-for-length/height, boys
Table 58 Weight-for-height for boys (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD80.0-0.352110.57810.082988.39.09.710.611.512.613.780.5-0.352110.67370.082908.49.19.810.711.612.713.881.0-0.352110.77180.082798.59.29.910.811.712.814.081.5-0.352110.87280.082688.69.310.010.911.812.914.182.0-0.352110.97720.082558.79.310.111.011.913.014.282.5-0.352111.08510.082418.79.410.211.112.113.114.483.0-0.352111.19660.082258.89.510.311.212.213.314.583.5-0.352111.31140.082098.99.610.411.312.313.414.684.0-0.352111.42900.081919.09.710.511.412.413.514.884.5-0.352111.54900.081749.19.910.711.512.513.714.985.0-0.352111.67070.081569.210.010.811.712.713.815.185.5-0.352111.79370.081389.310.110.911.812.813.915.286.0-0.352111.91730.081219.410.211.011.912.914.115.486.5-0.352112.04110.081059.510.311.112.013.114.215.587.0-0.352112.16450.080909.610.411.212.213.214.415.787.5-0.352112.28710.080769.710.511.312.313.314.515.888.0-0.352112.40890.080649.810.611.512.413.514.716.088.5-0.352112.52980.080549.910.711.612.513.614.816.189.0-0.352112.64950.0804510.010.811.712.613.714.916.389.5-0.352112.76830.0803810.110.911.812.813.915.116.490.0-0.352112.88640.0803210.211.011.912.914.015.216.690.5-0.352113.00380.0802810.311.112.013.014.115.316.791.0-0.352113.12090.0802510.411.212.113.114.215.516.991.5-0.352113.23760.0802410.511.312.213.214.415.617.092.0-0.352113.35410.0802510.611.412.313.414.515.817.292.5-0.352113.47050.0802710.711.512.413.514.615.917.393.0-0.352113.58700.0803110.811.612.613.614.716.017.593.5-0.352113.70410.0803610.911.712.713.714.916.217.694.0-0.352113.82170.0804311.011.812.813.815.016.317.894.5-0.352113.94030.0805111.111.912.913.915.116.517.9
Weight-for-length/height, boys
173Table 58 Weight-for-height for boys (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD95.0-0.352114.06000.0806011.112.013.014.115.316.618.195.5-0.352114.18110.0807111.212.113.114.215.416.718.396.0-0.352114.30370.0808311.312.213.214.315.516.918.496.5-0.352114.42820.0809711.412.313.314.415.717.018.697.0-0.352114.55470.0811211.512.413.414.615.817.218.897.5-0.352114.68320.0812911.612.513.614.715.917.418.998.0-0.352114.81400.0814611.712.613.714.816.117.519.198.5-0.352114.94680.0816511.812.813.814.916.217.719.399.0-0.352115.08180.0818511.912.913.915.116.417.919.599.5-0.352115.21870.0820612.013.014.015.216.518.019.7100.0-0.352115.35760.0822912.113.114.215.416.718.219.9100.5-0.352115.49850.0825212.213.214.315.516.918.420.1101.0-0.352115.64120.0827712.313.314.415.617.018.520.3101.5-0.352115.78570.0830212.413.414.515.817.218.720.5102.0-0.352115.93200.0832812.513.614.715.917.318.920.7102.5-0.352116.08010.0835412.613.714.816.117.519.120.9103.0-0.352116.22980.0838112.813.814.916.217.719.321.1103.5-0.352116.38120.0840812.913.915.116.417.819.521.3104.0-0.352116.53420.0843613.014.015.216.518.019.721.6104.5-0.352116.68890.0846413.114.215.416.718.219.921.8105.0-0.352116.84540.0849313.214.315.516.818.420.122.0105.5-0.352117.00360.0852113.314.415.617.018.520.322.2106.0-0.352117.16370.0855113.414.515.817.218.720.522.5106.5-0.352117.32560.0858013.514.715.917.318.920.722.7107.0-0.352117.48940.0861113.714.816.117.519.120.922.9107.5-0.352117.65500.0864113.814.916.217.719.321.123.2108.0-0.352117.82260.0867313.915.116.417.819.521.323.4108.5-0.352117.99240.0870414.015.216.518.019.721.523.7109.0-0.352118.16450.0873614.115.316.718.219.821.823.9109.5-0.352118.33900.0876814.315.516.818.320.022.024.2174
Weight-for-length/height, boys
Table 58 Weight-for-height for boys (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD110.0-0.352118.51580.0880014.415.617.018.520.222.224.4110.5-0.352118.69480.0883214.515.817.118.720.422.424.7111.0-0.352118.87590.0886414.615.917.318.920.722.725.0111.5-0.352119.05900.0889614.816.017.519.120.922.925.2112.0-0.352119.24390.0892814.916.217.619.221.123.125.5112.5-0.352119.43040.0896015.016.317.819.421.323.425.8113.0-0.352119.61850.0899115.216.518.019.621.523.626.0113.5-0.352119.80810.0902215.316.618.119.821.723.926.3114.0-0.352119.99900.0905415.416.818.320.021.924.126.6114.5-0.352120.19120.0908515.616.918.520.222.124.426.9115.0-0.352120.38460.0911615.717.118.620.422.424.627.2115.5-0.352120.57890.0914715.817.218.820.622.624.927.5116.0-0.352120.77410.0917716.017.419.020.822.825.127.8116.5-0.352120.97000.0920816.117.519.221.023.025.428.0117.0-0.352121.16660.0923916.217.719.321.223.325.628.3117.5-0.352121.36360.0927016.417.919.521.423.525.928.6118.0-0.352121.56110.0930016.518.019.721.623.726.128.9118.5-0.352121.75880.0933116.718.219.921.823.926.429.2119.0-0.352121.95680.0936216.818.320.022.024.126.629.5119.5-0.352122.15490.0939316.918.520.222.224.426.929.8120.0-0.352122.35300.0942417.118.620.422.424.627.230.1
Weight-for-length/height, boys
175Comparison with NCHS
322010-1(kg)15-2-3Weight10
5
WHO
NCHS
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 75 Comparison of WHO with NCHS weight-for-length z-scores for boys
176
Weight-for-length/height, boysWeight-for-length/height, boys177
3210-1-2-3
NCHSWHO
120115boys110scores for105z-height100-for-90 95Height (cm)with NCHS weight85WHO75 80Comparison of65 70Figure 76
30252015105Weight (kg)Comparison with CDC 2000
20
15
10 Weight (kg)
5
3
2
1
0
-1
-2
-3
WHO
CDC 2000
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 77 Comparison of WHO with CDC 2000 weight-for-length z-scores for boys
178
Weight-for-length/height, boys
50
40
(kg)30Weight20
10
3
2
1
0
-1
-2
-3
WHO
CDC 2000
65 70 75 80 85 90 95 100 105 110 115 120
Height (cm)
Figure 78 Comparison of WHO with CDC 2000 weight-for-height z-scores for boys
Weight-for-length/height, boys
179180 Weight-for-length/height, girls
5.3 Weight-for-length/height for girls
The choice of the model for constructing weight-for-length/height standards for girls followed similar steps as described for the analogous standards for boys (see section 5.1).
5.3.1 Sample size
There was a total of 13 623 records with weight and length/height measurements from both the longitudinal and cross-sectional samples. The sample sizes by length interval are presented in Table 59.
Table 59 Sample sizes for girls' weight-for-length/height by lengtha interval
LengthNLengthNLengthNLengthN(cm)(cm)(cm)(cm)<451063 to <6549483 to <85508103 to <10528245 to <478365 to <6756485 to <87454105 to <10726747 to <4933067 to <6959287 to <89357107 to <10924949 to <5152069 to <7163889 to <91282109 to <11124851 to <5348471 to <7361891 to <93234111 to <11320953 to <5548173 to <7554093 to <95220113 to <11515155 to <5743675 to <7747295 to <97228115 to <11714757 to <5938977 to <7944897 to <99233117 to <1199559 to <6136879 to <8148299 to <101229119 to <1215861 to <6342381 to <83510101 to <103223e"12167
Height values were converted to length before merging the data (length=height+0.7).
5.3.2 Model selection and results
As was the case for boys, there was no need to transform length (or height) and was thus set to 1. Model selection followed with a search for the best combination of df() and df(), using models with fixed =1 and =2. Table 60 summarizes the goodness-of-fit statistics for various combinations of df() and df(). Since the models with df()=12 to 14 and df()=4 resulted in comparable goodness of fit, the combination df()=12 and df()=4, which had the lowest total degrees of freedom, was selected for further evaluation.
Weight-for-length/height, girls181
Table 60 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for weight-for-length/height for girls
df()df()GDaAICaGAIC(3)aTotal df21215.01241.11254.1131131208.41236.41250.41441203.81233.81248.81551202.01234.01250.01661200.71234.71251.71721209.71237.81251.81431203.21233.21248.2151241198.71230.71246.71651196.81230.81247.81761195.51231.51249.51821206.21236.31251.41531199.71231.71247.7161341195.31229.31246.31751193.41229.41247.41861192.11230.11249.11921203.81235.91252.0161431197.41231.41248.41741192.91228.91246.91851191.11229.11248.11961189.81229.81249.82021202.11236.21253.2171531195.61231.61249.61841191.21229.21248.21951189.31229.31249.32061188.11230.11251.121
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 31 000.
Model 1: BCPE(x= length (or height+0.7), df()=12, df()=4, =1, =2)
Results of the Q-test indicated well fitted and curves, but residual skewness remained across almost all length groups (Table 61). Therefore, a new model including the modelling of parameter was sought.
182 Weight-for-length/height, girls
Table 61 Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7), df()=12, df()=4, =1, =2)] for weight-for-length/height for girls
Length (cm)Nz1z2z3z443 to <506850.050.322.53-0.4750 to <52502-0.32-1.223.670.9652 to <54486-0.13-0.452.700.0254 to <564580.27-0.091.93-0.9456 to <58405-0.37-0.181.43-1.5758 to <603640.920.211.20-1.1260 to <62393-0.191.741.42-1.7062 to <64474-0.361.612.84-1.4764 to <665240.01-0.102.06-2.0066 to <685990.49-0.662.79-1.1268 to <70599-0.04-0.883.27-0.4470 to <72643-0.41-0.063.25-0.2472 to <745850.47-0.783.240.1574 to <764840.642.025.051.4276 to <78472-0.490.524.491.3178 to <80457-0.300.563.781.0180 to <82509-0.29-0.203.671.1882 to <84493-1.18-1.033.100.1084 to <86486-0.20-0.743.190.2186 to <884251.13-0.344.532.1788 to <903090.99-0.113.962.0790 to <92242-0.310.671.961.3892 to <964600.570.163.35-0.5096 to <100455-0.21-0.941.46-2.26100 to <104482-0.59-0.361.56-0.85104 to <1085220.39-0.294.010.46108 to <112496-0.770.123.29-0.43112 to <116318-0.530.983.650.59116 to 1342961.811.372.48-0.94Overall Q stats13 62311.5820.15283.5741.09degrees of freedom17.026.529.029.0p-value0.82470.8052<0.010.0676
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 62 presents goodness of fit for various df() values, with the degrees of freedom for and from Model 1 and fixing =2.
Although the model with df()=2 yielded the smallest GAIC(3), the fitted curve in this case a straight line with a negative slope resulted in fitted values that caused the distribution to be excessively skewed at high height values. Since models with df()=2 and df()=1 presented similar GAIC(3), the latter was chosen because it resulted in a smoother curve.
Weight-for-length/height, girls183
Table 62 Goodness-of-fit summary for models BCPE(x=length (or height+0.7), df()=12, df()=4, df()=?, =2) for weight-for-length/height for girls
df()GDaGAIC(3)aTotal df1902.0953.0172898.0952.0183895.4952.5194892.9953.0205890.5953.5216888.9954.9227887.9956.923
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 31 000.
Model 2: BCPE(x=length (or height+0.7), df()=12, df()=4, df()=1, =2)
Figure 79 shows the parameter curve fittings. The patterns of residuals, i.e. empirical centiles minus fitted centiles (Figure 80), do not indicate any systematic biases.
20Weight0.098Weight (kg)15Transformed0.094Medianof5 10Dev of Box-Cox0. 0.086090St60801001206080100120Length (or Height + 0.7) (cm)Length (or Height + 0.7) (cm)Box-Cox Transform Power0.5-1.0 -0.5 0.06080100120
Length (or Height + 0.7) (cm)
Figure 79 Fitting of the , , and curves of Model 2 for weight-for-length/height for girls (dotted line) and their respective sample estimates (points with solid line)
184 Weight-for-length/height, girls
3rd Centile5th Centile10th Centile40.40.40.00.00.00.(kg)-0.4-0.4-0.4
Weight
60801006080100608010025th Centile50th Centile75th Centile
for40.40.40.Centile00.00.00.Fitted-0.4-0.4-0.4-40.40.40.Empirical80100801008010060606090th Centile95th Centile97th Centile00.00.00.-0.4-0.4-0.4608010060801006080100
Length (or Height+0.7) (cm)
Figure 80 Centile residuals from fitting Model 2 for weight-for-length/height for girls
Results of the Q-test for Model 2 are summarized in Table 63. Departures from normality and indications of misfit appeared in four of the 29 groups, with absolute values of z4 greater than 2, indicating residual kurtosis. However, the overall test for kurtosis was non-significant. The worm plots for this model indicated residual kurtosis for the same four length groups, as is evident in the S-shaped worms in Figure 81. No misfits in means, variances and skewness were observed.
Potential improvements in adjusting for kurtosis were investigated by modelling . The smoothing functions of Model 2 for the other three parameters were used. Values of df() between 1 and 8 were considered. The model with the smallest GAIC(3) was associated with the smoothing function f()=2.13 (GAIC(3)= 31 945.9). However, the difference between =2 and =2.13 had a negligible impact on the final centiles, despite the Q-test results for this model showing improvement and no residual kurtosis across all groups (Table 64). Moreover, results were slightly worse in terms of residual skewness in at least one group (74 to 76 cm), for which the resulting value of z3 was above 2. Plots of centile residuals for the model with =2.13 (not shown) demonstrated no significant changes in the fitted centiles compared to those produced by Model 2. There were two disadvantages of varying the parameter from 2: first, it would increase complexity in application of the standards, i.e. calculation of z-scores or centiles would require using a distribution other than a transform-to-normal distribution; second, it would create inconsistency between sexes. This alternative model fitting the fourth parameter was therefore discarded.
Weight-for-length/height, girls185
Table 63 Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7), df()=12, df()=4, df()=1, =2)] for weight-for-length/height for girls
Length (cm)Nz1z2z3z443 to <506850.060.35-1.21-0.3850 to <52502-0.47-1.440.54-0.2352 to <54486-0.29-0.50-0.39-0.5254 to <564580.23-0.07-0.97-0.7856 to <58405-0.270.01-1.16-1.2158 to <603641.120.24-1.42-0.5560 to <62393-0.101.96-1.18-2.0462 to <64474-0.301.590.11-2.5364 to <665240.080.04-0.79-2.0366 to <685990.49-0.69-0.32-1.6368 to <70599-0.07-0.870.06-1.0370 to <72643-0.490.10-0.24-0.9572 to <745850.59-0.79-0.02-1.0474 to <764840.651.481.940.0376 to <78472-0.380.361.46-0.1578 to <80457-0.280.540.68-0.1880 to <82509-0.32-0.140.39-0.1482 to <84493-1.25-0.730.14-0.6584 to <86486-0.27-0.620.15-0.1286 to <884251.10-0.771.540.4688 to <903090.99-0.501.221.0890 to <92242-0.400.90-0.690.4692 to <964600.530.000.68-1.5096 to <100455-0.24-0.60-1.03-2.14100 to <104482-0.680.11-1.47-0.75104 to <1085220.40-0.490.84-0.44108 to <112496-0.730.310.20-0.93112 to <116318-0.510.930.99-0.11116 to 1342961.861.170.08-1.47Overall Q stats13 62312.6018.8824.6735.97degrees of freedom17.026.528.029.0p-value0.76210.85850.64560.1745
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 65 compares expected and observed proportions of children below fitted centiles using Model 2. No systematic patterns of deviation were observed for any of the centiles across the length (or height+0.7) groups.
186 Weight-for-length/height, girls
-3-11 2 3-3 -11 2 3-3-11 2 340.100-104104-108108-112112-116116-13400.-0.484-8686-8888-9090-9292-9696-100
Deviation0 40.40.0.72-7474-7676-7878-8080-8282-84-60-6262-6464-6666-6868-7070-72
40.43-5050-5252-5454-5656-5858-6000.-0.4-3-11 2 3-3-11 2 3-3-11 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 81 Worm plots of z-scores for Model 2 for weight-for-length/height for girls
Weight-for-length/height, girls187
Table 64 Q-test for z-scores from model BCPE(x=length (or height+0.7), df()=12, df()=4, df()=1, =2.13) for weight-for-length/height for girls
Length (cm)Nz1z2z3z443 to <506850.070.36-1.320.3150 to <52502-0.47-1.460.580.2552 to <54486-0.28-0.51-0.430.0354 to <564580.26-0.08-1.06-0.1956 to <58405-0.230.01-1.27-0.6958 to <603641.160.25-1.50-0.0760 to <62393-0.062.00-1.23-1.4962 to <64474-0.271.610.11-1.9564 to <665240.070.02-0.85-1.4966 to <685990.47-0.71-0.35-1.0568 to <70599-0.09-0.890.02-0.4470 to <72643-0.510.10-0.28-0.3172 to <745850.56-0.830.06-0.4774 to <764840.631.562.060.5476 to <78472-0.430.381.530.3778 to <80457-0.330.560.710.3580 to <82509-0.37-0.140.420.4382 to <84493-1.28-0.770.08-0.0884 to <86486-0.30-0.660.080.5086 to <884251.08-0.781.730.9588 to <903090.98-0.471.311.4890 to <92242-0.430.93-0.710.9592 to <964600.54-0.030.72-0.9596 to <100455-0.23-0.67-1.11-1.49100 to <104482-0.680.10-1.58-0.17104 to <1085220.39-0.500.890.05108 to <112496-0.800.310.13-0.37112 to <116318-0.580.970.970.26116 to 1342961.771.180.13-1.03Overall Q stats13 62312.6219.9428.2519.92degrees of freedom17.026.528.028.0p-value0.76120.81440.45130.8672
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
new iteration was done using df()=1 to re-search for the best combination of df() and df(). Model 2 still presented the smallest value of GAIC(3) and very close AIC (31 936.0) to the model with smallest AIC, i.e. with df()=14 and df()=4 (31 934.7). Thus, there was no necessity to update Model 2.
In conclusion, the model BCPE(x=length (or height+0.7), df()=12, df()=4, df()=1, =2) was used to construct the weight-for-length and weight-for-height growth curves for girls. The centile curves for weight-for-height were constructed in the same way as described for boys, i.e. centiles were shifted back by 0.7 cm in the range 65.7 to 120.7 cm. Figures 82 and 83 show the weight-for-length centile curves, and Figures 84 and 85 show the weight-for-height centile curves for girls, including the empirical centiles.
Table 65 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for girls
Expected43 to <5050 to <5252 to <5454 to <5656 to <5858 to <6060 to <6262 to <6464 to <6666 to <6811.30.41.00.91.51.11.50.61.01.032.82.83.52.84.04.14.14.43.82.854.84.65.14.15.44.97.96.56.55.81010.410.09.79.610.49.313.011.210.19.02525.823.925.325.324.422.326.027.424.222.75049.551.850.048.949.145.947.651.351.549.67574.277.574.773.174.370.972.373.474.073.19089.691.091.889.789.687.987.888.489.188.59593.995.295.195.696.095.194.994.194.895.29796.896.897.396.998.396.496.796.897.197.59999.698.899.299.899.899.799.098.999.899.5
Expected68 to <7070 to <7272 to <7474 to <7676 to <7878 to <8080 to <8282 to <8484 to <8686 to <8810.70.90.51.00.80.70.80.81.20.532.73.12.22.53.22.83.33.02.11.654.25.14.85.24.95.35.75.33.54.7109.79.89.99.39.510.19.210.19.39.22524.026.325.025.826.125.625.128.226.122.45051.351.247.051.052.552.151.552.350.647.17576.374.075.275.476.374.475.276.775.775.89089.390.590.887.089.690.690.691.989.589.99594.795.294.592.893.995.095.396.194.994.19797.896.696.994.896.696.397.297.697.396.09999.598.998.898.198.198.598.899.299.298.4
188
Weight-for-length/height, girls
Table 65 Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for girls (continued)
Expected88 to <9090 to <9292 to <9696 to <100100 to <104104 to <108108 to <112112 to <116116 to 134Overall10.31.20.90.91.01.10.41.90.70.932.62.92.62.43.32.13.83.82.73.053.95.04.34.06.64.66.75.74.75.2107.412.48.911.011.49.211.39.79.110.02521.727.725.725.526.122.825.426.123.625.15049.849.253.049.948.849.453.455.746.650.37577.074.473.071.475.175.774.676.169.974.69088.790.587.890.391.189.588.787.787.589.69593.295.994.695.495.493.994.892.891.694.79795.897.997.098.596.995.696.695.093.996.89999.099.299.199.699.899.099.298.498.399.1
Note: Group labels correspond to the length (or height+0.7) intervals in Table 64.
Weight-for-length/height, girls
189190 Weight-for-length/height, girls
97th90th50th10th3rd90for girlslengthFittedEmpirical80empirical values: weight-for-70Length (cm)centile curves and60smoothed5010th, 50th, 90th, 97th3rd,141210864282FigureWeight (kg)
Weight-for-length/height, girls191
95th75th50th25th5th90length for girlsFittedEmpirical80empirical values: weight-for-70Length (cm)centile curves and60smoothed5025th, 50th, 75th, 95th5th,831412108642FigureWeight (kg)
192 Weight-for-length/height, girls
97th90th50th10th3rd120height for girlsFittedEmpirical110empirical values: weight-for-100Height (cm)centile curves and9097th smoothed803rd, 10th, 50th, 90th,2520151084FigureWeight (kg)
Weight-for-length/height, girls193
95th75th50th25th5th120height for girlsFittedEmpirical110empirical values: weight-for-100Height (cm)centile curves and9095th smoothed805th, 25th, 50th, 75th,2520151085FigureWeight (kg)
194 Weight-for-length/height, girls
5.3.3 WHO standards and their comparison with NCHS and CDC 2000 references
This section presents the final WHO weight-for-length and weight-for-height z-score and percentile charts (Figures 86 to 89) and tables (Tables 66 and 67) for girls. It also provides the z-score comparisons of the WHO versus NCHS (Figures 90 and 91) and CDC 2000 (Figures 92 and 93) curves.
Weight-for-length/height, girls195
3210-1-2-311010510095girls90for85z-scores65 70 75 80Length (cm)WHO weight-for-length60Figure 86555045252015105Weight (kg)
Charts196 Weight-for-length/height, girls
3210-1-2-3120115110105for girls100scoresz-90 95Height (cm)weight-for-height85WHO808775Figure706530252015105Weight (kg)
Weight-for-length/height, girls197
97th85th50th15th3rd11010510095girls70 75 80 85 90Length (cm)weight-for-length percentiles for65WHO55 60Figure 8850452015105Weight (kg)
198 Weight-for-length/height, girls
97th85th50th15th3rd120115110girls85 90 95 100 105Height (cm)WHO weight-for-height percentiles for808975Figure7065252015105Weight (kg)
Tables
Table 66 Weight-for-length for girls
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th45.0-0.38332.46070.090292.02.12.12.22.32.52.62.72.92.93.145.5-0.38332.54570.090332.12.22.22.32.42.52.72.83.03.03.246.0-0.38332.63060.090372.12.22.32.42.52.62.82.93.13.13.346.5-0.38332.71550.090402.22.32.32.52.62.72.93.03.23.23.447.0-0.38332.80070.090442.32.42.42.62.62.83.03.13.33.33.547.5-0.38332.88670.090482.42.42.52.62.72.93.13.23.43.43.648.0-0.38332.97410.090522.42.52.62.72.83.03.23.33.53.53.748.5-0.38333.06360.090562.52.62.72.82.93.13.33.43.63.73.849.0-0.38333.15600.090602.62.72.72.93.03.23.43.53.73.83.949.5-0.38333.25200.090642.72.82.83.03.13.33.53.63.83.94.150.0-0.38333.35180.090682.72.82.93.13.23.43.63.73.94.04.250.5-0.38333.45570.090722.82.93.03.23.33.53.73.84.04.14.351.0-0.38333.56360.090762.93.03.13.23.43.63.83.94.24.34.451.5-0.38333.67540.090803.03.13.23.43.53.73.94.04.34.44.652.0-0.38333.79110.090853.13.23.33.53.63.84.04.24.44.54.752.5-0.38333.91050.090893.23.33.43.63.73.94.24.34.64.74.953.0-0.38334.03320.090933.33.43.53.73.84.04.34.44.74.85.053.5-0.38334.15910.090983.43.53.63.83.94.24.44.64.95.05.254.0-0.38334.28750.091023.53.63.73.94.04.34.64.75.05.15.354.5-0.38334.41790.091063.63.73.84.04.24.44.74.95.25.35.555.0-0.38334.54980.091103.73.93.94.14.34.54.85.05.35.45.755.5-0.38334.68270.091143.84.04.04.34.44.75.05.25.55.65.856.0-0.38334.81620.091183.94.14.24.44.54.85.15.35.65.86.056.5-0.38334.95000.091214.04.24.34.54.75.05.35.55.85.96.2
Weight-for-length/height, girls
199Table 66 Weight-for-length for girls (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th57.0-0.38335.08370.091254.14.34.44.64.85.15.45.65.96.16.357.5-0.38335.21730.091284.34.44.54.84.95.25.65.76.16.26.558.0-0.38335.35070.091304.44.54.64.95.05.45.75.96.26.46.758.5-0.38335.48340.091324.54.64.75.05.25.55.86.06.46.56.859.0-0.38335.61510.091344.64.84.95.15.35.66.06.26.66.77.059.5-0.38335.74540.091354.74.95.05.25.45.76.16.36.76.97.260.0-0.38335.87420.091364.85.05.15.45.55.96.36.56.97.07.360.5-0.38336.00140.091374.95.15.25.55.66.06.46.67.07.27.561.0-0.38336.12700.091375.05.25.35.65.86.16.56.77.27.37.661.5-0.38336.25110.091365.15.35.45.75.96.36.76.97.37.57.862.0-0.38336.37380.091355.25.45.55.86.06.46.87.07.47.68.062.5-0.38336.49480.091335.35.55.65.96.16.56.97.27.67.88.163.0-0.38336.61440.091315.45.65.76.06.26.67.07.37.77.98.363.5-0.38336.73280.091295.55.75.86.16.36.77.27.47.98.08.464.0-0.38336.85010.091265.65.85.96.26.46.97.37.58.08.28.564.5-0.38336.96620.091235.75.96.06.36.67.07.47.78.18.38.765.0-0.38337.08120.091195.86.06.16.56.77.17.57.88.38.58.865.5-0.38337.19500.091155.96.16.26.66.87.27.77.98.48.69.066.0-0.38337.30760.091106.06.26.36.76.97.37.88.08.58.79.166.5-0.38337.41890.091066.16.36.46.87.07.47.98.28.78.99.367.0-0.38337.52880.091016.16.46.56.97.17.58.08.38.89.09.467.5-0.38337.63750.090966.26.56.67.07.27.68.18.48.99.19.568.0-0.38337.74480.090906.36.66.77.17.37.78.28.59.09.29.768.5-0.38337.85090.090856.46.76.87.27.47.98.48.69.29.49.869.0-0.38337.95590.090796.56.76.97.37.58.08.58.89.39.59.969.5-0.38338.05990.090746.66.87.07.37.68.18.68.99.49.610.070.0-0.38338.16300.090686.76.97.17.47.78.28.79.09.59.710.270.5-0.38338.26510.090626.77.07.17.57.88.38.89.19.69.910.371.0-0.38338.36660.090566.87.17.27.67.98.48.99.29.810.010.471.5-0.38338.46760.090506.97.27.37.78.08.59.09.39.910.110.5
200
Weight-for-length/height, girls
Table 66 Weight-for-length for girls (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th72.0-0.38338.56790.090437.07.37.47.88.18.69.19.410.010.210.772.5-0.38338.66740.090377.17.47.57.98.28.79.29.510.110.310.873.0-0.38338.76610.090317.27.47.68.08.38.89.39.610.210.410.973.5-0.38338.86380.090257.27.57.78.18.38.99.49.710.310.611.074.0-0.38338.96010.090187.37.67.88.28.49.09.59.910.410.711.274.5-0.38339.05520.090127.47.77.88.38.59.19.610.010.510.811.375.0-0.38339.14900.090057.57.87.98.38.69.19.710.110.710.911.475.5-0.38339.24180.089997.67.88.08.48.79.29.810.210.811.011.576.0-0.38339.33370.089927.67.98.18.58.89.39.910.310.911.111.676.5-0.38339.42520.089857.78.08.28.68.99.410.010.411.011.211.777.0-0.38339.51660.089797.88.18.28.79.09.510.110.511.111.311.877.5-0.38339.60860.089727.98.28.38.89.19.610.210.611.211.411.978.0-0.38339.70150.089657.98.28.48.99.19.710.310.711.311.512.178.5-0.38339.79570.089598.08.38.58.99.29.810.410.811.411.712.279.0-0.38339.89150.089528.18.48.69.09.39.910.510.911.511.812.379.5-0.38339.98920.089468.28.58.79.19.410.010.611.011.611.912.480.0-0.383310.08910.089408.38.68.79.29.510.110.711.111.712.012.580.5-0.383310.19160.089348.38.78.89.39.610.210.811.211.912.112.781.0-0.383310.29650.089288.48.88.99.49.710.310.911.312.012.212.881.5-0.383310.40410.089238.58.89.09.59.810.411.111.412.112.412.982.0-0.383310.51400.089188.68.99.19.69.910.511.211.612.212.513.182.5-0.383310.62630.089148.79.09.29.710.010.611.311.712.412.613.283.0-0.383310.74100.089108.89.19.39.810.110.711.411.812.512.813.383.5-0.383310.85780.089068.99.29.49.910.210.911.511.912.612.913.584.0-0.383310.97670.089039.09.39.510.010.311.011.712.112.813.113.684.5-0.383311.09740.089009.19.49.610.110.511.111.812.212.913.213.885.0-0.383311.21980.088989.29.59.710.210.611.211.912.313.013.313.985.5-0.383311.34350.088979.39.69.810.410.711.312.112.513.213.514.186.0-0.383311.46840.088959.49.89.910.510.811.512.212.613.313.614.286.5-0.383311.59400.088959.59.910.110.610.911.612.312.713.513.814.4
Weight-for-length/height, girls
201Table 66 Weight-for-length for girls (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th87.0-0.383311.72010.088959.610.010.210.711.011.712.512.913.613.914.587.5-0.383311.84610.088959.710.110.310.811.211.812.613.013.814.114.788.0-0.383311.97200.088969.810.210.410.911.312.012.713.213.914.214.988.5-0.383312.09760.088989.910.310.511.011.412.112.913.314.114.415.089.0-0.383312.22290.0890010.010.410.611.211.512.213.013.414.214.515.289.5-0.383312.34770.0890310.110.510.711.311.612.313.113.614.414.715.390.0-0.383312.47230.0890610.210.610.811.411.812.513.313.714.514.815.590.5-0.383312.59650.0890910.310.710.911.511.912.613.413.814.615.015.691.0-0.383312.72050.0891310.410.811.011.612.012.713.514.014.815.115.891.5-0.383312.84430.0891810.510.911.111.712.112.813.714.114.915.315.992.0-0.383312.96810.0892310.611.011.211.812.213.013.814.215.115.416.192.5-0.383313.09200.0892810.711.111.312.012.313.113.914.415.215.616.393.0-0.383313.21580.0893410.811.211.512.112.513.214.014.515.415.716.493.5-0.383313.33990.0894110.911.311.612.212.613.314.214.715.515.916.694.0-0.383313.46430.0894811.011.411.712.312.713.514.314.815.716.016.794.5-0.383313.58920.0895511.111.511.812.412.813.614.414.915.816.216.995.0-0.383313.71460.0896311.211.611.912.512.913.714.615.116.016.317.095.5-0.383313.84080.0897211.311.812.012.613.013.814.715.216.116.517.296.0-0.383313.96760.0898111.411.912.112.713.214.014.915.416.316.617.496.5-0.383314.09530.0899011.512.012.212.913.314.115.015.516.416.817.597.0-0.383314.22390.0900011.612.112.313.013.414.215.115.616.616.917.797.5-0.383314.35370.0901011.712.212.413.113.514.415.315.816.717.117.998.0-0.383314.48480.0902111.812.312.513.213.614.515.415.916.917.318.098.5-0.383314.61740.0903311.912.412.713.313.814.615.516.117.017.418.299.0-0.383314.75190.0904412.012.512.813.513.914.815.716.217.217.618.499.5-0.383314.88820.0905712.212.612.913.614.014.915.816.417.417.818.5100.0-0.383315.02670.0906912.312.713.013.714.115.016.016.517.517.918.7100.5-0.383315.16760.0908312.412.913.113.814.315.216.116.717.718.118.9101.0-0.383315.31080.0909612.513.013.214.014.415.316.316.917.918.319.1101.5-0.383315.45640.0911012.613.113.414.114.515.516.417.018.018.519.3
202
Weight-for-length/height, girls
Table 66 Weight-for-length for girls (continued)
Percentiles (weight in kg)Length (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th102.0-0.383315.60460.0912512.713.213.514.214.715.616.617.218.218.619.5102.5-0.383315.75530.0913912.813.313.614.414.815.816.817.418.418.819.7103.0-0.383315.90870.0915513.013.513.714.515.015.916.917.518.619.019.9103.5-0.383316.06450.0917013.113.613.914.615.116.117.117.718.819.220.1104.0-0.383316.22290.0918613.213.714.014.815.316.217.317.919.019.420.3104.5-0.383316.38370.0920313.313.914.114.915.416.417.418.119.119.620.5105.0-0.383316.54700.0921913.514.014.315.115.616.517.618.219.319.820.7105.5-0.383316.71290.0923613.614.114.415.215.716.717.818.419.520.020.9106.0-0.383316.88140.0925413.714.314.615.415.916.918.018.619.720.221.1106.5-0.383317.05270.0927113.914.414.715.516.017.118.218.820.020.421.4107.0-0.383317.22690.0928914.014.514.815.716.217.218.419.020.220.621.6107.5-0.383317.40390.0930714.114.715.015.816.417.418.519.220.420.921.8108.0-0.383317.58390.0932614.314.815.116.016.517.618.719.420.621.122.1108.5-0.383317.76680.0934414.415.015.316.216.717.818.919.620.821.322.3109.0-0.383317.95260.0936314.615.115.516.316.918.019.119.821.021.522.5109.5-0.383318.14120.0938214.715.315.616.517.018.119.320.021.321.822.8110.0-0.383318.33240.0940114.915.415.816.717.218.319.520.221.522.023.0
Weight-for-length/height, girls
203Table 66 Weight-for-length for girls (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD45.0-0.38332.46070.090291.92.12.32.52.73.03.345.5-0.38332.54570.090332.02.12.32.52.83.13.446.0-0.38332.63060.090372.02.22.42.62.93.23.546.5-0.38332.71550.090402.12.32.52.73.03.33.647.0-0.38332.80070.090442.22.42.62.83.13.43.747.5-0.38332.88670.090482.22.42.62.93.23.53.848.0-0.38332.97410.090522.32.52.73.03.33.64.048.5-0.38333.06360.090562.42.62.83.13.43.74.149.0-0.38333.15600.090602.42.62.93.23.53.84.249.5-0.38333.25200.090642.52.73.03.33.63.94.350.0-0.38333.35180.090682.62.83.13.43.74.04.550.5-0.38333.45570.090722.72.93.23.53.84.24.651.0-0.38333.56360.090762.83.03.33.63.94.34.851.5-0.38333.67540.090802.83.13.43.74.04.44.952.0-0.38333.79110.090852.93.23.53.84.24.65.152.5-0.38333.91050.090893.03.33.63.94.34.75.253.0-0.38334.03320.090933.13.43.74.04.44.95.453.5-0.38334.15910.090983.23.53.84.24.65.05.554.0-0.38334.28750.091023.33.63.94.34.75.25.754.5-0.38334.41790.091063.43.74.04.44.85.35.955.0-0.38334.54980.091103.53.84.24.55.05.56.155.5-0.38334.68270.091143.63.94.34.75.15.76.356.0-0.38334.81620.091183.74.04.44.85.35.86.456.5-0.38334.95000.091213.84.14.55.05.46.06.657.0-0.38335.08370.091253.94.34.65.15.66.16.857.5-0.38335.21730.091284.04.44.85.25.76.37.058.0-0.38335.35070.091304.14.54.95.45.96.57.158.5-0.38335.48340.091324.24.65.05.56.06.67.359.0-0.38335.61510.091344.34.75.15.66.26.87.559.5-0.38335.74540.091354.44.85.35.76.36.97.7
204
Weight-for-length/height, girls
Table 66 Weight-for-length for girls (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD60.0-0.38335.87420.091364.54.95.45.96.47.17.860.5-0.38336.00140.091374.65.05.56.06.67.38.061.0-0.38336.12700.091374.75.15.66.16.77.48.261.5-0.38336.25110.091364.85.25.76.36.97.68.462.0-0.38336.37380.091354.95.35.86.47.07.78.562.5-0.38336.49480.091335.05.45.96.57.17.88.763.0-0.38336.61440.091315.15.56.06.67.38.08.863.5-0.38336.73280.091295.25.66.26.77.48.19.064.0-0.38336.85010.091265.35.76.36.97.58.39.164.5-0.38336.96620.091235.45.86.47.07.68.49.365.0-0.38337.08120.091195.55.96.57.17.88.69.565.5-0.38337.19500.091155.56.06.67.27.98.79.666.0-0.38337.30760.091105.66.16.77.38.08.89.866.5-0.38337.41890.091065.76.26.87.48.19.09.967.0-0.38337.52880.091015.86.36.97.58.39.110.067.5-0.38337.63750.090965.96.47.07.68.49.210.268.0-0.38337.74480.090906.06.57.17.78.59.410.368.5-0.38337.85090.090856.16.67.27.98.69.510.569.0-0.38337.95590.090796.16.77.38.08.79.610.669.5-0.38338.05990.090746.26.87.48.18.89.710.770.0-0.38338.16300.090686.36.97.58.29.09.910.970.5-0.38338.26510.090626.46.97.68.39.110.011.071.0-0.38338.36660.090566.57.07.78.49.210.111.171.5-0.38338.46760.090506.57.17.78.59.310.211.372.0-0.38338.56790.090436.67.27.88.69.410.311.472.5-0.38338.66740.090376.77.37.98.79.510.511.573.0-0.38338.76610.090316.87.48.08.89.610.611.773.5-0.38338.86380.090256.97.48.18.99.710.711.874.0-0.38338.96010.090186.97.58.29.09.810.811.974.5-0.38339.05520.090127.07.68.39.19.910.912.0
Weight-for-length/height, girls
205Table 66 Weight-for-length for girls (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD75.0-0.38339.14900.090057.17.78.49.110.011.012.275.5-0.38339.24180.089997.17.88.59.210.111.112.376.0-0.38339.33370.089927.27.88.59.310.211.212.476.5-0.38339.42520.089857.37.98.69.410.311.412.577.0-0.38339.51660.089797.48.08.79.510.411.512.677.5-0.38339.60860.089727.48.18.89.610.511.612.878.0-0.38339.70150.089657.58.28.99.710.611.712.978.5-0.38339.79570.089597.68.29.09.810.711.813.079.0-0.38339.89150.089527.78.39.19.910.811.913.179.5-0.38339.98920.089467.78.49.110.010.912.013.380.0-0.383310.08910.089407.88.59.210.111.012.113.480.5-0.383310.19160.089347.98.69.310.211.212.313.581.0-0.383310.29650.089288.08.79.410.311.312.413.781.5-0.383310.40410.089238.18.89.510.411.412.513.882.0-0.383310.51400.089188.18.89.610.511.512.613.982.5-0.383310.62630.089148.28.99.710.611.612.814.183.0-0.383310.74100.089108.39.09.810.711.812.914.283.5-0.383310.85780.089068.49.19.910.911.913.114.484.0-0.383310.97670.089038.59.210.111.012.013.214.584.5-0.383311.09740.089008.69.310.211.112.113.314.785.0-0.383311.21980.088988.79.410.311.212.313.514.985.5-0.383311.34350.088978.89.510.411.312.413.615.086.0-0.383311.46840.088958.99.710.511.512.613.815.286.5-0.383311.59400.088959.09.810.611.612.713.915.487.0-0.383311.72010.088959.19.910.711.712.814.115.587.5-0.383311.84610.088959.210.010.911.813.014.215.788.0-0.383311.97200.088969.310.111.012.013.114.415.988.5-0.383312.09760.088989.410.211.112.113.214.516.089.0-0.383312.22290.089009.510.311.212.213.414.716.289.5-0.383312.34770.089039.610.411.312.313.514.816.4
206
Weight-for-length/height, girls
Table 66 Weight-for-length for girls (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD90.0-0.383312.47230.089069.710.511.412.513.715.016.590.5-0.383312.59650.089099.810.611.512.613.815.116.791.0-0.383312.72050.089139.910.711.712.713.915.316.991.5-0.383312.84430.0891810.010.811.812.814.115.517.092.0-0.383312.96810.0892310.110.911.913.014.215.617.292.5-0.383313.09200.0892810.111.012.013.114.315.817.493.0-0.383313.21580.0893410.211.112.113.214.515.917.593.5-0.383313.33990.0894110.311.212.213.314.616.117.794.0-0.383313.46430.0894810.411.312.313.514.716.217.994.5-0.383313.58920.0895510.511.412.413.614.916.418.095.0-0.383313.71460.0896310.611.512.613.715.016.518.295.5-0.383313.84080.0897210.711.612.713.815.216.718.496.0-0.383313.96760.0898110.811.712.814.015.316.818.696.5-0.383314.09530.0899010.911.812.914.115.417.018.797.0-0.383314.22390.0900011.012.013.014.215.617.118.997.5-0.383314.35370.0901011.112.113.114.415.717.319.198.0-0.383314.48480.0902111.212.213.314.515.917.519.398.5-0.383314.61740.0903311.312.313.414.616.017.619.599.0-0.383314.75190.0904411.412.413.514.816.217.819.699.5-0.383314.88820.0905711.512.513.614.916.318.019.8100.0-0.383315.02670.0906911.612.613.715.016.518.120.0100.5-0.383315.16760.0908311.712.713.915.216.618.320.2101.0-0.383315.31080.0909611.812.814.015.316.818.520.4101.5-0.383315.45640.0911011.913.014.115.517.018.720.6102.0-0.383315.60460.0912512.013.114.315.617.118.920.8102.5-0.383315.75530.0913912.113.214.415.817.319.021.0103.0-0.383315.90870.0915512.313.314.515.917.519.221.3103.5-0.383316.06450.0917012.413.514.716.117.619.421.5104.0-0.383316.22290.0918612.513.614.816.217.819.621.7104.5-0.383316.38370.0920312.613.715.016.418.019.821.9
Weight-for-length/height, girls
207Table 66 Weight-for-length for girls (continued)
Z-scores (weight in kg)Length (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD105.0-0.383316.54700.0921912.713.815.116.518.220.022.2105.5-0.383316.71290.0923612.814.015.316.718.420.222.4106.0-0.383316.88140.0925413.014.115.416.918.520.522.6106.5-0.383317.05270.0927113.114.315.617.118.720.722.9107.0-0.383317.22690.0928913.214.415.717.218.920.923.1107.5-0.383317.40390.0930713.314.515.917.419.121.123.4108.0-0.383317.58390.0932613.514.716.017.619.321.323.6108.5-0.383317.76680.0934413.614.816.217.819.521.623.9109.0-0.383317.95260.0936313.715.016.418.019.721.824.2109.5-0.383318.14120.0938213.915.116.518.120.022.024.4110.0-0.383318.33240.0940114.015.316.718.320.222.324.7
208
Weight-for-length/height, girls
Table 67 Weight-for-height for girls
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th65.0-0.38337.24020.091135.96.16.36.66.87.27.78.08.48.69.065.5-0.38337.35230.091096.06.26.46.76.97.47.88.18.68.89.266.0-0.38337.46300.091046.16.36.56.87.07.57.98.28.78.99.366.5-0.38337.57240.090996.26.46.56.97.17.68.18.38.89.09.467.0-0.38337.68060.090946.36.56.67.07.27.78.28.59.09.29.667.5-0.38337.78740.090886.46.66.77.17.37.88.38.69.19.39.768.0-0.38337.89300.090836.46.76.87.27.47.98.48.79.29.49.868.5-0.38337.99760.090776.56.86.97.37.58.08.58.89.39.510.069.0-0.38338.10120.090716.66.97.07.47.68.18.68.99.49.710.169.5-0.38338.20390.090656.77.07.17.57.78.28.79.09.69.810.270.0-0.38338.30580.090596.87.07.27.67.88.38.89.19.79.910.370.5-0.38338.40710.090536.97.17.37.77.98.48.99.39.810.010.571.0-0.38338.50780.090476.97.27.47.88.08.59.09.49.910.110.671.5-0.38338.60780.090417.07.37.47.98.18.69.29.510.010.310.772.0-0.38338.70700.090357.17.47.57.98.28.79.39.610.110.410.872.5-0.38338.80530.090287.27.57.68.08.38.89.49.710.310.511.073.0-0.38338.90250.090227.37.67.78.18.48.99.59.810.410.611.173.5-0.38338.99830.090167.47.67.88.28.59.09.69.910.510.711.274.0-0.38339.09280.090097.47.77.98.38.69.19.710.010.610.811.374.5-0.38339.18620.090037.57.88.08.48.79.29.810.110.710.911.475.0-0.38339.27860.089967.67.98.08.58.79.39.910.210.811.111.575.5-0.38339.37030.089897.78.08.18.68.89.410.010.310.911.211.776.0-0.38339.46170.089837.78.08.28.68.99.510.110.411.011.311.876.5-0.38339.55330.089767.88.18.38.79.09.610.210.511.111.411.977.0-0.38339.64560.089697.98.28.48.89.19.610.310.611.211.512.077.5-0.38339.73900.089638.08.38.48.99.29.710.410.711.311.612.178.0-0.38339.83380.089568.08.48.59.09.39.810.510.811.411.712.278.5-0.38339.93030.089508.18.48.69.19.49.910.610.911.611.812.379.0-0.383310.02890.089438.28.58.79.29.410.010.711.011.711.912.579.5-0.383310.12980.089378.38.68.89.29.510.110.811.111.812.112.6
Weight-for-length/height, girls
209Table 67 Weight-for-height for girls (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th80.0-0.383310.23320.089328.48.78.99.39.610.210.911.211.912.212.780.5-0.383310.33930.089268.58.89.09.49.710.311.011.412.012.312.881.0-0.383310.44770.089218.68.99.19.59.810.411.111.512.212.413.081.5-0.383310.55860.089168.69.09.29.69.910.611.211.612.312.613.182.0-0.383310.67190.089128.79.19.39.710.110.711.311.712.412.713.282.5-0.383310.78740.089088.89.29.49.910.210.811.511.912.512.813.483.0-0.383310.90510.089058.99.39.510.010.310.911.612.012.713.013.583.5-0.383311.02480.089029.09.49.610.110.411.011.712.112.813.113.784.0-0.383311.14620.088999.19.59.710.210.511.111.812.213.013.313.884.5-0.383311.26910.088979.29.69.810.310.611.312.012.413.113.414.085.0-0.383311.39340.088969.39.79.910.410.711.412.112.513.213.514.185.5-0.383311.51860.088959.49.810.010.510.911.512.212.713.413.714.386.0-0.383311.64440.088959.59.910.110.611.011.612.412.813.513.814.486.5-0.383311.77050.088959.610.010.210.811.111.812.512.913.714.014.687.0-0.383311.89650.088969.710.110.310.911.211.912.613.113.814.114.887.5-0.383312.02230.088979.910.210.411.011.312.012.813.214.014.314.988.0-0.383312.14780.0889910.010.310.511.111.412.112.913.314.114.415.188.5-0.383312.27290.0890110.110.410.611.211.612.313.013.514.314.615.289.0-0.383312.39760.0890410.210.510.811.311.712.413.213.614.414.715.489.5-0.383312.52200.0890710.310.610.911.411.812.513.313.814.614.915.590.0-0.383312.64610.0891110.410.811.011.511.912.613.413.914.715.015.790.5-0.383312.77000.0891510.510.911.111.712.012.813.614.014.915.215.991.0-0.383312.89390.0892010.611.011.211.812.112.913.714.215.015.316.091.5-0.383313.01770.0892510.711.111.311.912.313.013.814.315.115.516.292.0-0.383313.14150.0893110.811.211.412.012.413.114.014.415.315.616.392.5-0.383313.26540.0893710.911.311.512.112.513.314.114.615.415.816.593.0-0.383313.38960.0894411.011.411.612.212.613.414.214.715.615.916.693.5-0.383313.51420.0895111.111.511.712.312.713.514.414.915.716.116.894.0-0.383313.63930.0895911.211.611.812.412.813.614.515.015.916.216.994.5-0.383313.76500.0896711.311.711.912.613.013.814.615.116.016.417.1
210
Weight-for-length/height, girls
Table 67 Weight-for-height for girls (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th95.0-0.383313.89140.0897511.411.812.012.713.113.914.815.316.216.517.395.5-0.383314.01860.0898411.511.912.112.813.214.014.915.416.316.717.496.0-0.383314.14660.0899411.612.012.312.913.314.115.015.616.516.917.696.5-0.383314.27570.0900411.712.112.413.013.414.315.215.716.617.017.897.0-0.383314.40590.0901511.812.212.513.113.614.415.315.816.817.217.997.5-0.383314.53760.0902611.912.312.613.313.714.515.516.016.917.318.198.0-0.383314.67100.0903712.012.412.713.413.814.715.616.117.117.518.398.5-0.383314.80620.0904912.112.612.813.513.914.815.716.317.317.718.499.0-0.383314.94340.0906212.212.712.913.614.114.915.916.417.417.818.699.5-0.383315.08280.0907512.312.813.013.814.215.116.016.617.618.018.8100.0-0.383315.22460.0908812.412.913.213.914.315.216.216.817.818.219.0100.5-0.383315.36870.0910212.513.013.314.014.515.416.416.917.918.319.2101.0-0.383315.51540.0911612.713.113.414.114.615.516.517.118.118.519.4101.5-0.383315.66460.0913112.813.313.514.314.715.716.717.218.318.719.5102.0-0.383315.81640.0914612.913.413.714.414.915.816.817.418.518.919.7102.5-0.383315.97070.0916113.013.513.814.515.016.017.017.618.719.119.9103.0-0.383316.12760.0917713.113.613.914.715.216.117.217.818.819.320.2103.5-0.383316.28700.0919313.313.814.114.815.316.317.317.919.019.520.4104.0-0.383316.44880.0920913.413.914.215.015.516.417.518.119.219.720.6104.5-0.383316.61310.0922613.514.014.315.115.616.617.718.319.419.920.8105.0-0.383316.78000.0924313.614.214.515.315.816.817.918.519.620.121.0105.5-0.383316.94960.0926113.814.314.615.415.916.918.118.719.820.321.2106.0-0.383317.12200.0927813.914.514.815.616.117.118.218.920.020.521.4106.5-0.383317.29730.0929614.114.614.915.716.317.318.419.120.220.721.7107.0-0.383317.47550.0931514.214.715.115.916.417.518.619.320.521.021.9107.5-0.383317.65670.0933314.314.915.216.116.617.718.819.520.721.222.1108.0-0.383317.84070.0935214.515.015.416.216.817.819.019.720.921.422.4108.5-0.383318.02770.0937114.615.215.516.416.918.019.219.921.121.622.6109.0-0.383318.21740.0939014.815.415.716.617.118.219.420.121.421.922.9109.5-0.383318.40960.0940914.915.515.816.717.318.419.620.321.622.123.1
Weight-for-length/height, girls
211Table 67 Weight-for-height for girls (continued)
Percentiles (weight in kg)Height (cm)LMS1st3rd5th15th25th50th75th85th95th97th99th110.0-0.383318.60430.0942815.115.716.016.917.518.619.820.621.822.423.4110.5-0.383318.80150.0944815.215.816.217.117.718.820.120.822.122.623.7111.0-0.383319.00090.0946715.416.016.317.317.819.020.321.022.322.823.9111.5-0.383319.20240.0948715.516.216.517.418.019.220.521.222.623.124.2112.0-0.383319.40600.0950715.716.316.717.618.219.420.721.522.823.424.5112.5-0.383319.61160.0952715.916.516.817.818.419.620.921.723.123.624.7113.0-0.383319.81900.0954616.016.717.018.018.619.821.221.923.323.925.0113.5-0.383320.02800.0956616.216.817.218.218.820.021.422.223.624.125.3114.0-0.383320.23850.0958616.317.017.418.419.020.221.622.423.824.425.6114.5-0.383320.45020.0960616.517.217.518.519.220.521.822.624.124.725.8115.0-0.383320.66290.0962616.717.317.718.719.420.722.122.924.324.926.1115.5-0.383320.87660.0964616.817.517.918.919.620.922.323.124.625.226.4116.0-0.383321.09090.0966617.017.718.119.119.821.122.523.424.925.526.7116.5-0.383321.30590.0968617.217.918.319.320.021.322.823.625.125.727.0117.0-0.383321.52130.0970717.318.018.419.520.221.523.023.825.426.027.3117.5-0.383321.73700.0972717.518.218.619.720.421.723.224.125.626.327.5118.0-0.383321.95290.0974717.718.418.819.920.622.023.524.325.926.527.8118.5-0.383322.16900.0976717.818.619.020.120.822.223.724.626.226.828.1119.0-0.383322.38510.0978818.018.719.120.321.022.423.924.826.427.128.4119.5-0.383322.60120.0980818.218.919.320.521.222.624.225.126.727.428.7120.0-0.383322.81730.0982818.319.119.520.621.422.824.425.327.027.629.0
212
Weight-for-length/height, girls
Table 67 Weight-for-height for girls (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD65.0-0.38337.24020.091135.66.16.67.27.98.79.765.5-0.38337.35230.091095.76.26.77.48.18.99.866.0-0.38337.46300.091045.86.36.87.58.29.010.066.5-0.38337.57240.090995.86.46.97.68.39.110.167.0-0.38337.68060.090945.96.47.07.78.49.310.267.5-0.38337.78740.090886.06.57.17.88.59.410.468.0-0.38337.89300.090836.16.67.27.98.79.510.568.5-0.38337.99760.090776.26.77.38.08.89.710.769.0-0.38338.10120.090716.36.87.48.18.99.810.869.5-0.38338.20390.090656.36.97.58.29.09.910.970.0-0.38338.30580.090596.47.07.68.39.110.011.170.5-0.38338.40710.090536.57.17.78.49.210.111.271.0-0.38338.50780.090476.67.17.88.59.310.311.371.5-0.38338.60780.090416.77.27.98.69.410.411.572.0-0.38338.70700.090356.77.38.08.79.510.511.672.5-0.38338.80530.090286.87.48.18.89.710.611.773.0-0.38338.90250.090226.97.58.18.99.810.711.873.5-0.38338.99830.090167.07.68.29.09.910.812.074.0-0.38339.09280.090097.07.68.39.110.011.012.174.5-0.38339.18620.090037.17.78.49.210.111.112.275.0-0.38339.27860.089967.27.88.59.310.211.212.375.5-0.38339.37030.089897.27.98.69.410.311.312.576.0-0.38339.46170.089837.38.08.79.510.411.412.676.5-0.38339.55330.089767.48.08.79.610.511.512.777.0-0.38339.64560.089697.58.18.89.610.611.612.877.5-0.38339.73900.089637.58.28.99.710.711.712.978.0-0.38339.83380.089567.68.39.09.810.811.813.178.5-0.38339.93030.089507.78.49.19.910.912.013.279.0-0.383310.02890.089437.88.49.210.011.012.113.379.5-0.383310.12980.089377.88.59.310.111.112.213.4
Weight-for-length/height, girls
213Table 67 Weight-for-height for girls (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD80.0-0.383310.23320.089327.98.69.410.211.212.313.680.5-0.383310.33930.089268.08.79.510.311.312.413.781.0-0.383310.44770.089218.18.89.610.411.412.613.981.5-0.383310.55860.089168.28.99.710.611.612.714.082.0-0.383310.67190.089128.39.09.810.711.712.814.182.5-0.383310.78740.089088.49.19.910.811.813.014.383.0-0.383310.90510.089058.59.210.010.911.913.114.583.5-0.383311.02480.089028.59.310.111.012.113.314.684.0-0.383311.14620.088998.69.410.211.112.213.414.884.5-0.383311.26910.088978.79.510.311.312.313.514.985.0-0.383311.39340.088968.89.610.411.412.513.715.185.5-0.383311.51860.088958.99.710.611.512.613.815.386.0-0.383311.64440.088959.09.810.711.612.714.015.486.5-0.383311.77050.088959.19.910.811.812.914.215.687.0-0.383311.89650.088969.210.010.911.913.014.315.887.5-0.383312.02230.088979.310.111.012.013.214.515.988.0-0.383312.14780.088999.410.211.112.113.314.616.188.5-0.383312.27290.089019.510.311.212.313.414.816.389.0-0.383312.39760.089049.610.411.412.413.614.916.489.5-0.383312.52200.089079.710.511.512.513.715.116.690.0-0.383312.64610.089119.810.611.612.613.815.216.890.5-0.383312.77000.089159.910.711.712.814.015.416.991.0-0.383312.89390.0892010.010.911.812.914.115.517.191.5-0.383313.01770.0892510.111.011.913.014.315.717.392.0-0.383313.14150.0893110.211.112.013.114.415.817.492.5-0.383313.26540.0893710.311.212.113.314.516.017.693.0-0.383313.38960.0894410.411.312.313.414.716.117.893.5-0.383313.51420.0895110.511.412.413.514.816.317.994.0-0.383313.63930.0895910.611.512.513.614.916.418.194.5-0.383313.76500.0896710.711.612.613.815.116.618.3
214
Weight-for-length/height, girls
Table 67 Weight-for-height for girls (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD95.0-0.383313.89140.0897510.811.712.713.915.216.718.595.5-0.383314.01860.0898410.811.812.814.015.416.918.696.0-0.383314.14660.0899410.911.912.914.115.517.018.896.5-0.383314.27570.0900411.012.013.114.315.617.219.097.0-0.383314.40590.0901511.112.113.214.415.817.419.297.5-0.383314.53760.0902611.212.213.314.515.917.519.398.0-0.383314.67100.0903711.312.313.414.716.117.719.598.5-0.383314.80620.0904911.412.413.514.816.217.919.799.0-0.383314.94340.0906211.512.513.714.916.418.019.999.5-0.383315.08280.0907511.612.713.815.116.518.220.1100.0-0.383315.22460.0908811.712.813.915.216.718.420.3100.5-0.383315.36870.0910211.912.914.115.416.918.620.5101.0-0.383315.51540.0911612.013.014.215.517.018.720.7101.5-0.383315.66460.0913112.113.114.315.717.218.920.9102.0-0.383315.81640.0914612.213.314.515.817.419.121.1102.5-0.383315.97070.0916112.313.414.616.017.519.321.4103.0-0.383316.12760.0917712.413.514.716.117.719.521.6103.5-0.383316.28700.0919312.513.614.916.317.919.721.8104.0-0.383316.44880.0920912.613.815.016.418.119.922.0104.5-0.383316.61310.0922612.813.915.216.618.220.122.3105.0-0.383316.78000.0924312.914.015.316.818.420.322.5105.5-0.383316.94960.0926113.014.215.516.918.620.522.7106.0-0.383317.12200.0927813.114.315.617.118.820.823.0106.5-0.383317.29730.0929613.314.515.817.319.021.023.2107.0-0.383317.47550.0931513.414.615.917.519.221.223.5107.5-0.383317.65670.0933313.514.716.117.719.421.423.7108.0-0.383317.84070.0935213.714.916.317.819.621.724.0108.5-0.383318.02770.0937113.815.016.418.019.821.924.3109.0-0.383318.21740.0939013.915.216.618.220.022.124.5109.5-0.383318.40960.0940914.115.416.818.420.322.424.8
Weight-for-length/height, girls
215Table 67 Weight-for-height for girls (continued)
Z-scores (weight in kg)Height (cm)LMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD110.0-0.383318.60430.0942814.215.517.018.620.522.625.1110.5-0.383318.80150.0944814.415.717.118.820.722.925.4111.0-0.383319.00090.0946714.515.817.319.020.923.125.7111.5-0.383319.20240.0948714.716.017.519.221.223.426.0112.0-0.383319.40600.0950714.816.217.719.421.423.626.2112.5-0.383319.61160.0952715.016.317.919.621.623.926.5113.0-0.383319.81900.0954615.116.518.019.821.824.226.8113.5-0.383320.02800.0956615.316.718.220.022.124.427.1114.0-0.383320.23850.0958615.416.818.420.222.324.727.4114.5-0.383320.45020.0960615.617.018.620.522.625.027.8115.0-0.383320.66290.0962615.717.218.820.722.825.228.1115.5-0.383320.87660.0964615.917.319.020.923.025.528.4116.0-0.383321.09090.0966616.017.519.221.123.325.828.7116.5-0.383321.30590.0968616.217.719.421.323.526.129.0117.0-0.383321.52130.0970716.317.819.621.523.826.329.3117.5-0.383321.73700.0972716.518.019.821.724.026.629.6118.0-0.383321.95290.0974716.618.219.922.024.226.929.9118.5-0.383322.16900.0976716.818.420.122.224.527.230.3119.0-0.383322.38510.0978816.918.520.322.424.727.430.6119.5-0.383322.60120.0980817.118.720.522.625.027.730.9120.0-0.383322.81730.0982817.318.920.722.825.228.031.2
216
Weight-for-length/height, girls
Comparison with NCHS
25322010-1(kg)15-2-3Weight10
5
WHO
NCHS
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 90 Comparison of WHO with NCHS weight-for-length z-scores for girls
Weight-for-length/height, girls
217218 Weight-for-length/height, girls
3210-1-2-3
NCHSWHO
120
115girls110scores for105height z-100-for-90 95Height (cm)with NCHS weight85WHO75 80Comparison of70Figure 9165
30252015105Weight (kg)
Comparison with CDC 2000
25
20
(kg)15Weight10
5
3
2
1
0
-1
-2
-3
WHO
CDC 2000
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 92 Comparison of WHO with CDC 2000 weight-for-length z-scores for girls
Weight-for-length/height, girls
219
40
30Weight (kg)20
10
3
2
1
0
-1
-2
-3
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CDC 2000
65 70 75 80 85 90 95 100 105 110 115 120
Height (cm)
Figure 93 Comparison of WHO with CDC 2000 weight-for-height z-scores for girls
220
Weight-for-length/height, girlsWeight-for-length/height, boys & girls221
5.4 Comparisons between boys and girls
This section presents the weight-for-length and weight-for-height z-score comparisons between boys and girls for WHO standards (Figures 94 and 95), and for NCHS (Figures 96 and 97) and CDC 2000 (Figures 98 and 99) references.
5.4.1 WHO
25322010-1(kg)15-2-3Weight10
5
Boys
Girls
45 50 55 60 65 70 75 80 85 90 95 100 105 110
Length (cm)
Figure 94 Comparison of boys' and girls' WHO weight-for-length z-scores
222
Weight-for-length/height, boys & girlsWeight-for-length/height, boys & girls223
3210-1-2-3
GirlsBoys
120
105 110 115for-height z-scores100weight-95(cm)WHO90Heightand girls'85boys'75 80Comparison of70Figure 9565
30252015105Weight (kg)224 Weight-for-length/height, boys & girls
3210-1-2-384
79z-scores74-for-lengthBoysGirlsweight64 69Length (cm)and girls' NCHS59Comparison of boys'5496Figure491412108642Weight (kg)
NCHS
5.4.2Weight-for-length/height, boys & girls225
3210-1-2-3
GirlsBoys
120
115scoresz-110-for-height100 105Height (cm)and girls' NCHS weight95Comparison of boys'9097Figure85
3025201510(kg)Weight
5.4.3 CDC 2000
25
32021(Kg)150-1Weight-2-310
5
Boys
Girls
45 50 55 60 65 70 75 80 85 90 95 100 105
Length (cm)
Figure 98 Comparison of boys' and girls' CDC 2000 weight-for-length z-scores
226
Weight-for-length/height, boys & girlsWeight-for-length/height, boys & girls227
3210-1-2-3
GirlsBoys
120
115scoresz-110height105weight-for-95 100Height (cm)girls' CDC 200090boys' and85Comparison of809975Figure
5040302010Weight (kg)
CONSTRUCTION OF THE BODY MASS INDEX-FOR-AGE STANDARDS 6.1 Indicator-specific methodology
Body mass index (BMI) is the ratio weight (in kg)/recumbent length or standing height (in m2). To address the difference between length and height, the approach used for constructing the BMI-for-age standards was different from that described for length/height-for-age. Because BMI is a ratio with squared length or height in the denominator, adding 0.7 cm to the height values and back-transforming them after fitting was not feasible. The solution adopted was to construct the standards for the younger and the older children separately based on two sets of data with an overlapping range of ages below and above 24 months. To construct the BMI-for-age standard based on length (birth to 2 years), the longitudinal sample's length data and the cross-sectional sample's height data (18 to 30 months) were combined after adding 0.7 cm to the height values. Analogously, to construct the standard from 2 to 5 years, the cross-sectional sample's height plus longitudinal sample's length data (18 to 24 months) were combined after subtracting 0.7 cm from the length values. Thus, a common set of data from 18 to 30 months was used to generate the BMI standards for the younger and the older children. The resulting disjunction between the two standards thus in essence reflects the 0.7 cm difference between length and height. This does not mean, however, that a child at a specific age will have the same length- and height-based BMI-for-age z-score as this is mathematically impossible given the nature of the BMI ratio. The WHO length- and height-based BMI-for-age standards do not overlap, i.e. the length-based interval ends at 730 days and the height-based interval starts at 731 days.
The BMI curve's steep rise from birth to 6 or 7 months required a power transformation of age with power very close to zero to stretch the x-axis before fitting the model. This created a large gap between the observations at birth and at 14 days on the transformed age scale. This fact, combined with the use of flexible cubic splines to model the median curve, resulted in an artificial pattern in that age interval when back-transformed to the original age scale. To avoid this problem and ensure that the curves remained closely patterned on the empirical values, an alternative choice was to create individual BMI values at age 7 days and then linearly interpolate between birth and 7 days, and between 7 and 14 days. Although weight was measured at 7 days, there was no corresponding length measurement to calculate BMI at that age. Therefore to create BMI values for age 7 days, individual lengths for that age were estimated by linear interpolation, i.e. the mid point between length at birth and at 14 days was used.
Q-test, worm plots and comparisons of observed and expected proportions of children with BMI values below fitted centiles presented hereafter included the interpolated values for age group 7 days. It was reassuring to see that the empirical centiles remained very close to the fitted values at the observed ages, birth and 14 days, when the model included the interpolated values.
- 229 -
230 BMI-for-age, boys
6.2 BMI-for-age for boys
Steps similar to those used to fit the weight-for-age standard were used to select the best model for the BMI-for-age standards for boys. The diagnostic tools to evaluate and compare different models also were the same.
6.2.1 Sample size
There were 13 362 records with both weight and length/height for boys. The longitudinal and cross-sectional sample sizes by visit and age are presented in the Tables 68 and 69.
Table 68 Longitudinal sample sizes for BMI-for-age for boys
VisitBirth123456Age02 wk4 wk6 wk2 mo3 mo4 moN890424423422423419411Visit78910111213Age5 mo6 mo7 mo8 mo9 mo10 mo11 moN413417415415410407418Visit14151617181920Age12 mo14 mo16 mo18 mo20 mo22 mo24 moN416415418416422417420
Table 69 Cross-sectional sample sizes for BMI-for-age for boys
Age (mo)<1818 2021 2324 2627 2930 3233 35N3171180231254223254Age (mo)36 3839 4142 4445 4748 5051 5354 56N267249255238237221228Age (mo)57 5960 6263 6566 6869 71>71N2412282152182144
6.2.2 Model selection and results
Length-based BMI-for-age for boys
The model BCPE(x=age, df()=9, df()=4, df()=4, =2) was used initially to assess variations in the age-transformation power and to determine the best fit as reflected by global deviance. Table 70 shows the global deviance for a grid of values between 0 and 0.5. The smallest global deviance was associated with the age-transformation power =0.01. However, =0.05 was selected because the problem caused in fitting cubic splines in the transformed age scale and back-transforming afterwards was worse with =0.01 than with =0.05, yet the global deviance for the latter was not much larger.
BMI-for-age, boys231
Table 70 Global deviance (GD) for models within the class BCPE(x=age, df()=9, df()=4, df()=4, =2) for length-based BMI-for-age for boys
0.010.050.100.150.200.25GDa702.7704.2706.4709.0711.5713.90.300.350.400.450.50GDa716.0718.4722.7731.0745.4
In excess of 35 000.
The search for the best df() and df() was carried out using =0.05 as the age-transformation power and comparing the goodness of fit of various models with fixed parameters =1 and =2. All possible combinations of df() 7 to 15 and df() 2 to 10 were considered. Partial results are presented in Table
The best combination of AIC and GAIC(3) corresponded to df()=10 and df()=4. Worm plots and Q-test for this model also were examined.
Table 71 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for length-based BMI-for-age for boys
df()df()GDaAICaGAIC(3)aTotal df3899.3921.3932.31184892.9916.9928.9125890.7916.7929.7136889.6917.6931.6143892.9916.9928.91294886.4912.4925.4135884.2912.2926.2146883.1913.1928.1153889.4915.4928.413104883.0911.0925.0145880.8910.8925.8156879.7911.7927.7163887.3915.3929.314114880.9910.9925.9155878.6910.6926.6166877.5911.5928.5173885.7915.7930.715124879.3911.3927.3165877.0911.0928.0176875.9911.9929.918
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 35 000.
232 BMI-for-age, boys
Model 1: BCPE(x=age0.05, df()=10, df()=4, =1, =2)
Worm plots (Figure 100) and Q-test results (Table 72) indicated misfit across various age intervals due to residual skewness and/or kurtosis. The worms were U-shaped for many of the age groups, indicating residual skewness. In the Q-test results most of the groups had absolute values of z3 larger than 2, suggesting residual skewness, and three age groups presented values of z4 larger than 2, indicating residual kurtosis. The overall tests for both skewness and kurtosis combining all age groups were significant.
This model was therefore considered inadequate. The next step involved fitting the parameter , to adjust for skewness, using the BCPE distribution and fixing only the parameter =2. Table 73 shows GAIC(3) values for various choices of df(), maintaining df() and df() as selected for Model 1.
-0.4 0.0 0.4
Deviation0 40.40.0.-
-0.4 0.0 0.4
-3-1 0 1 2 3-3-1 0 12 322 mo24 mo28 mo-3-1 0 1 2 312 mo14 mo16 mo18 mo20 mo
7 mo8 mo9 mo10 mo11 mo
2 mo3 mo4 mo5 mo6 mo
Birth7 d14 d28 d42 d
-3 -1 0 1 2 3 -3 -1 0 1 2 3
-0.4 00. 40.
-0.4 00. 40.
Unit normal quantile
Figure 100 Worm plots of z-scores for Model 1 for length-based BMI-for-age for boys
BMI-for-age, boys233
Table 72 Q-test for z-scores from Model 1 [BCPE(x=age0.05, df()=10, df()=4, =1, =2)] for length-based BMI-for-age for boys
Age (days)GroupNz1z2z3z40Birth8900.00-0.014.450.761 to 117 d3870.451.361.90-1.5012 to 1614 d418-0.980.200.59-0.5717 to 3428 d4260.14-0.630.56-0.4735 to 4942 d4210.18-1.050.850.5050 to 692 mo4230.140.631.690.6370 to 993 mo4190.490.223.251.91100 to 1294 mo408-0.82-1.502.150.47130 to 1595 mo4100.37-0.532.961.32160 to 1896 mo411-0.39-0.611.26-0.67190 to 2197 mo4060.430.792.530.83220 to 2498 mo4200.900.621.970.06250 to 2799 mo392-0.72-0.341.890.41280 to 30910 mo4000.680.582.01-1.25310 to 34911 mo461-0.39-0.012.120.37350 to 37912 mo4110.14-0.472.28-0.46380 to 43914 mo4170.03-0.482.731.05440 to 49916 mo4160.080.734.703.00500 to 55918 mo4420.461.113.491.27560 to 61920 mo518-0.200.475.052.10620 to 67922 mo545-1.170.813.441.71680 to 74924 mo587-0.61-1.055.042.32750 to 91328 mo4291.14-0.721.93-0.71Overall Q stats10 4577.8912.90188.8237.77degrees of freedom13.020.523.023.0p-value0.85100.8978< 0.010.0269
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 73 Goodness-of-fit summary for models BCPE(x=age0.05, df()=10, df()=4, df()=?, =2) for length-based BMI-for-age for boys
df()GDaGAIC(3)aTotal df1720.7765.7152720.4768.4163702.8753.8174700.9754.9185699.4756.4196697.5757.520
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 35 000.
The smallest GAIC(3) was associated with df()=3 and this model's goodness-of-fit was investigated further.
234 BMI-for-age, boys
Model 2: BCPE(x=age0.05, df()=10, df()=4, df()=3, =2)
Figure 101 shows the fitting of the parameters , and for Model 2 with their respective sample estimates. The fitted curve underestimated the high peak in the empirical curve (the St Dev Box-Cox transformed BMI) at 7 days. The smoothing function of the Box-Cox transformation power ( curve) did not follow the unstable pattern of the empirical curve, and thus partially controlled the skewness associated with parameter at the end of the 0 to 24 month age interval.
of Body Mass Index (kg/m)15 16 17Box-Cox Transformed BMI085 095 1050.0.0.Median14St Dev0750.024681012141618202224024681012141618202224Age (months)Age (months)Transform Power-0.5 0. 0.05Box-Cox-1.0-1.5
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 101 Fitting of the , , and curves of Model 2 for length-based BMI-for-age from 0 to 24 months for boys (dotted line) and their respective sample estimates (points with solid line)
Figure 102 shows the distribution of the centile residuals, i.e. empirical minus fitted centiles, for the longitudinal sample (0 to 24 months). There was no evidence of systematic bias. The worm plots for this model (Figure 103) showed that adjustment for skewness corrected the previous model's misfit (Figure 100), i.e. U-shaped worms flattened fairly well. Few age groups still retained slightly S-shaped worms but all constrained within the 95% confidence intervals.
BMI-for-age, boys235
3rd Centile5th Centile10th Centile0.40.40.4Index(kg/m)-0.4 0.0246812162024-0.4 0.0246812162024-0.4 0.0246812162024000Body Mass25th Centile50th Centile75th Centile0.40.40.4for0.00.00.0Centile-0.490th Centile-0.495th Centile-0.497th CentileFitted024620240246202402462024812168121681216Empirical-0. 0.040. 0.040. 0.04-0.4-0.4-0.4024681216202402468121620240246812162024
Age (months)
Figure 102 Centile residuals from fitting Model 2 for length-based
BMI-for-age from 0 to 24 months for boys
Q-test results of the z-scores from Model 2 are shown in Table 74. All absolute values for the statistics z1, z2, z3 and z4 were smaller than 2, apart from one z4 value at age 7 days indicating residual kurtosis. P-values for overall tests were all non-significant, indicating adequate fit for the BMI-for-age growth curves for boys. Table 75 presents observed percentages below the fitted centiles, which give no indication of systematic bias.
Since residual kurtosis was indicated for only one out of 23 age groups and the overall test was not significant, modelling the parameter and thus increasing the model's complexity was considered unnecessary.
236 BMI-for-age, boys
-3-1 0 1 2 3-3-1 0 1 2 340.22 mo24 mo28 mo00.-0.4-3-1 0 1 2 312 mo14 mo16 mo18 mo20 mo
Deviation0 40.40.0.7 mo8 mo9 mo10 mo11 mo-2 mo3 mo4 mo5 mo6 mo
40.Birth7 d14 d28 d42 d00.-0.4-3-1 0 1 2 3-3-1 0 1 2 3
-40. 00. 40.
-0.4 00. 40.
Unit normal quantile
Figure 103 Worm plots of z-scores for Model 2 for length-based BMI-for-age for boys
Model 2, BCPE(x= age0.05, df()=10, df()=4 ,df()=3, =2), was selected to fit the BMI-for-age growth curves for boys from birth to 24 months. This model adjusts only for skewness and belongs to the same class of models used for the LMS method. A further iteration was done, fixing df()=3 and re-searching for the best combination of df() and df(), but Model 2 still presented the best performance in both AIC and GAIC(3). Then, using the selected degrees of freedom for , and curves, the best was re-searched. Results confirmed that values of close to zero resulted in the lowest global deviance. However, for reasons stated previously (see discussion in connection with Table 70) was kept at value 0.05.
The final centile curves are shown in Figures 104 and 105 plotted with the empirical centiles.
BMI-for-age, boys237
Table 74 Q-test for z-scores from Model 2 [BCPE(x=age0.05, df()=10, df()=4, df()=3, =2)] for length-based BMI-for-age for boys
Age (days)GroupNz1z2z3z40Birth8900.00-0.020.11-0.061 to 117 d3870.561.220.99-2.0112 to 1614 d418-0.980.30-0.70-0.6617 to 3428 d4260.07-0.59-0.95-0.4035 to 4942 d4210.17-0.99-1.010.9650 to 692 mo4230.130.63-0.440.9570 to 993 mo4190.44-0.010.911.21100 to 1294 mo408-0.87-1.420.08-0.15130 to 1595 mo4100.31-0.690.590.50160 to 1896 mo411-0.39-0.40-0.92-0.63190 to 2197 mo4060.400.73-0.090.36220 to 2498 mo4200.910.59-0.57-0.30250 to 2799 mo392-0.68-0.11-0.660.00280 to 30910 mo4000.660.56-0.23-1.57310 to 34911 mo461-0.390.21-0.73-0.27350 to 37912 mo4110.19-0.43-0.07-1.63380 to 43914 mo4170.11-0.42-0.190.25440 to 49916 mo4160.110.411.191.84500 to 55918 mo4420.480.980.30-0.11560 to 61920 mo518-0.130.161.81-0.12620 to 67922 mo545-1.251.15-0.390.12680 to 74924 mo587-0.57-1.171.460.10750 to 91328 mo4291.07-0.59-1.090.02Overall Q stats10 4577.9011.7615.3117.50degrees of freedom13.020.520.023.0p-value0.84990.93580.75840.7841
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Table 75 Observed proportions of children with measurements below the fitted centiles from Model 2, length-based BMI-for-age for boys
ExpectedBirth7 d14 d28 d42 d2 mo3 mo4 mo5 mo6 mo7 mo8 mo11.00.31.00.71.40.70.50.71.01.21.21.432.42.63.63.11.92.82.92.72.93.63.73.654.84.76.24.52.95.25.34.74.45.45.95.51010.310.910.510.18.811.39.510.39.310.510.19.52525.826.128.225.125.724.123.924.523.726.822.924.05050.450.450.249.147.551.848.452.249.350.948.045.07576.071.375.474.476.074.276.476.574.975.774.673.89089.886.690.490.690.388.989.592.292.290.588.788.39594.894.396.796.596.094.194.596.695.195.194.193.39797.196.698.397.997.696.596.497.596.897.396.396.99998.998.799.099.399.398.698.399.398.899.598.898.8
Expected9 mo10 mo11 mo12 mo14 mo16 mo18 mo20 mo22 mo24 mo28 moOverall11.01.00.90.50.51.40.90.61.10.30.90.934.32.83.71.92.42.43.82.35.01.91.62.956.15.05.23.94.83.46.14.17.33.93.34.91010.711.511.911.210.310.111.311.211.49.98.610.42525.025.526.726.525.225.024.225.928.626.722.825.45049.547.547.949.448.751.448.050.451.050.148.549.57578.173.875.574.273.675.774.075.574.777.271.875.09090.387.390.589.592.190.989.690.291.091.189.590.09594.994.595.995.495.794.593.794.495.695.794.495.09796.797.097.698.397.195.995.596.597.196.897.297.09999.599.099.199.398.398.198.498.598.998.899.598.9
Note: Group labels correspond to the age intervals in Table 74.
238
BMI-for-age, boys
20
1897thIndex (kg/m)90th1650thMassBody1410th3rd12FittedEmpirical
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 104 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: length-based BMI-for-age for boys from birth to 24 months
BMI-for-age, boys
239
20
1895th(kg/m)75thIndex1650thMass25thBody145th12FittedEmpirical
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (months)
Figure 105 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: length-based BMI-for-age for boys from birth to 24 months
240
BMI-for-age, boysBMI-for-age, boys241
Height-based BMI-for-age for boys
To construct the BMI-for-age growth standard using height, the need for an age-transformation power
before fitting the model was evaluated. Results indicated that no age transformation was necessary. The class of models selected for constructing the length-based standard was the first option to be considered for constructing the height-based BMI-for-age standard.
Using the BCPE distribution, the and parameter curves were modelled and parameters and were fixed at values 1 and 2, respectively. The search for the best df() and df() was carried out by comparing the goodness of fit of various models. All possible combinations of df() 3 to 10 and df() 2 to 6 were considered. Partial results are presented in Table 76. The best combination of AIC and GAIC(3) corresponded to df()=4 and df()=3. This model was used as a first step to search for the best degrees of freedom for the parameter . Table 77 shows a summary of the goodness-of-fit results from various models.
Table 76 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for height-based BMI-for-age for boys
df()df()GDaAICaGAIC(3)aTotal df2184.3194.5199.5533177.6189.6195.664176.5190.5197.575175.8191.8199.882178.0190.1196.2643171.8185.8192.874170.7186.7194.785169.9187.9196.992176.3190.5197.5753170.2186.2194.284169.1187.1196.195168.3188.3198.3102174.7190.8198.9863168.5186.5195.594167.4187.4197.4105166.7188.7199.7112173.1191.2200.3973166.8186.9196.9104165.7187.7198.7115165.0189.0201.012
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 19 000.
242 BMI-for-age, boys
Table 77 Goodness-of-fit summary for models BCPE(x=age, df()=4, df()=3, df()=?, =2) for height-based BMI-for-age for boys
df()GDaGAIC(3)aTotal df130.854.88230.157.39325.655.610424.757.711524.460.412624.063.013
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 19 000.
Although the smallest GAIC(3) corresponded to df()=1, the fitting of a constant led to the underestimation of this parameter, resulting in an overestimation of skewness in the age interval of interest, i.e. 24 to 60 months. Therefore, the option df()=3, which was associated with the second smallest GAIC(3) value (Table 77), was selected. This model's goodness-of-fit was investigated further.
Model 1: BCPE(x=age, df()=4, df()=3, df()=3, =2)
Figure 106 shows the fitting of the parameters , and for Model 1 with their respective sample estimates.
of Body Mass Index (kg/m)15. 15. 16.482Box-Cox Transformed BMI080 0900.0.Median15.0St Dev0700.192531374349556167192531374349556167Age (months)Age (months)Power0.0Transform-0.5Box-Cox-1.0-1.5192531374349556167
Age (months)
Figure 106 Fitting of the , , and curves of Model 1 for height-based BMI-for-age from 18 to 71 months for boys (dotted line) and their respective sample estimates (points with solid line)
BMI-for-age, boys243
Figure 107 shows the distribution of the centile residuals, i.e. the difference between empirical and fitted centiles, using only the cross-sectional sample from 18 to 71 months. There was a tendency to slightly underestimate values of the central centiles (25th, 50th and 75th) at the beginning of the age interval. But this indication of bias was not confirmed by the proportions of children with observed BMI values below fitted centiles (Table 78). The results in Table 78 show no evidence of bias in any of the centiles.
3rd Centile5th Centile10th Centile0.40.40.40.20.20.2Index(kg/m)-0.4 0.02531374349556167-0.4 0.02531374349556167-0.4 0.02531374349556167191919Mass25th Centile50th Centile75th Centile0.40.40.4Body0.20.20.2for0.00.00.0Centile-0.490th Centile-0.495th Centile-0.497th CentileFitted192531616719253161671925316167374349553743495537434955Empirical-0. 0. 0.0240. 0. 0.0240. 0. 0.024-0.4-0.4-0.4192531374349556167192531374349556167192531374349556167
Age (months)
Figure 107 Centile residuals from fitting Model 1 for height-based BMI-for-age from 18 to 71 months for boys
Table 78 Observed proportions of children with measurements below the fitted centiles from Model 1, height-based BMI-for-age for boys
Expected18 19 mo20 22 mo23 25 mo26 28 mo29 31 mo32 34 mo35 37 mo38 40 mo41 43 mo44 46 mo10.70.80.31.21.31.21.50.80.41.232.94.11.62.02.73.32.94.62.43.154.76.13.93.54.95.35.15.95.64.3109.711.410.19.810.710.710.211.810.99.32524.326.426.224.820.525.425.127.327.423.65049.049.151.147.650.050.449.549.255.647.37572.374.578.972.073.772.574.276.577.875.29088.690.891.690.289.786.992.488.292.787.69594.095.596.494.594.293.497.196.295.692.69796.196.897.596.996.495.998.597.596.895.39998.798.799.199.699.198.899.399.299.298.4
Expected47 49 mo50 52 mo53 55 mo56 58 mo59 61 mo62 64 mo65 67 mo68 71 moOverall11.30.90.00.40.50.90.90.30.833.93.51.83.25.13.62.23.13.155.65.72.76.96.05.05.33.85.01010.09.66.612.99.810.914.28.710.42522.125.322.625.826.520.827.122.725.05048.549.349.651.247.452.055.650.350.07573.672.176.573.075.371.574.276.674.79090.988.291.289.190.787.890.787.189.99596.195.295.195.694.992.396.094.495.19797.096.596.596.898.695.997.895.896.89998.798.399.198.099.599.198.799.098.9
Note: Group labels correspond to the age intervals in Table 79.
244
BMI-for-age, boysBMI-for-age, boys245
Table 79 Q-test for z-scores from Model 1 [BCPE(x=age, df()=4, df()=3, df()=3, =2)] for height-based BMI-for-age for boys
Age (months)Nz1z2z3z418 195961.230.760.68-0.7520 22870-0.440.89-0.50-0.1723 25634-0.97-2.011.35-0.0226 282540.42-0.08-0.84-0.0129 312240.540.16-0.76-0.1332 342440.451.30-0.18-0.9435 37275-0.36-0.79-1.09-0.6038 40238-0.830.18-0.32-0.2641 43248-1.23-0.970.64-0.7744 462580.860.180.17-0.3047 492310.40-0.49-0.780.2750 522290.220.63-0.140.2353 552260.62-1.651.17-0.1556 58248-0.471.030.36-1.2759 61215-0.39-0.16-0.87-1.0162 642210.810.69-0.03-0.5765 67225-0.940.59-0.06-1.4668 712860.50-0.440.760.09Overall Q stats57229.1314.219.067.84degrees of freedom14.016.015.018.0p-value0.82240.58300.87430.9809
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Q-test results of the z-scores from the selected model are shown in Table 79. No indication of misfit was noted for any of the four distributional parameters. Only one age group (23 25 mo) had an absolute value of z2 slightly above 2. This was likely the result of smoothing out the irregularity at the merging point of the longitudinal and cross-sectional sub-samples. Figure 108 shows the worm plots for the z-scores derived from Model 1. The plots show no evidence of departure from the normal distribution or misfit of the selected model. Worms were fairly flat across all age groups, apart from two groups (23 25 and 53 55 mo) whose worms had slopes indicating a slight misfit of the variance. No adjustment for kurtosis appeared to be necessary.
246 BMI-for-age, boys
-3 -1 0 1 2 3 -3 -1 0 1 2 3
62-6465-6768-710.40.20.0-0.4-1 0 1 2 3-340.47-4950-5253-5556-5859-6120.00.Deviation-0.432-3435-3738-4041-4344-46
40.18-1920-2223-2526-2829-3120.00.4-0.-3-1 0 1 2 3-3-1 0 1 2 3
-0.4 00. 20. 40.
Unit normal quantile
Figure 108 Worm plots of z-scores for Model 1 for height-based BMI-for-age for boys
A new iteration to re-search for the best values of df() and df() with respect to AIC and GAIC(3) was done using df()=3, but the previous choice was confirmed and there was no need to update the model. In conclusion, the model selected for the height-based BMI-for-age curves for boys was BCPE(x=age, df()=4, df()=3,df()=3,=2). The standard's fitted centile curves and empirically derived centiles are shown in Figures 109 and 110.
1897th1790thIndex (kg/m)16Mass1550thBody1410th13FittedEmpirical3rd2225283134374043464952555861646770Age (months)
Figure 109 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: height-based BMI-for-age for boys from 24 to 71 months
BMI-for-age, boys
247
1895th17(kg/m)1675thIndexMass1550thBody1425th13Fitted5thEmpirical2225283134374043464952555861646770Age (months)
Figure 110 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: height-based BMI-for-age for boys from 24 to 71 months
248
BMI-for-age, boysBMI-for-age, boys249
6.2.3 WHO standards and their comparison with CDC 2000 reference
This section presents the final WHO BMI-for-age z-score and percentile charts (Figures 111 to 114) and tables (Tables 80 to 82) for boys. It also provides the z-score comparison of the WHO versus CDC 2000 curves (Figure 115).
250 BMI-for-age, boys
3210-1-2-3
22 24months20birth to 2418from16boys10 12 14Age (months)BMI-for-age z-scores for8based6length-4WHO21110Figure
22201816141210Body Mass Index (kg/m)
Charts
20
(kg/m)18Mass Index16Body14
12
3
2
1
0
-1
-2
-3
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60
Age (months)
Figure 112 WHO height-based BMI-for-age z-scores for boys from 24 to 60 months
BMI-for-age, boys
251252 BMI-for-age, boys
97th85th50th15th3rd
22 2424 months20birth to18from16for boys12 14Age (months)-age percentiles10for8based BMI-6length-4WHO21130Figure
2018161412Body Mass Index (kg/m)BMI-for-age, boys253
97th85th50th15th3rd
58 60months56to 60542452from50boys48for40 42 44 46Age (months)for-age percentiles38BMI-32 34 36height-based30WHO24 26 28Figure 114
181716151413Body Mass Index (kg/m)Tables
Table 80 Length-based BMI-for-age for boys, age in weeks
Percentiles (BMI in kg/m2)WeekLMS1st3rd5th15th25th50th75th85th95th97th99th0-0.305313.40690.0956010.811.311.512.212.613.414.314.815.816.116.910.524713.34210.0982110.511.011.312.012.513.314.214.715.615.916.620.417713.63770.0945410.811.311.612.312.813.614.515.015.916.216.830.344914.22410.0923011.411.912.212.913.414.215.115.616.516.817.540.288114.77140.0907211.912.412.713.413.914.815.716.217.117.418.150.240915.23550.0895312.312.813.113.914.315.216.216.717.618.018.760.200315.61070.0885912.613.213.514.214.715.616.617.118.018.419.170.164515.91690.0878212.913.513.814.515.015.916.917.418.418.719.580.132416.16980.0871713.213.714.014.815.216.217.117.718.619.019.890.103216.37870.0866113.413.914.215.015.416.417.417.918.919.320.0100.076616.54940.0861213.514.114.415.115.616.517.518.119.119.420.2110.052016.68820.0856913.714.214.515.315.716.717.718.219.219.620.3120.029116.80160.0853113.814.314.615.415.916.817.818.419.319.720.5130.007716.89500.0849613.914.414.715.516.016.917.918.419.419.820.6
254
BMI-for-age, boys
Table 80 Length-based BMI-for-age for boys, age in weeks (continued)
Z-scores (BMI in kg/m2)WeekLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0-0.305313.40690.0956010.211.112.213.414.816.318.110.524713.34210.098219.710.812.113.314.716.117.520.417713.63770.0945410.111.212.413.615.016.417.830.344914.22410.0923010.611.813.014.215.617.018.540.288114.77140.0907211.112.313.514.816.217.619.250.240915.23550.0895311.512.713.915.216.618.219.860.200315.61070.0885911.913.014.315.617.018.620.270.164515.91690.0878212.213.314.615.917.418.920.680.132416.16980.0871712.413.614.816.217.619.220.990.103216.37870.0866112.613.815.016.417.919.421.2100.076616.54940.0861212.713.915.216.518.019.621.4110.052016.68820.0856912.914.015.316.718.219.821.5120.029116.80160.0853113.014.215.416.818.319.921.7130.007716.89500.0849613.114.315.516.918.420.021.8
BMI-for-age, boys
255Table 81 Length-based BMI-for-age for boys, age in years and months
Percentiles (BMI in kg/m2)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th0: 00-0.305313.40690.0956010.811.311.512.212.613.414.314.815.816.116.90:110.270814.94410.0902712.012.612.813.614.114.915.916.417.317.618.30:220.111816.31950.0867713.313.814.114.915.416.317.317.818.819.219.90:330.006816.89870.0849513.914.414.715.516.016.917.918.519.419.820.60: 44-0.072717.15790.0837814.114.715.015.716.217.218.218.719.720.120.90: 55-0.137017.29190.0829614.314.815.115.916.417.318.318.919.820.221.00: 66-0.191317.34220.0823414.414.915.215.916.417.318.318.919.920.321.10: 77-0.238517.32880.0818314.414.915.215.916.417.318.318.919.920.321.10: 88-0.280217.26470.0814014.414.915.115.916.317.318.218.819.820.221.00: 99-0.317617.16620.0810214.314.815.115.816.317.218.118.719.720.120.80:1010-0.351617.04880.0806814.214.715.015.716.217.018.018.619.519.920.70:1111-0.382816.92390.0803714.114.614.915.616.016.917.918.419.419.820.51: 012-0.411516.79810.0800914.014.514.815.515.916.817.718.319.219.620.41: 113-0.438216.67430.0798213.914.414.715.415.816.717.618.119.119.520.21: 214-0.463016.55480.0795813.914.314.615.315.716.617.518.018.919.320.11: 315-0.486316.44090.0793513.814.214.515.215.616.417.417.918.819.219.91: 416-0.508216.33350.0791313.714.214.415.115.516.317.217.818.719.119.81: 517-0.528916.23290.0789213.614.114.315.015.416.217.117.618.618.919.71: 618-0.548416.13920.0787313.614.014.214.915.316.117.017.518.518.819.61: 719-0.566916.05280.0785413.513.914.214.815.216.116.917.418.418.719.51: 820-0.584615.97430.0783613.413.914.114.815.216.016.917.418.318.619.41: 921-0.601415.90390.0781813.413.814.114.715.115.916.817.318.218.619.31:1022-0.617415.84120.0780213.313.814.014.615.015.816.717.218.118.519.21:1123-0.632815.78520.0778613.313.714.014.615.015.816.717.118.018.419.12: 024a-0.647315.73560.0777113.313.713.914.514.915.716.617.118.018.319.1
24 months corresponds to 730 days.
256
BMI-for-age, boys
Table 81 Length-based BMI-for-age for boys, age in years and months (continued)
Z-scores (BMI in kg/m2)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD0: 00-0.305313.40690.0956010.211.112.213.414.816.318.10:110.270814.94410.0902711.312.413.614.916.317.819.40:220.111816.31950.0867712.513.715.016.317.819.421.10:330.006816.89870.0849513.114.315.516.918.420.021.80: 44-0.072717.15790.0837813.414.515.817.218.720.322.10: 55-0.137017.29190.0829613.514.715.917.318.820.522.30: 66-0.191317.34220.0823413.614.716.017.318.820.522.30: 77-0.238517.32880.0818313.714.816.017.318.820.522.30: 88-0.280217.26470.0814013.614.715.917.318.720.422.20: 99-0.317617.16620.0810213.614.715.817.218.620.322.10:1010-0.351617.04880.0806813.514.615.717.018.520.122.00:1111-0.382816.92390.0803713.414.515.616.918.420.021.81: 012-0.411516.79810.0800913.414.415.516.818.219.821.61: 113-0.438216.67430.0798213.314.315.416.718.119.721.51: 214-0.463016.55480.0795813.214.215.316.618.019.521.31: 315-0.486316.44090.0793513.114.115.216.417.819.421.21: 416-0.508216.33350.0791313.114.015.116.317.719.321.01: 517-0.528916.23290.0789213.013.915.016.217.619.120.91: 618-0.548416.13920.0787312.913.914.916.117.519.020.81: 719-0.566916.05280.0785412.913.814.916.117.418.920.71: 820-0.584615.97430.0783612.813.714.816.017.318.820.61: 921-0.601415.90390.0781812.813.714.715.917.218.720.51:1022-0.617415.84120.0780212.713.614.715.817.218.720.41:1123-0.632815.78520.0778612.713.614.615.817.118.620.32: 024a-0.647315.73560.0777112.713.614.615.717.018.520.3
24 months corresponds to 730 days.
BMI-for-age, boys
257Table 82 Height-based BMI-for-age for boys, age in years and months
Percentiles (BMI in kg/m2)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th2: 024a-0.618716.01890.0778513.513.914.214.815.216.016.917.418.318.719.42: 125-0.584015.98000.0779213.513.914.114.815.216.016.917.418.318.619.42: 226-0.549715.94140.0780013.413.814.114.715.115.916.817.318.218.619.32: 327-0.516615.90360.0780813.413.814.014.715.115.916.817.318.218.519.22: 428-0.485015.86670.0781813.313.814.014.715.115.916.717.218.118.519.22: 529-0.455215.83060.0782913.313.714.014.615.015.816.717.218.118.419.12: 630-0.427415.79530.0784113.313.713.914.615.015.816.717.218.018.419.12: 731-0.401615.76060.0785413.213.713.914.515.015.816.617.118.018.419.12: 832-0.378215.72670.0786713.213.613.914.514.915.716.617.118.018.319.02: 933-0.357215.69340.0788213.113.613.814.514.915.716.617.017.918.319.02:1034-0.338815.66100.0789713.113.513.814.414.915.716.517.017.918.218.92:1135-0.323115.62940.0791413.113.513.814.414.815.616.517.017.918.218.93: 036-0.310115.59880.0793113.013.513.714.414.815.616.517.017.818.218.93: 137-0.300015.56930.0795013.013.513.714.414.815.616.416.917.818.118.83: 238-0.292715.54100.0796913.013.413.714.314.715.516.416.917.818.118.83: 339-0.288415.51400.0799012.913.413.614.314.715.516.416.917.718.118.83: 440-0.286915.48850.0801212.913.413.614.314.715.516.416.817.718.118.83: 541-0.288115.46450.0803612.913.313.614.214.715.516.316.817.718.018.73: 642-0.291915.44200.0806112.913.313.614.214.615.416.316.817.718.018.73: 743-0.298115.42100.0808712.813.313.514.214.615.416.316.817.718.018.73: 844-0.306715.40130.0811512.813.313.514.214.615.416.316.817.718.018.73: 945-0.317415.38270.0814412.813.213.514.214.615.416.316.817.618.018.73:1046-0.330315.36520.0817412.813.213.514.114.515.416.216.717.618.018.73:1147-0.345215.34850.0820512.813.213.514.114.515.316.216.717.618.018.74: 048-0.362215.33260.0823812.713.213.414.114.515.316.216.717.618.018.7
258
BMI-for-age, boys
Table 82 Height-based BMI-for-age for boys, age in years and months (continued)
Percentiles (BMI in kg/m2)Year: MonthMonthLMS1st3rd5th15th25th50th75th85th95th97th99th4: 149-0.381115.31740.0827212.713.213.414.114.515.316.216.717.618.018.74: 250-0.401915.30290.0830712.713.213.414.114.515.316.216.717.618.018.74: 351-0.424515.28910.0834312.713.113.414.014.515.316.216.717.618.018.74: 452-0.448815.27590.0838012.713.113.414.014.415.316.216.717.618.018.74: 553-0.474715.26330.0841812.713.113.314.014.415.316.216.717.618.018.74: 654-0.501915.25140.0845712.613.113.314.014.415.316.216.717.618.018.84: 755-0.530315.24000.0849612.613.113.314.014.415.216.216.717.618.018.84: 856-0.559915.22910.0853612.613.113.314.014.415.216.116.717.618.018.84: 957-0.590515.21880.0857712.613.013.314.014.415.216.116.717.618.018.84:1058-0.622315.20910.0861712.613.013.313.914.415.216.116.717.618.018.84:1159-0.655215.20000.0865912.613.013.313.914.415.216.116.717.718.118.95: 060-0.689215.19160.0870012.613.013.313.914.315.216.116.717.718.118.9
24 months corresponds to 731 days.
BMI-for-age, boys
259Table 82 Height-based BMI-for-age for boys, age in years and months (continued)
Z-scores (BMI in kg/m2)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD2: 024a-0.618716.01890.0778512.913.814.816.017.318.920.62: 125-0.584015.98000.0779212.813.814.816.017.318.820.52: 226-0.549715.94140.0780012.813.714.815.917.318.820.52: 327-0.516615.90360.0780812.713.714.715.917.218.720.42: 428-0.485015.86670.0781812.713.614.715.917.218.720.42: 529-0.455215.83060.0782912.713.614.715.817.118.620.32: 630-0.427415.79530.0784112.613.614.615.817.118.620.22: 731-0.401615.76060.0785412.613.514.615.817.118.520.22: 832-0.378215.72670.0786712.513.514.615.717.018.520.12: 933-0.357215.69340.0788212.513.514.515.717.018.520.12:1034-0.338815.66100.0789712.513.414.515.717.018.420.02:1135-0.323115.62940.0791412.413.414.515.616.918.420.03: 036-0.310115.59880.0793112.413.414.415.616.918.420.03: 137-0.300015.56930.0795012.413.314.415.616.918.319.93: 238-0.292715.54100.0796912.313.314.415.516.818.319.93: 339-0.288415.51400.0799012.313.314.315.516.818.319.93: 440-0.286915.48850.0801212.313.214.315.516.818.219.93: 541-0.288115.46450.0803612.213.214.315.516.818.219.93: 642-0.291915.44200.0806112.213.214.315.416.818.219.83: 743-0.298115.42100.0808712.213.214.215.416.718.219.83: 844-0.306715.40130.0811512.213.114.215.416.718.219.83: 945-0.317415.38270.0814412.213.114.215.416.718.219.83:1046-0.330315.36520.0817412.113.114.215.416.718.219.83:1147-0.345215.34850.0820512.113.114.215.316.718.219.94: 048-0.362215.33260.0823812.113.114.115.316.718.219.9
260
BMI-for-age, boys
Table 82 Height-based BMI-for-age for boys, age in years and months (continued)
Z-scores (BMI in kg/m2)Year: MonthMonthLMS-3 SD-2 SD-1 SDMedian1 SD2 SD3 SD4: 149-0.381115.31740.0827212.113.014.115.316.718.219.94: 250-0.401915.30290.0830712.113.014.115.316.718.219.94: 351-0.424515.28910.0834312.113.014.115.316.618.219.94: 452-0.448815.27590.0838012.013.014.115.316.618.219.94: 553-0.474715.26330.0841812.013.014.115.316.618.220.04: 654-0.501915.25140.0845712.013.014.015.316.618.220.04: 755-0.530315.24000.0849612.013.014.015.216.618.220.04: 856-0.559915.22910.0853612.012.914.015.216.618.220.14: 957-0.590515.21880.0857712.012.914.015.216.618.220.14:1058-0.622315.20910.0861712.012.914.015.216.618.320.24:1159-0.655215.20000.0865912.012.914.015.216.618.320.25: 060-0.689215.19160.0870012.012.914.015.216.618.320.3
24 months corresponds to 731 days.
BMI-for-age, boys
261Comparison with CDC 2000
22(Kg/m)2018Mass Index16Body141210
3
2
1
0
-1
-2
-3
WHO
CDC 2000
0 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Age (months)
Figure 115 Comparison of WHO with CDC 2000 BMI-for-age z-scores for boys
262
BMI-for-age, boysBMI-for-age, girls263
6.3 BMI-for-age for girls
Steps similar to those used for fitting the equivalent standards for boys were followed to select the best model to fit the BMI-for-age growth standards for girls. The diagnostic tools used to evaluate and compare different models were the same.
6.3.1 Sample size
A total of 13 623 records with both weight and length/height were available for constructing the BMI-for-age curves for girls. The longitudinal and cross-sectional sample sizes by visit and age are presented in the Tables 83 and 84.
Table 83 Longitudinal sample sizes for BMI-for-age for girls
VisitBirth123456Age02 wk4 wk6 wk2 mo3 mo4 moN838449447447447446444Visit78910111213Age5 mo6 mo7 mo8 mo9 mo10 mo11 moN447445444440446444443Visit14151617181920Age12 mo14 mo16 mo18 mo20 mo22 mo24 moN449449440447442437448
Table 84 Cross-sectional sample sizes for BMI-for-age for girls
Age (mo)<1818 2021 2324 2627 2930 3233 35N2158164235213229224Age (mo)36 3839 4142 4445 4748 5051 5354 56N223235247209224201231Age (mo)57 5960 6263 6566 6869 71>71N2412172052252010
6.3.2 Model selection and results
Length-based BMI-for-age for girls
The model BCPE(x=age, df()=9, df()=4, df()=4, =2) was used to begin the search for the best age-transformation power . Table 85 shows the global deviance for a grid of values of between 0 and 0.5. As for boys, the smallest global deviance corresponded to an age-transformation power of =0.01 but =0.05 yielded very close global deviance. For the same reasons described earlier for the boys' corresponding standard, the age-transformation power =0.05 was selected.
264 BMI-for-age, girls
Table 85 Global deviance (GD) for models within the class BCPE(x=age, df()=9, df()=4, df()=4, =2) for length-based BMI-for-age for girls
0.010.050.100.150.200.25GDa375.9376.1376.6377.4378.4379.40.300.350.400.450.50GDa380.4381.7384.4390.0400.0
In excess of 38 000.
Using =0.05 as the age-transformation power, the search for the best df() and df() was carried out by comparing the goodness of fit of various models, fixing =1 and =2. All possible combinations of df() 7 to 15 and df() 2 to 10 were considered. Partial results are presented in Table 86.
Table 86 Goodness-of-fit summary for models using the BCPE distribution with fixed =1 and =2 for length-based BMI-for-age for girls
df()df()GDaAICaGAIC(3)aTotal df2607.9627.9637.9103575.6597.6608.61184573.2597.2609.2125569.7595.7608.7136566.8594.8608.8147565.4595.4610.4152601.0623.0634.0113568.8592.8604.81294566.4592.4605.4135563.0591.0605.0146560.2590.2605.2157558.8590.8606.8162597.1621.1633.1123565.0591.0604.013104562.7590.7604.7145559.3589.3604.3156556.5588.5604.5167555.2589.2606.2172594.4620.4633.4133562.6590.6604.614114560.2590.2605.2155556.9588.9604.9166554.1588.1605.1177552.8588.8606.8182593.1621.1635.1143560.8590.8605.815124558.4590.4606.4165555.1589.1606.1176552.3588.3606.3187551.0589.0608.019
GD, Global Deviance; AIC, Akaike Information Criterion;
GAIC(3), Generalized AIC with penalty equal to 3;
In excess of 38 000.
BMI-for-age, girls265
The smallest value of AIC corresponded to df()=11 and df()=6, while the smallest value of GAIC(3) was associated with df()=10 and df()=3. Using 6 degrees of freedom to fit the curve resulted in a very irregular pattern (Figure 116) compared to the boys' curve (Figure 101). The model that appeared to have the best smoothing outcome in the centile curves (df()=10 and df()=3) was therefore evaluated further.
1150.
1050.
0950.
0850.
df()=6
df()=5
df()=3
0 5 10 15 20
Age (months)
Figure 116 Cubic splines fitted for the curve with varying numbers of degrees of freedom
Model 1: BCPE(x= age0.05, df()=10, df()=3, =1, =2)
Q-test results (Table 87) showed that, for 14 out of 23 age groups, absolute values of z3 were above 2, showing residual skewness. Only one age group (7 days) had an absolute value of z2 above 2, which indicated misfit of variance, and another group (24 mo) had an absolute value of z4 larger than 2, pointing to residual kurtosis.
266 BMI-for-age, girls
Table 87 Q-test for z-scores fromModel 1 [BCPE(x=age0.05, df()=10, df()=3, =1, =2)] forlength-based BMI-for-age for girlsAge (days)GroupNz1z2z3z40Birth8380.02-0.163.550.751 to 117 d3920.232.250.87-0.6412 to 1614 d446-0.73-0.661.04-0.1717 to 3428 d4490.35-1.011.760.8835 to 4942 d4440.33-0.911.16-0.2350 to 692 mo445-0.08-0.221.27-1.0870 to 993 mo444-0.110.591.00-1.09100 to 1294 mo444-0.510.661.78-1.27130 to 1595 mo441-0.231.372.29-0.71160 to 1896 mo4410.200.181.49-1.97190 to 2197 mo4320.400.831.97-0.88220 to 2498 mo4350.070.312.68-1.01250 to 2799 mo4390.68-0.792.69-1.26280 to 30910 mo444-0.41-0.263.570.82310 to 34911 mo4790.290.023.910.32350 to 37912 mo451-0.13-0.032.990.03380 to 43914 mo446-0.040.363.811.36440 to 49916 mo442-0.11-0.993.250.30500 to 55918 mo4690.04-1.082.971.10560 to 61920 mo5420.71-0.203.941.02620 to 67922 mo539-0.73-0.044.321.74680 to 74924 mo591-1.010.394.262.62750 to 91328 mo4091.03-0.252.66-0.90Overall Q stats10 9025.2214.10180.6029.23degrees of freedom13.021.023.023.0p-value0.96990.8652< 0.010.1726
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Worm plots mostly supported the findings of the Q-test results (Figure 117). The majority of the worms were U-shaped and the group at 7 days presented a worm with a slope. The group with absolute value of z4 larger than 2 in the Q-test did not have an S-shaped worm, likely due to the fact that the residual kurtosis was an effect of the misfit in the skewness. Model 1 was thus considered inadequate. The search for the best model proceeded with the modelling of the curve in addition to and .
BMI-for-age, girls267
-3-1 0 1 2 3-3-1 0 1 2 30.422 mo24 mo28 mo0.0-0.4-3-1 0 1 2 312 mo14 mo16 mo18 mo20 mo
Deviation0.4 0. 0.047 mo8 mo9 mo10 mo11 mo-2 mo3 mo4 mo5 mo6 mo
0.4Birth7 d14 d28 d42 d0.0-0.4-3-1 0 1 2 3-3-1 0 1 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 117 Worm plots of z-scores for Model 1 for length-based BMI-for-age for girls
The summary statistics in Table 88 show that the best combination of AIC and GAIC(3) corresponded to df()=3. An evaluation of this model followed by comparing fitted with empirical values, examining worm plots and assessing Q-test results.
Table 88 Goodness-of-fit summary for models BCPE(x=age0.05, df()=10, df()=3, df()=?, =2) for length-based BMI-for-age for girls
df()GDaGAIC(3)aTotal df1398.3440.3142396.8441.7153376.1424.1164374.9425.9175373.8427.8186373.0430.019
GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;
In excess of 38 000.
268 BMI-for-age, girls
Model 2: BCPE(x=age0.05, df()=10, df()=3, df()=3, =2)
Figure 118 compares the fitting of the parameters , and for Model 2 with their respective empirical estimates.
of Body Mass Index (kg/m)17Box-Cox Transformed BMI095 1050.0.15 1614MedianSt Dev0850.
024681012141618202224024681012141618202224Age (months)Age (months)0.6Power0. 0.24Transform0.0Box-Cox-0.4-0.8024681012141618202224
Age (months)
Figure 118 Fitting of the , , and curves of Model 2 for length-based BMI-for-age from 0 to 24 months for girls (dotted line) and their respective sample estimates (points with solid line)
BMI-for-age, girls269
3rd Centile5th Centile10th Centile0.20.20.2(kg/m)-0.2 0.0-0.2 0.0-0.2 0.0Index024681216202402468121620240246812162024Body Mass25th Centile50th Centile75th Centile0.20.20.2for0.00.00.0Centile-0.290th Centile-0.295th Centile-0.297th CentileFitted024620240246202402462024812168121681216Empirical-0. 0.020. 0.020. 0.02-0.2-0.2-0.2024681216202402468121620240246812162024
Age (months)
Figure 119 Centile residuals from fitting Model 2 for length-based BMI-for-age from 0 to 24 months for girls
Figure 119 shows the distribution of the centile residuals, i.e. the difference between empirical and fitted centiles for the longitudinal sample. Although the 50th centile curve tends to be overestimated, the average bias is very small (around 0.05 kg/m2).
270 BMI-for-age, girls
-3-1 0 1 2 3-3-1 0 1 2 30.422 mo24 mo28 mo0.0-0.4-3-1 0 1 2 312 mo14 mo16 mo18 mo20 mo
Deviation0.4 0. 0.047 mo8 mo9 mo10 mo11 mo-2 mo3 mo4 mo5 mo6 mo
0.4Birth7 d14 d28 d42 d0.0-0.4-3-1 0 1 2 3-3-1 0 1 2 3
-0.4 0.0 0.4
-0.4 0.0 0.4
Unit normal quantile
Figure 120 Worm plots of z-scores for Model 2 for length-based BMI-for-age for girls
The worm plots for Model 2 (Figure 120) are mostly flat, i.e. with no obvious indication of misfit. Worms with slight slopes were noted for a few groups, the most evident being at 7 days, the imputed age group. Q-test results for the z-scores from Model 2 are shown in Table 89. For the selected age groups, there were no absolute values larger than 2 for any of the statistics z1 and z3, indicating no misfit of the median or skewness. For only one age group (7 days), the test indicated misfit of the variance, and for two age groups (6 and 9 mo) results suggested mild residual kurtosis (i.e. absolute values of z4 marginally above 2). The overall tests' p-values were all non-significant, indicating an adequate fit of this model for the BMI-for-age for girls from birth to 2 years. Table 90 presents the observed percentages of the sample that were below the fitted centiles. No indications of systematic bias were noted for any of the centiles.
BMI-for-age, girls271
Table 89 Q-test for z-scores from Model 2 [BCPE(x=age0.05, df()=10, df()=3, df()=3, =2)] for length-based BMI-for-age for girls
Age (days)GroupNz1z2z3z40Birth8380.00-0.170.15-0.021 to 117 d3920.342.180.00-0.7212 to 1614 d446-0.77-0.65-0.14-0.2017 to 3428 d4490.26-1.080.120.7335 to 4942 d4440.26-0.89-0.52-0.1950 to 692 mo445-0.09-0.12-0.51-0.7870 to 993 mo444-0.050.79-0.99-1.31100 to 1294 mo444-0.400.81-0.30-1.55130 to 1595 mo441-0.161.44-0.02-1.15160 to 1896 mo4410.320.32-0.65-2.07190 to 2197 mo4320.430.89-0.47-1.05220 to 2498 mo4350.090.280.33-1.51250 to 2799 mo4390.74-0.910.47-2.07280 to 30910 mo444-0.43-0.330.750.13310 to 34911 mo4790.24-0.221.22-0.87350 to 37912 mo451-0.20-0.010.16-0.63380 to 43914 mo446-0.170.220.650.17440 to 49916 mo442-0.16-1.010.40-0.70500 to 55918 mo4690.00-0.98-0.520.73560 to 61920 mo5420.63-0.410.46-0.45620 to 67922 mo539-0.80-0.040.480.59680 to 74924 mo591-1.080.58-0.361.24750 to 91328 mo4091.14-0.36-0.25-0.88Overall Q stats10 9025.7315.176.1724.20degrees of freedom13.021.020.023.0p-value0.95550.81420.99870.3927
Note: Absolute values of z1, z2, z3 or z4 larger than 2 indicate misfit of, respectively, mean, variance, skewness or kurtosis.
Since residual kurtosis was noted for only two out of the 23 age groups and the overall test was not significant, as with the boys' curves, modelling parameter was not considered necessary.
The model BCPE(x=age0.05, df()=10, df()=3, df()=3, =2) was used to fit the BMI-for-age curves for girls from birth to 24 months. A new iteration was then done, fixing df()=3 and re-searching for the best combination of df() and df(), but Model 2 still presented the smallest value of GAIC(3) and its performance was very close to that of the model with the smallest AIC. A re-search was then done for the best value with the selected degrees of freedom for the , and curves. Results confirmed that values closest to zero were associated with the lowest global deviance, but for the reasons stated earlier for boys, =0.05 was selected in preference to =0.01. Thus, Model 2 was not updated.
The fitted curves are compared to empirical centiles in Figures 121 and 122.
Table 90 Observed proportions__