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## 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.].

1. 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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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 Araújo (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 Araújo, Cesar G. Victora, Elaine Albernaz, Elaine Tomasi, Rita de Cássia Fossati da Silveira, Gisele Nader (Departamento de Nutrição and Departamento de Medicina Social, Universidade Federal de Pelotas; and Núcleo de Pediatria and Escola de Psicologia, Universidade Católica 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 summary xvii

Introduction 1

Methodology 3

Design of the WHO Multicentre Growth Reference Study 3

Anthropometry methods 3

Sample description 4

Data cleaning procedures and exclusions 5

Statistical methods for constructing the growth curves 7

Construction of the length/height-for-age standards 13

Indicator-specific methodology 13

Length/height-for-age for boys 13

Sample size 13

Model selection and results 14

WHO standards and their comparison with NCHS and CDC 2000 references 32

Charts 33

Tables 37

Comparison with NCHS 45

Comparison with CDC 2000 46

Length/height-for-age for girls 47

Sample size 47

Model selection and results 47

WHO standards and their comparison with NCHS and CDC 2000 references 59

Charts 60

Tables 64

Comparison with NCHS 72

Comparison with CDC 2000 73

Comparisons between boys and girls 74

WHO 75

NCHS 76

3.4.3 CDC 2000 77

Construction of the weight-for-age standards 79

Indicator-specific methodology 79

Weight-for-age for boys 79

Sample size 79

Model selection and results 79

WHO standards and their comparison with NCHS and CDC 2000 references 94

Charts 95

Tables 97

Comparison with NCHS 105

Comparison with CDC 2000 106

Weight-for-age for girls 107

Sample size 107

Model selection and results 107

WHO standards and their comparison with NCHS and CDC 2000 references 122

Charts 123

Tables 125

Comparison with NCHS 133

Comparison with CDC 2000 134

Comparisons between boys and girls 135

4.4.1 WHO 136

4.4.2 NCHS 137

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4.4.3 CDC 2000 138

Construction of the weight-for-length and weight-for-height standards 139 | ||

5.1 | Indicator-specific methodology | 139 |

5.2 | Weight-for-length/height for boys | 139 |

5.2.1 Sample size | 139 | |

5.2.2 Model selection and results | 140 | |

5.2.3 WHO standards and their comparison with NCHS and CDC 2000 references | 153 | |

Charts | 154 | |

Tables | 158 | |

Comparison with NCHS | 176 | |

Comparison with CDC 2000 | 178 | |

5.3 | Weight-for-length/height for girls | 180 |

5.3.1 Sample size | 180 | |

5.3.2 Model selection and results | 180 | |

5.3.3 WHO standards and their comparison with NCHS and CDC 2000 references | 194 | |

Charts | 195 | |

Tables | 199 | |

Comparison with NCHS | 217 | |

Comparison with CDC 2000 | 219 | |

5.4 | Comparisons between boys and girls | 221 |

5.4.1 WHO | 222 | |

5.4.2 NCHS | 224 | |

5.4.3 CDC 2000 | 226 | |

Construction of the body mass index-for-age standards 229 | ||

6.1 | Indicator-specific methodology | 229 |

6.2 | BMI-for-age for boys | 230 |

6.2.1 Sample size | 230 | |

6.2.2 Model selection and results | 230 | |

Length-based BMI-for-age for boys | 230 | |

Height-based BMI-for-age for boys | 241 | |

6.2.3 WHO standards and their comparison with CDC 2000 reference | 249 | |

Charts | 250 | |

Tables | 254 | |

Comparison with CDC 2000 | 262 | |

6.3 | BMI-for-age for girls | 263 |

6.3.1 Sample size | 263 | |

6.3.2 Model selection and results | 263 | |

Length-based BMI-for-age for girls | 263 | |

Height-based BMI-for-age for girls | 275 | |

6.3.3 WHO standards and their comparison with CDC 2000 reference | 284 | |

Charts | 285 | |

Tables | 289 | |

Comparison with CDC 2000 | 297 | |

6.4 | Comparisons between boys and girls | 298 |

6.4.1 WHO | 299 | |

6.4.2 CDC 2000 | 300 |

5.

6.

Computation of centiles and z-scores for length/height-for-age, weight-for-age,

weight-for-length, weight-for-height and BMI-for-age 301

Conclusion 305

Bibliography 309

Appendix A. Model specifications of the WHO child growth standards 312

vi

Figures | ||

Figure 1 | Worm plots of z-scores for candidate model with df(µ)=11 and df(σ)=6 with age transformation age0.35 for length/height-for-age for boys | 16 |

Figure 2 | Fitting of µ and σ curves of Model 1 for length/height-for-age for boys | |

(dotted line) and their respective sample estimates (points with solid line) | 17 | |

Figure 3 | Centile residuals from fitting Model 1 for length/height-for-age from | |

0 to 24 months for boys | 18 | |

Figure 4 | Centile residuals from fitting Model 1 for length/height-for-age from | |

24 to 71 months for boys | 18 | |

Figure 5 | Worm plots of z-scores for Model 1 for length/height-for-age for boys | 19 |

Figure 6 | Worm plots of z-scores for Model 2 for length/height-for-age for boys | 24 |

Figure 7 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: | |

length-for-age for boys from birth to 24 months | 28 | |

Figure 8 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: | |

length-for-age for boys from birth to 24 months | 29 | |

Figure 9 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: | |

height-for-age for boys from 24 to 71 months | 30 | |

Figure 10 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: | |

height-for-age for boys from 24 to 71 months | 31 | |

Figure 11 | WHO length-for-age z-scores for boys from birth to 24 months | 33 |

Figure 12 | WHO height-for-age z-scores for boys from 24 to 60 months | 34 |

Figure 13 | WHO length-for-age percentiles for boys from birth to 24 months | 35 |

Figure 14 | WHO height-for-age percentiles for boys from 24 to 60 months | 36 |

Figure 15 | Comparison of WHO with NCHS length/height-for-age z-scores for boys | 45 |

Figure 16 | Comparison of WHO with CDC 2000 length/height-for-age z-scores for boys | 46 |

Figure 17 | Fitting of the µ and σ curves of Model 1 for length/height-for-age for girls | |

(dotted line) and their respective sample estimates (points with solid line) | 49 | |

Figure 18 | Centile residuals from fitting Model 1 for length/height-for-age from | |

0 to 24 months for girls | 50 | |

Figure 19 | Centile residuals from fitting Model 1 for length/height-for-age from | |

24 to 71 months for girls | 50 | |

Figure 20 | Worm plots of z-scores for Model 1 for length/height-for-age for girls | 51 |

Figure 21 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: | |

length-for-age for girls from birth to 24 months | 55 | |

Figure 22 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: | |

length-for-age for girls from birth to 24 months | 56 | |

Figure 23 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: | |

height-for-age for girls from 24 to 71 months | 57 | |

Figure 24 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: | |

height-for-age for girls from 24 to 71 months | 58 | |

Figure 25 | WHO length-for-age z-scores for girls from birth to 24 months | 60 |

Figure 26 | WHO height-for-age z-scores for girls from 24 to 60 months | 61 |

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Figure 27 | WHO length-for-age percentiles for girls from birth to 24 months | 62 |

Figure 28 | WHO height-for-age percentiles for girls from 24 to 60 months | 63 |

Figure 29 | Comparison of WHO with NCHS length/height-for-age z-scores for girls | 72 |

Figure 30 | Comparison of WHO with CDC 2000 length/height-for-age z-scores for girls | 73 |

Figure 31 | Comparison of boys' and girls' WHO length/height-for-age z-scores | 75 |

Figure 32 | Comparison of boys' and girls' NCHS length/height-for-age z-scores | 76 |

Figure 33 | Comparison of boys' and girls' CDC 2000 length/height-for-age z-scores | 77 |

Figure 34 | Worm plots of z-scores for Model 1 for weight-for-age for boys | 81 |

Figure 35 | Fitting of the µ, σ, and ν 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) | 84 |

Figure 36 | Centile residuals from fitting Model 2 for weight-for-age from 0 to 24 months for boys | 85 |

Figure 37 | Centile residuals from fitting Model 2 for weight-for-age from 24 to 71 months for boys | 85 |

Figure 38 | Worm plots of z-scores for Model 2 for weight-for-age for boys | 86 |

Figure 39 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for boys from birth to 24 months | 90 |

Figure 40 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for boys from birth to 24 months | 91 |

Figure 41 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for boys from 24 to 71 months | 92 |

Figure 42 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for boys from 24 to 71 months | 93 |

Figure 43 | WHO weight-for-age z-scores for boys from birth to 60 months | 95 |

Figure 44 | WHO weight-for-age percentiles for boys from birth to 60 months | 96 |

Figure 45 | Comparison of WHO with NCHS weight-for-age z-scores for boys | 105 |

Figure 46 | Comparison of WHO with CDC 2000 weight-for-age z-scores for boys | 106 |

Figure 47 | Cubic splines fitted for the ν curve with varying numbers of degrees of freedom | 110 |

Figure 48 | Fitting of the µ, σ, and ν 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) | 113 |

Figure 49 | Centile residuals from fitting Model 3 for weight-for-age from 0 to 24 months for girls | 114 |

Figure 50 | Centile residuals from fitting Model 3 for weight-for-age from 24 to 71 months for girls | 114 |

Figure 51 | Worm plots of z-scores for Model 3 for weight-for-age for girls | 115 |

Figure 52 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for girls from birth to 24 months | 118 |

Figure 53 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for girls from birth to 24 months | 119 |

viii

Figure 54 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-age for girls from 24 to 71 months | 120 |

Figure 55 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-age for girls from 24 to 71 months | 121 |

Figure 56 | WHO weight-for-age z-scores for girls from birth to 60 months | 123 |

Figure 57 | WHO weight-for-age percentiles for girls from birth to 60 months | 124 |

Figure 58 | Comparison of WHO with NCHS weight-for-age z-scores for girls | 133 |

Figure 59 | Comparison of WHO with CDC 2000 weight-for-age z-scores for girls | 134 |

Figure 60 | Comparison of boys' and girls' WHO weight-for-age z-scores | 136 |

Figure 61 | Comparison of boys' and girls' NCHS weight-for-age z-scores | 137 |

Figure 62 | Comparison of boys' and girls' CDC 2000 weight-for-age z-scores | 138 |

Figure 63 | Worm plots of z-scores for Model 1 for weight-for-length/height for boys | 141 |

Figure 64 | Fitting of the µ, σ, and ν curves of Model 2 for weight-for-length/height for boys (dotted line) and their respective sample estimates (points with solid line) | 143 |

Figure 65 | Centile residuals from fitting Model 2 for weight-for-length/height for boys | 144 |

Figure 66 | Worm plots of z-scores for Model 2 for weight-for-length/height for boys | 146 |

Figure 67 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-length for boys | 149 |

Figure 68 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-length for boys | 150 |

Figure 69 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-height for boys | 151 |

Figure 70 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-height for boys | 152 |

Figure 71 | WHO weight-for-length z-scores for boys from 45 to 110 cm | 154 |

Figure 72 | WHO weight-for-height z-scores for boys from 65 to 120 cm | 155 |

Figure 73 | WHO weight-for-length percentiles for boys from 45 to 110 cm | 156 |

Figure 74 | WHO weight-for-height percentiles for boys from 65 to 120 cm | 157 |

Figure 75 | Comparison of WHO with NCHS weight-for-length z-scores for boys | 176 |

Figure 76 | Comparison of WHO with NCHS weight-for-height z-scores for boys | 177 |

Figure 77 | Comparison of WHO with CDC 2000 weight-for-length z-scores for boys | 178 |

Figure 78 | Comparison of WHO with CDC 2000 weight-for-height z-scores for boys | 179 |

Figure 79 | Fitting of the µ, σ, and ν curves of Model 2 for weight-for-length/height for girls (dotted line) and their respective sample estimates (points with solid line) | 183 |

Figure 80 | Centile residuals from fitting Model 2 for weight-for-length/height for girls | 184 |

Figure 81 | Worm plots of z-scores for Model 2 for weight-for-length/height for girls | 186 |

Figure 82 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-length for girls | 190 |

- ix -

Figure 83 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-length for girls | 191 |

Figure 84 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: weight-for-height for girls | 192 |

Figure 85 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: weight-for-height for girls | 193 |

Figure 86 | WHO weight-for-length z-scores for girls | 195 |

Figure 87 | WHO weight-for-height z-scores for girls | 196 |

Figure 88 | WHO weight-for-length percentiles for girls | 197 |

Figure 89 | WHO weight-for-height percentiles for girls | 198 |

Figure 90 | Comparison of WHO with NCHS weight-for-length z-scores for girls | 217 |

Figure 91 | Comparison of WHO with NCHS weight-for-height z-scores for girls | 218 |

Figure 92 | Comparison of WHO with CDC 2000 weight-for-length z-scores for girls | 219 |

Figure 93 | Comparison of WHO with CDC 2000 weight-for-height z-scores for girls | 220 |

Figure 94 | Comparison of boys' and girls' WHO weight-for-length z-scores | 222 |

Figure 95 | Comparison of boys' and girls' WHO weight-for-height z-scores | 223 |

Figure 96 | Comparison of boys' and girls' NCHS weight-for-length z-scores | 224 |

Figure 97 | Comparison of boys' and girls' NCHS weight-for-height z-scores | 225 |

Figure 98 | Comparison of boys' and girls' CDC 2000 weight-for-length z-scores | 226 |

Figure 99 | Comparison of boys' and girls' CDC 2000 weight-for-height z-scores | 227 |

Figure 100 | Worm plots of z-scores for Model 1 for length-based BMI-for-age for boys | 232 |

Figure 101 | Fitting of the µ, σ, and ν 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) | 234 |

Figure 102 | Centile residuals from fitting Model 2 for length-based BMI-for-age from 0 to 24 months for boys | 235 |

Figure 103 | Worm plots of z-scores for Model 2 for length-based BMI-for-age for boys | 236 |

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 | 239 |

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 |

Figure 106 | Fitting of the µ, σ, and ν 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) | 242 |

Figure 107 | Centile residuals from fitting Model 1 for height-based BMI-for-age from 18 to 71 months for boys | 243 |

Figure 108 | Worm plots of z-scores for Model 1 for height-based BMI-for-age for boys | 246 |

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 | 247 |

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 |

x

Figure 111 | WHO length-based BMI-for-age z-scores for boys from birth to 24 months | 250 |

Figure 112 | WHO height-based BMI-for-age z-scores for boys from 24 to 60 months | 251 |

Figure 113 | WHO length-based BMI-for-age percentiles for boys from birth to 24 months | 252 |

Figure 114 | WHO height-based BMI-for-age percentiles for boys from 24 to 60 months | 253 |

Figure 115 | Comparison of WHO with CDC 2000 BMI-for-age z-scores for boys | 262 |

Figure 116 | Cubic splines fitted for the σ curve with varying numbers of degrees of freedom | 265 |

Figure 117 | Worm plots of z-scores for Model 1 for length-based BMI-for-age for girls | 267 |

Figure 118 | Fitting of the µ, σ, and ν 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) | 268 |

Figure 119 | Centile residuals from fitting Model 2 for length-based BMI-for-age from 0 to 24 months for girls | 269 |

Figure 120 | Worm plots of z-scores for Model 2 for length-based BMI-for-age for girls | 270 |

Figure 121 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: length-based BMI-for-age for girls from birth to 24 months | 273 |

Figure 122 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: length-based BMI-for-age for girls from birth to 24 months | 274 |

Figure 123 | Cubic splines fitted for the µ curve with varying numbers of degrees of freedom | 276 |

Figure 124 | Fitting of the µ, σ, and ν curves of Model 1 for height-based BMI-for-age from 18 to 71 months for girls (dotted line) and their respective sample estimates (points with solid line) | 277 |

Figure 125 | Centile residuals from fitting Model 1 for height-based BMI-for-age from 18 to 71 months for girls | 278 |

Figure 126 | Worm plots of z-scores for Model 1 for height-based BMI-for-age for girls | 279 |

Figure 127 | 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: height-based BMI-for-age for girls from 24 to 71 months | 282 |

Figure 128 | 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: height-based BMI-for-age for girls from 24 to 71 months | 283 |

Figure 129 | WHO length-based BMI-for-age z-scores for girls from birth to 24 months | 285 |

Figure 130 | WHO height-based BMI-for-age z-scores for girls from 24 to 60 months | 286 |

Figure 131 | WHO length-based BMI-for-age percentiles for girls from birth to 24 months | 287 |

Figure 132 | WHO height-based BMI-for-age percentiles for girls from 24 to 60 months | 288 |

Figure 133 | Comparison of WHO with CDC 2000 BMI-for-age z-scores for girls | 297 |

Figure 134 | Comparison of boys' and girls' WHO BMI-for-age z-scores | 299 |

Figure 135 | Comparison of boys' and girls' CDC 2000 BMI-for-age z-scores | 300 |

Figure 136 | Examples of children ranked according to the WHO BMI-for-age standards | 303 |

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Tables | ||

Table 1 | Total sample and number of compliant children in the longitudinal component | 4 |

Table 2 | Comparison of mean size at birth for compliant newborns and those that contributed only birth measurements | 5 |

Table 3 | Total sample of children in the cross-sectional component | 5 |

Table 4 | Total sample of children in the cross-sectional component by number of visits and total number of records | 5 |

Table 5 | Number of observations by sex and study component included and excluded on the basis of weight-for-length/height | 6 |

Table 6 | Number of observations used in the construction of the WHO child growth standards by sex and anthropometric indicator | 7 |

Table 7 | Interpretation of various patterns in the worm plot | 10 |

Table 8 | Summary of differences between recumbent length and standing height in a sample of children measured both ways | 13 |

Table 9 | Longitudinal sample sizes for length/height-for-age for boys | 14 |

Table 10 | Cross-sectional sample sizes for length/height-for-age for boys | 14 |

Table 11 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=10, df(σ)=6, ν=1, τ=2) for length/height-for-age for boys | 14 |

Table 12 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for length/height-for-age for boys | 15 |

Table 13 | Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for boys | 20 |

Table 14 | Q-test for z-scores from Model 1 [BCPE(x=age0.35, df(µ)=12, df(σ)=6, ν=1, τ=2)] for length/height-for-age for boys | 22 |

Table 15 | Goodness-of-fit summary for models BCPE(x=age0.35, df(µ)=12, df(σ)=6, df(ν)=?, τ=2) for length/height-for-age for boys | 23 |

Table 16 | Q-test for z-scores from Model 2 [BCPE(x=age0.35, df(µ)=12, df(σ)=6, df(ν)=6, τ=2)] for length/height-for-age for boys | 25 |

Table 17 | Observed proportions of children with measurements below the fitted centiles from Model 2, length/height-for-age for boys | 26 |

Table 18 | Length-for-age for boys, age in weeks | 37 |

Table 19 | Length-for-age for boys, age in years and months | 39 |

Table 20 | Height-for age for boys, age in years and months | 41 |

Table 21 | Longitudinal sample sizes for length/height-for-age for girls | 47 |

Table 22 | Cross-sectional sample sizes for length/height-for-age for girls | 47 |

Table 23 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=10, df(σ)=6, ν=1, τ=2) for length/height-for-age for girls | 48 |

Table 24 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for length/height-for-age for girls | 48 |

Table 25 | Observed proportions of children with measurements below the fitted centiles from Model 1, length/height-for-age for girls | 52 |

xii

Table 26 | Q-test for z-scores from Model 1 [BCPE(x=age0.35, df(µ)=10, df(σ)=5, ν=1, τ=2)] for length/height-for-age for girls | 54 |

Table 27 | Length-for-age for girls, age in weeks | 64 |

Table 28 | Length-for-age for girls, age in years and months | 66 |

Table 29 | Height-for-age for girls, age in years and months | 68 |

Table 30 | Longitudinal sample sizes for weight-for-age for boys | 79 |

Table 31 | Cross-sectional sample sizes for weight-for-age for boys | 79 |

Table 32 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=9, df(σ)=4, df(ν)=4, τ=2) for weight-for-age for boys | 80 |

Table 33 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for weight-for-age for boys | 80 |

Table 34 | Q-test for z-scores from Model 1 [BCPE(x=age0.35, df(µ)=11, df(σ)=7, ν=1, τ=2)] for weight-for-age for boys | 82 |

Table 35 | Goodness-of-fit summary for models BCPE(x=age0.35, df(µ)=11, df(σ)=7, df(ν)=?, τ=2) for weight-for-age for boys | 83 |

Table 36 | Q-test for z-scores from Model 2 [BCPE(x=age0.35, df(µ)=11, df(σ)=7, df(ν)=2, τ=2)] for weight-for-age for boys | 87 |

Table 37 | Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-age for boys | 88 |

Table 38 | Weight-for-age for boys, age in weeks | 97 |

Table 39 | Weight-for-age for boys, age in years and months | 99 |

Table 40 | Longitudinal sample sizes for weight-for-age for girls | 107 |

Table 41 | Cross-sectional sample sizes for weight-for-age for girls | 107 |

Table 42 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=9, df(σ)=4, df(ν)=4, τ=2) for weight-for-age for girls | 108 |

Table 43 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for weight-for-age for girls | 108 |

Table 44 | Q-test for z-scores from Model 1 [BCPE(x=age0.35, df(µ)=11, df(σ)=7, ν=1, τ=2)] for weight-for-age for girls | 109 |

Table 45 | Goodness-of-fit summary for models BCPE(x= age0.35, df(µ)=11, df(σ)=7, df(ν)=?, τ=2) for weight-for-age for girls | 110 |

Table 46 | Q-test for z-scores from Model 2 [BCPE(x=age0.35, df(µ)=11, df(σ)=7, df(ν)=5, τ=2)] for weight-for-age for girls | 111 |

Table 47 | Q-test for z-scores from Model 3 [BCPE(x=age0.35, df(µ)=11, df(σ)=7, df(ν)=3, τ=2)] for weight-for-age for girls | 112 |

Table 48 | Observed proportions of children with measurements below the fitted centiles from Model 3, weight-for-age for girls | 116 |

Table 49 | Weight-for-age for girls, age in weeks | 125 |

Table 50 | Weight-for-age for girls, age in years and months | 127 |

Table 51 | Sample sizes for boys' weight-for-length/height by length interval | 139 |

Table 52 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for weight-for-length/height for boys | 140 |

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Table 53 | Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7), df(µ)=13, df(σ)=6, ν=1, τ=2)] for weight-for-length/height for boys | 142 |

Table 54 | Goodness-of-fit summary for models BCPE(x=length (or height+0.7), df(µ)=13, df(σ)=6, df(ν)=?, τ=2) for weight-for-length/height for boys | 142 |

Table 55 | Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7), df(µ)=13, df(σ)=6, df(ν)=1, τ=2)] for weight-for-length/height for boys | 145 |

Table 56 | Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for boys | 147 |

Table 57 | Weight-for-length for boys | 158 |

Table 58 | Weight-for-height for boys | 168 |

Table 59 | Sample sizes for girls' weight-for-length/height by length interval | 180 |

Table 60 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for weight-for-length/height for girls | 181 |

Table 61 | Q-test for z-scores from Model 1 [BCPE(x=length (or height+0.7), df(µ)=12, df(σ)=4, ν=1, τ=2)] for weight-for-length/height for girls | 182 |

Table 62 | Goodness-of-fit summary for models BCPE(x=length (or height+0.7), df(µ)=12, df(σ)=4, df(ν)=?, τ=2) for weight-for-length/height for girls | 183 |

Table 63 | Q-test for z-scores from Model 2 [BCPE(x=length (or height+0.7), df(µ)=12, df(σ)=4, df(ν)=1, τ=2)] for weight-for-length/height for girls | 185 |

Table 64 | Q-test for z-scores from model BCPE(x=length (or height+0.7), df(µ)=12, df(σ)=4, df(ν)=1, τ=2.13) for weight-for-length/height for girls | 187 |

Table 65 | Observed proportions of children with measurements below the fitted centiles from Model 2, weight-for-length/height for girls | 188 |

Table 66 | Weight-for-length for girls | 199 |

Table 67 | Weight-for-height for girls | 209 |

Table 68 | Longitudinal sample sizes for BMI-for-age for boys | 230 |

Table 69 | Cross-sectional sample sizes for BMI-for-age for boys | 230 |

Table 70 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=9, df(σ)=4, df(ν)=4, τ=2) for length-based BMI-for-age for boys | 231 |

Table 71 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for length-based BMI-for-age for boys | 231 |

Table 72 | Q-test for z-scores from Model 1 [BCPE(x=age0.05, df(µ)=10, df(σ)=4, ν=1, τ=2)] for length-based BMI-for-age for boys | 233 |

Table 73 | Goodness-of-fit summary for models BCPE(x=age0.05, df(µ)=10, df(σ)=4, df(ν)=?, τ=2) for length-based BMI-for-age for boys | 233 |

Table 74 | Q-test for z-scores from Model 2 [BCPE(x=age0.05, df(µ)=10, df(σ)=4, df(ν)=3, τ=2)] for length-based BMI-for-age for boys | 237 |

Table 75 | Observed proportions of children with measurements below the fitted centiles from Model 2, length-based BMI-for-age for boys | 238 |

Table 76 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for height-based BMI-for-age for boys | 241 |

Table 77 | Goodness-of-fit summary for models BCPE(x=age, df(µ)=4, df(σ)=3, df(ν)=?, τ=2) for height-based BMI-for-age for boys | 242 |

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Table 78 | Observed proportions of children with measurements below the fitted centiles from Model 1, height-based BMI-for-age for boys | 244 |

Table 79 | Q-test for z-scores from Model 1 [BCPE(x=age, df(µ)=4, df(σ)=3, df(ν)=3, τ=2)] for height-based BMI-for-age for boys | 245 |

Table 80 | Length-based BMI-for-age for boys, age in weeks | 254 |

Table 81 | Length-based BMI-for-age for boys, age in years and months | 256 |

Table 82 | Height-based BMI-for-age for boys, age in years and months | 258 |

Table 83 | Longitudinal sample sizes for BMI-for-age for girls | 263 |

Table 84 | Cross-sectional sample sizes for BMI-for-age for girls | 263 |

Table 85 | Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=9, df(σ)=4, df(ν)=4, τ=2) for length-based BMI-for-age for girls | 264 |

Table 86 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for length-based BMI-for-age for girls | 264 |

Table 87 | Q-test for z-scores from Model 1 [BCPE(x=age0.05, df(µ)=10, df(σ)=3, ν=1, τ=2)] for length-based BMI-for-age for girls | 266 |

Table 88 | Goodness-of-fit summary for models BCPE(x=age0.05, df(µ)=10, df(σ)=3, df(ν)=?, τ=2) for length-based BMI-for-age for girls | 267 |

Table 89 | Q-test for z-scores from Model 2 [BCPE(x=age0.05, df(µ)=10, df(σ)=3, df(ν)=3, τ=2)] for length-based BMI-for-age for girls | 271 |

Table 90 | Observed proportions of children with measurements below the fitted centiles from Model 2 for length-based BMI-for-age for girls | 272 |

Table 91 | Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and τ=2 for height-based BMI-for-age for girls | 275 |

Table 92 | Goodness-of-fit summary for models BCPE(x=age, df(µ)=4, df(σ)=4, df(ν)=?, τ=2) for height-based BMI-for-age for girls | 276 |

Table 93 | Q-test for z-scores from Model 1 [BCPE(x=age, df(µ)=4, df(σ)=4, df(ν)=1, τ=2)] for height-based BMI-for age for girls | 280 |

Table 94 | Observed proportions of children with measurements below the fitted centiles from Model 1 for height-based BMI-for-age for girls | 281 |

Table 95 | Length-based BMI-for-age for girls, age in weeks | 289 |

Table 96 | Length-based BMI-for-age for girls, age in years and months | 291 |

Table 97 | Height-based BMI-for-age for girls, age in years and months | 293 |

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Glossary

BCPE The Box-Cox power exponential distribution.

µ The median of the Box-Cox power exponential distribution.

o The approximate coefficient of variation of the Box-Cox power exponential distribution — related to the variance.

ν The power of the Box-Cox transformation (to the normal distribution) of the Box-Cox power exponential distribution - related to the skewness.

τ The power exponential parameter of the Box-Cox power exponential distribution — related to the kurtosis.

λ The power of the age (or length/height) transformation.

Body mass index (BMI) The ratio weight (in kg) / recumbent length or standing height

(in m2).

Box-Cox transformation A power transformation to the normal distribution.

Coefficient of variation The ratio of the standard deviation to the mean.

**Cubic spline **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.

Cut-off A designated limit beyond which a subject or observation is classified according to a pre-set condition.

Degrees of freedom (df) The number of control points used to fit the cubic splines.

Kurtosis 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.

P-value 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.

Q-test A statistical test which combines overall and local tests assessing departures from the normal distribution with respect to median, variance, skewness and kurtosis.

Skewness A statistical term used to describe a distribution's asymmetry in relation to a normal distribution.

Standard deviation score (SD) See z-score.

Worm plots A set of detrended Q-Q plots — plots that compare the distribution of a given set of observations to the normal distribution.

Z-score 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

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, 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.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 ≥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).

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

Boys

Girls

Total

Brazil

309

29

37

66

Ghana

328

103

124

227

India

301

84

89

173

Norway

300

75

73

148

Oman

291

73

76

149

USA

208

64

55

119

Site N

Complianta

All 1737 428 454 882

a Compliant with infant-feeding and no-smoking criteria and completed the 24-month follow-up.

Methodology 5

Table 2 Comparison of mean size at birth for compliant newborns and those that contributed only birth measurements

N=882

N=855

Weight (g)

3325

3306

Length (cm)

49.6

49.5

Head circumference (cm)

34.1

34.2

Measurement Complianta

Non-compliant

a 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

Site

Boys

Girls

Total

Brazil

237

243

480

Ghana

684

719

1403

India

840

647

1487

Norway

725

660

1385

Oman

714

724

1438

USA

250

226

476

All 3450 3219 6669

Table 4 Total sample of children in the cross-sectional component by number of visits and total number of records

Site

Brazil

Ghana

India

Norway

Oman

USA

All

One visit

34

1403

1487

1385

1438

55

5802

Two visits

36

0

0

0

0

61

97

Three visits

410

0

0

0

0

360

770

No. of children

480

1403

1487

1385

1438

476

6669

No. of records

1336

1403

1487

1385

1438

1257

8306

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

Boys

LS

%

CS

%

Total

%

Included

9233

99.3

4135

97.2

13 368

98.6

Excluded Lower

11

0.1

2

0.1

13

0.1

Upper

56

0.6

116

2.7

172

1.3

Total

9300

100.0

4253

100.0

13 553

100.0

Girls

LS

%

CS

%

Total

%

Included

9740

99.6

3886

97.2

13 626

98.9

Excluded Lower

7

0.1

3

0.1

10

0.1

Upper

35

0.3

110

2.7

145

1.0

Total

9782

100.0

3999

100.0

13 781

100.0

LS, Longitudinal study; CS, Cross-sectional study.

Methodology 7

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

Indicator

Girls

Boys

Total

Weight-for-length/height

13 623

13 362

26 985

Weight-for-age

14 056

13 797

27 853

Length/height-for-age

13 783

13 551

27 334

BMI-for-age

13 623

13 362

26 985

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 — µ (for the median), σ (coefficient of variation), ν (Box-Cox transformation power) and τ (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 ν=1 and τ=2, and when ν≠1 and τ=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 τ (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} .div1 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(µ)=n1, df(σ)=n2, df(ν)=n3, df(τ)=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).

Methodology 9

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(λ)=ageλ*, 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 λ for the age power transformation. For this, an arbitrary starting model was used to search for the best age-transformation power (λ) based only on the global deviance values over a preset grid of λ values, since the degrees of freedom remained unchanged. The grid of λ 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.

*ν*=1 or*τ*=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) 2*L*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(µ) and df(σ), both criteria were used in parallel. In cases of disagreement,*AIC*was used to select df(µ) and*GAIC(3)*to select df(σ), 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(ν) and, whenever needed, df(τ). 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 Shape Moment If the worm Then the

Intercept Mean passes above the origin, fitted mean is too small.

passes below the origin, fitted mean is too large.

Slope Variance has a positive slope, fitted variance is too small.

has a negative slope, fitted variance is too large.

Parabola Skewness has a U-shape, fitted distribution is too skew to

the left.

has an inverted U-shape, fitted distribution is too skew to

the 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.

a 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

Methodology 11

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 µ and σ curves, while keeping fixed ν=1 and τ=2 as described in section (a) above. The next step was to fit the ν curve, fixing only τ=2 and using the df(µ) and df(σ) 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 τ 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 (µ, σ and ν).

With df(ν) thus selected (i.e. when ν was not fixed to value 1), a new iteration was done to re-search for df(µ) and df(σ). However, none of the additional iterations indicated any need to change either df(µ) or df(σ). A further iteration was carried out to investigate if it was necessary to change the age- transformation power λ. 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

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 <21

21 to <24

24 to <27

27 to ≤30

18 to ≤30

Sample size

334

354

476

461

1625

Mean (cm)a

0.75

0.69

0.72

0.77

0.73

St Deviation (cm)a

0.61

0.67

0.61

0.61

0.62

a 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.

Length/height-for-age for boys

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.

- 13 -

14 Length/height-for-age, boys

9 Longitudinal sample sizes for length/height-for-age for boys

Visit

Birth

1

2

3

4

5

6

Age

0

2 wk

4 wk

6 wk

2 mo

3 mo

4 mo

N

893

425

424

424

424

420

419

Visit

7

8

9

10

11

12

13

Age

5 mo

6 mo

7 mo

8 mo

9 mo

10 mo

11 mo

N

420

424

420

420

416

411

422

Visit

14

15

16

17

18

19

20

Age

12 mo

14 mo

16 mo

18 mo

20 mo

22 mo

24 mo

N

422

419

418

417

422

418

421

10 Cross-sectional sample sizes for length/height-for-age for boys

Table

Table

Age (mo)

N

<18

3

18–20

177

21–23

185

24–26

238

27–29

263

30–32

232

33–35

259

Age (mo)

36–38

39–41

42–44

45–47

48–50

51–53

54–56

N

273

255

263

244

245

229

234

Age (mo)

57–59

60–62

63–65

66–68

69–71

>71

N

245

236

221

225

221

4

Model selection and results

The model BCPE(x=ageλ, df(µ)=10, df(σ)=6, ν=1, τ=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 λ. Table 11 shows the global deviance for a grid of λ values. The smallest global deviance corresponds to age-transformation power λ=0.35.

Table 11 Global deviance (GD) for models within the class BCPE(x=ageλ, df(µ)=10, df(σ)=6,

ν=1, τ=2) for length/height-for-age for boys

λ

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

GDa

339.9

333.7

329.1

325.6

323.0

321.3

320.8

322.2

326.2

332.6

λ

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

GDa

340.5

347.1

349.4

345.5

337.2

331.4

340.8

383.1

479.1

648.0

a In excess of 65 000

Having chosen the age-transformation power λ=0.35, the search for the best df(µ) and df(σ) followed, comparing models in which the parameters ν and τ had the fixed values 1 and 2, respectively. For this, all possible combinations of df(µ) ranging from 5 to 15 and df(σ) from 2 to 10 were considered. Partial results are presented in Table 12.

Length/height-for-age, boys 15

Table 12 Goodness-of-fit summary for models using the BCPE distribution with fixed ν=1 and

τ=2 for length/height-for-age for boys

df(µ)

df(σ)

GDa

AICa

GAIC(3)a

Total df

4

338.5

364.5

377.5

13

5

330.1

358.1

372.1

14

9

6

326.5

356.5

371.5

15

7

324.5

356.6

372.6

16

8

323.1

357.1

374.1

17

4

332.9

360.9

374.9

14

5

324.5

354.5

369.5

15

10

6

320.8

352.8

368.8

16

7

318.9

352.9

369.9

17

8

317.5

353.5

371.5

18

4

329.8

359.8

374.8

15

5

321.4

353.4

369.4

16

11

6

317.7

351.7

368.7

17

7

315.8

351.8

369.8

18

8

314.4

352.4

371.4

19

4

327.8

359.8

375.8

16

5

319.4

353.4

370.4

17

12

6

315.7

351.7

369.7

18

7

313.8

351.8

370.8

19

8

312.4

352.4

372.4

20

4

326.4

360.4

377.4

17

5

317.9

353.9

371.9

18

13

6

314.2

352.2

371.2

19

7

312.3

352.3

372.3

20

8

311.0

353.0

374.0

21

GD, Global Deviance; AIC, Akaike Information Criterion; GAIC(3), Generalized AIC with penalty equal to 3;

a In excess of 65 000.

The best combination of

*AIC*and*GAIC(3)*corresponds to df(µ)=11 or 12 and df(σ)=6. To select between df(µ)=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(µ)=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(µ) to 12 (Figure 5), and thus the combination of df(µ)=12 and df(σ)=6 was chosen. Further evaluations of this model were carried out by examining the fit of the µ and σ curves and the patterns of the centile residuals (the empirical minus the fitted centiles) across age.16 Length/height-for-age, boys

-3 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

0.0

0.4

46 mo 52 mo 58 mo 64 mo 70 mo

-0.4

0.0

0.4

20 mo 22 mo 24 mo 28 mo 34 mo 40 mo

Deviation

0.0

0.4

-0.4

10 mo 11 mo 12 mo 14 mo 16 mo 18 mo

-0.4

0.0

0.4

4 mo 5 mo 6 mo 7 mo 8 mo 9 mo

0.0

0.4

-0.4

Birth 14 d 28 d 42 d 2 mo 3 mo

-0.4

-3 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

Unit normal quantile

Figure 1 Worm plots of z-scores for candidate model with df(µ)=11 and df(σ)=6 with age transformation age0.35 for length/height-for-age for boys

Model 1: BCPE(x=age0.35, df(µ)=12, df(σ)=6, ν=1, τ=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.

80

90

0.038

Length/height-for-age, boys 17

Height Median (cm)

85 90 95 100 105 110 115

Length Median (cm)

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

24 30 36 42 48 54 60 66 72

Length Coeff of Variation

0.032 0.034 0.036

0 2 4 6 8 10 12 14 16 18 20 22 24

Height Coeff of Variation

0.036 0.038 0.040 0.042 0.044

0.030

24 30 36 42 48 54 60 66 72

Age (months)

Figure 2 Fitting of µ and σ 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

0.2

0.6

3rd Centile

Empirical-Fitted Centile for Length (cm)

-0.6

-0.2

0 2 4 6 8 12 16 20 24

0.2

0.6

25th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

0.2

0.6

90th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

5th Centile

-0.6

-0.2

0.2

0.6

0 2 4 6 8 12 16 20 24

0.2

0.6

50th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

0.2

0.6

95th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

Age (months)

10th Centile

-0.6

-0.2

0.2

0.6

0 2 4 6 8 12 16 20 24

0.2

0.6

75th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

0.2

0.6

97th Centile

-0.6

-0.2

0 2 4 6 8 12 16 20 24

Figure 3 Centile residuals from fitting Model 1 for length/height-for-age

from 0 to 24 months for boys

0.5

1.5

3rd Centile

Empirical-Fitted Centile for Height (cm)

-1.5

-0.5

25 31 37 43 49 55 61 67

0.5

1.5

25th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

0.5

1.5

90th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

5th Centile

-1.5

-0.5

0.5

1.5

25 31 37 43 49 55 61 67

0.5

1.5

50th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

0.5

1.5

95th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

Age (months)

10th Centile

-1.5

-0.5

0.5

1.5

25 31 37 43 49 55 61 67

0.5

1.5

75th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

0.5

1.5

97th Centile

-1.5

-0.5

25 31 37 43 49 55 61 67

Figure 4 Centile residuals from fitting Model 1 for length/height-for-age

from 24 to 71 months for boys

Length/height-for-age, boys 19

-3 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

0.0

0.4

J

, o\

I

6J6 \ I

:,:': \•- -ij- O \

I I I

'

46 mo 52 mo 58 mo \ '64 mo 70 mo

t -.- ..

,. ,

0

,

0 0 q, .

/.,..,,- - - .. \ /.,.- - .. ..'.0

-0.4

, ' ,

' '' ' 0

0'

'0,

'/,,"'1,o - .... - - - - - - •

...,---.....,

'0

202020 mmmooo 222222 momomo 242424 momomo 282828 momomo

0.4

\

\ ,ti'o\0

34 mo ' ' 40 mor0

-0.4 0.0

-- -o

,--··•, 0 , -,

/ ' 0 , '

r \

CIJ: \ I \

I \

10 mo 11 mo , '12 mo 14 mo '

\

16 mo ,

18 mo

Deviation

0.4

\----;'i \

'

'

- --..-:

\

,' I

/ 0

'

''1\;- ..-:.-,'

0.0

,,

1 0c oo llffJI S o'b

0 ,. " , ---. -

' '

0 S

__,'1__.0 "

0 .....- - .....

-0.4

/ ' ' \

' '

--..... rr .....

,,... .. ..,. , o / ..- - - -,

,a,

0 ....... - - ..... ,,o

\

' '

00,-----,,

' \

\

eo,- otfo

0 /

\

*0*/ \' ',o

444 momomo 555 momomo

777 mmmooo

0.4

i\ , ,. ...mr:o

0

.... ' ......

...;

0 ' ' 6 mo 8 mo ,,,, \

9 mo r:,'

S tPoo -

I;.,,. ..-. - ',

,/

- - - .,,... .,,.I ooo_o_ - "o---

0.0

j,,..---...... 0 ,,,, .. -- -,

-0.4

/0 \ / I \ 0

' ''

0.4

'• ,' o', ,l,o {,,

'----- / O ,..,_,..,.o.a.,_o Do

\Birth

\14 d

,' \28 d

,,

,

2 mo ,' /_

*-, r -*--0.0

J

- -_,o.aaJ!'-0- - -C6 - ..JJ ....,,,,:!f,.. - - ho'lf' o o

/ ...-. - - - - ... 0 , ... -- ....., .... ----,

-0.4

,' \ ,' : '\ 0 / \

' '

oo -:w

444222 ddd

3 mo

0 '... , '

'\

'

0 ,.- ..'I'!:"..

/ '

' ' \

'

I I '1 I I

-3 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

Unit normal quantile

Figure 5 Worm plots of z-scores for Model 1 for length/height-for-age for boys

20

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

Expected

Birth

14 d

28 d

42 d

2 mo

3 mo

4 mo

5 mo

6 mo

7 mo

1

0.7

0.5

0.7

1.2

0.2

1.2

1.0

0.5

0.5

0.7

3

2.0

2.9

3.0

2.6

4.0

2.9

2.6

2.4

3.1

4.6

5

5.2

6.4

4.4

4.0

5.7

5.0

4.1

4.1

5.5

5.6

10

11.1

11.7

10.3

9.0

9.7

9.3

8.2

10.1

8.6

10.7

25

25.5

25.5

24.6

24.6

24.1

22.9

24.5

24.3

24.6

22.6

50

48.9

55.1

51.8

52.7

54.2

51.9

50.5

49.5

50.6

49.4

75

74.4

74.5

74.0

74.0

76.2

75.0

74.0

75.0

76.6

78.6

90

88.0

88.8

91.1

89.8

89.2

90.2

90.6

89.7

90.7

91.2

95

94.8

95.0

95.1

94.8

94.8

95.2

94.2

94.0

94.7

94.2

97

97.4

96.9

97.0

96.5

96.9

96.7

95.7

95.0

97.1

96.1

99

99.4

98.3

98.8

98.8

98.6

98.6

97.8

98.3

98.8

98.8

Expected

8 mo

9 mo

10 mo

11 mo

12 mo

14 mo

16 mo

18 mo

20 mo

22 mo

1

0.9

1.0

1.5

1.7

1.2

1.7

1.2

1.4

1.2

0.7

3

4.7

3.8

3.7

3.2

3.4

4.0

4.6

3.2

3.1

2.6

5

6.4

5.8

5.7

4.7

6.0

5.5

5.8

4.3

4.8

3.6

10

10.6

10.3

10.1

9.0

9.4

10.2

11.1

7.0

10.4

9.3

25

22.4

23.1

24.0

23.9

24.7

23.5

25.5

24.1

26.9

22.8

50

52.1

50.8

49.9

50.8

49.6

49.4

50.0

50.7

51.1

49.2

75

75.5

77.9

72.6

72.0

75.3

72.9

75.2

73.9

75.6

74.5

90

91.0

91.2

89.4

91.4

90.6

89.3

92.5

92.1

90.8

90.5

95

96.0

95.7

95.8

95.1

96.4

94.1

95.9

95.5

95.6

95.3

97

97.2

96.2

96.8

97.2

97.6

97.9

96.9

97.5

97.3

97.1

99

99.1

98.0

98.8

98.9

99.0

99.5

98.6

99.1

99.2

99.6

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)

Expected

24 mo

28 mo

34 mo

40 mo

46 mo

52 mo

58 mo

64 mo

70 mo

Overall

1

1.2

0.4

1.3

1.0

0.8

1.2

0.4

1.5

0.7

1.0

3

4.0

3.1

2.3

2.1

1.7

3.9

3.2

3.4

2.4

3.1

5

5.2

4.8

5.3

4.4

3.6

5.5

5.7

4.2

5.1

5.0

10

11.5

10.2

10.4

10.7

9.0

10.1

11.5

9.1

8.8

10.0

25

25.3

23.1

24.3

26.7

22.8

22.3

26.3

25.9

22.1

24.3

50

50.9

48.8

50.7

56.0

50.7

49.3

52.4

52.2

45.9

50.9

75

75.5

71.5

75.1

75.6

74.8

75.1

75.3

75.8

70.7

74.8

90

91.2

89.4

89.5

89.7

91.4

91.7

91.1

88.2

87.1

90.2

95

94.9

95.0

94.2

94.5

95.2

96.1

96.0

94.9

95.6

95.1

97

97.6

96.5

95.9

96.2

97.1

97.8

97.4

96.6

98.0

96.9

99

99.5

98.8

97.6

97.7

98.7

99.4

99.4

99.2

100.0

98.9

21

Note: Group labels correspond to the age intervals in Table 14.

22 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(µ)=12, df(σ)=6, ν=1, τ=2)] for length/height-for-age for boys

Age (days)

Group

N

z1

z2

z3

z4

0

Birth

893

0.21

-0.30

0.07

-2.24

1 to 16

14 d

419

-0.46

1.02

1.29

0.08

17 to 34

28 d

427

-0.21

0.08

0.39

0.24

35 to 49

42 d

423

0.01

0.23

0.29

1.25

50 to 69

2 mo

424

-0.25

-0.15

1.12

0.80

70 to 99

3 mo

420

0.11

-0.28

1.09

1.38

100 to 129

4 mo

416

0.75

0.65

1.15

0.72

130 to 159

5 mo

416

0.27

0.23

1.73

-0.07

160 to 189

6 mo

419

-0.02

-0.62

0.57

0.16

190 to 219

7 mo

411

-0.36

-0.01

0.16

0.30

220 to 249

8 mo

424

-0.30

-0.16

-0.74

0.23

250 to 279

9 mo

398

-0.38

-0.14

0.69

0.91

280 to 309

10 mo

405

0.49

0.18

-0.54

0.12

310 to 349

11 mo

465

0.29

-0.18

-0.83

-0.42

350 to 379

12 mo

417

-0.34

-0.36

-1.02

-0.41

380 to 439

14 mo

421

0.21

0.37

-1.04

0.13

440 to 499

16 mo

416

-0.28

-0.02

-0.59

1.51

500 to 559

18 mo

444

0.00

-0.96

-0.15

1.69

560 to 619

20 mo

521

-0.23

0.09

-0.60

1.81

620 to 679

22 mo

549

0.51

-0.92

-1.05

0.83

680 to 749

24 mo

593

-0.96

0.04

-0.81

-0.23

750 to 929

28 mo

480

1.02

0.15

0.63

0.11

930 to 1119

34 mo

531

0.27

1.52

0.29

1.37

1120 to 1309

40 mo

525

-0.52

1.46

3.55

1.82

1310 to 1499

46 mo

523

0.37

-0.62

2.01

1.47

1500 to 1689

52 mo

507

-0.12

-0.72

-1.47

-0.32

1690 to 1879

58 mo

494

-1.04

-0.38

0.09

-2.07

1880 to 2069

64 mo

475

-0.13

0.46

0.36

0.48

2070 to 2249

70 mo

295

1.39

-0.25

-1.86

-1.23

Overall Q stats

13 551

7.76

10.07

38.51

33.73

degrees of freedom

17.0

25.5

29.0

29.0

p-value

0.9714

0.9972

0.1113

0.2494

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 τ=2 and modelling the other three parameters was considered. The degrees of freedom of the cubic splines for µ and σ 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 ν was then sought.

Length/height-for-age, boys 23

Table 15 Goodness-of-fit summary for models BCPE(x=age0.35, df(µ)=12, df(σ)=6, df(ν)=?, τ=2) for length/height-for-age for boys

df(ν)

GDa

GAIC(3)a

Total df

3

312.1

375.1

21

4

307.4

373.4

22

5

301.4

370.4

23

6

297.0

369.0

24

7

294.4

369.4

25

8 292.7 370.7 26

GD, Global Deviance; GAIC(3), Generalized Akaike Information Criterion with penalty equal to 3;

a 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(ν)=6 presented the best fit, so the corresponding model was selected for further evaluation.Model 2: BCPE(x=age0.35, df(µ)=12, df(σ)=6, df(ν)=6, τ=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 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

0.0

0.4

46 mo 52 mo 58 mo 64 mo 70 mo

-0.4

0.4

20 mo 22 mo 24 mo 28 mo 34 mo 40 mo

Deviation

0.0

0.4

-0.4 0.0

10 mo 11 mo 12 mo 14 mo 16 mo 18 mo

-0.4

0.4

4 mo 5 mo 6 mo 7 mo 8 mo 9 mo

0.0

0.4

-0.4 0.0

Birth 14 d 28 d 42 d 2 mo 3 mo

-0.4

-3 -1 1 2 3 -3 -1 1 2 3 -3 -1 1 2 3

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 ν=1 and τ=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 ν 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(µ) and df(σ) equal to 12 and 6, respectively, to re-search the best age-transformation power λ. The smallest global deviance in this case was for λ=0.4 (GD=65 315.6), but with only a very minor difference from the model using λ=0.35 (GD=65 315.7). There was thus no need for updating λ, and the selected model for constructing the length/height-for-age growth curves for boys remained BCPE(x= age0.35, df(µ)=12, df(σ)=6, ν=1, τ=2).

Length/height-for-age, boys 25

Table 16 Q-test for z-scores from Model 2 [BCPE(x=age0.35, df(µ)=12, df(σ)=6, df(ν)=6, τ=2)] for length/height-for-age for boys

Age (days)

Group

N

z1

z2

z3

z4

0

Birth

893

0.21

-0.30

-0.20

-2.24

1 to 16

14 d

419

-0.43

1.00

0.56

-0.03

17 to 34

28 d

427

-0.19

0.10

-0.41

0.38

35 to 49

42 d

423

0.02

0.26

-0.67

1.53

50 to 69

2 mo

424

-0.25

-0.15

0.24

0.76

70 to 99

3 mo

420

0.11

-0.29

0.19

1.27

100 to 129

4 mo

416

0.75

0.61

0.40

0.65

130 to 159

5 mo

416

0.26

0.20

1.23

-0.21

160 to 189

6 mo

419

-0.02

-0.60

0.23

0.10

190 to 219

7 mo

411

-0.37

0.01

-0.02

0.29

220 to 249

8 mo

424

-0.30

-0.14

-0.76

0.24

250 to 279

9 mo

398

-0.38

-0.13

0.82

0.94

280 to 309

10 mo

405

0.49

0.19

-0.30

0.12

310 to 349

11 mo

465

0.30

-0.18

-0.50

-0.48

350 to 379

12 mo

417

-0.35

-0.39

-0.64

-0.46

380 to 439

14 mo

421

0.22

0.35

-0.54

0.03

440 to 499

16 mo

416

-0.28

-0.04

0.01

1.56

500 to 559

18 mo

444

-0.01

-0.95

0.40

1.72

560 to 619

20 mo

521

-0.22

0.09

-0.08

1.78

620 to 679

22 mo

549

0.53

-0.91

-0.76

0.72

680 to 749

24 mo

593

-0.93

0.05

-0.70

-0.25

750 to 929

28 mo

480

1.07

0.16

0.35

0.04

930 to 1119

34 mo

531

0.30

1.59

-0.70

1.63

1120 to 1309

40 mo

525

-0.54

1.34

2.41

1.30

1310 to 1499

46 mo

523

0.35

-0.67

1.03

1.10

1500 to 1689

52 mo

507

-0.13

-0.63

-1.90

-0.18

1690 to 1879

58 mo

494

-1.06

-0.34

0.07

-2.06

1880 to 2069

64 mo

475

-0.12

0.46

0.84

0.43

2070 to 2249

70 mo

295

1.42

-0.29

-1.34

-1.65

Overall Q stats

13 551

7.94

9.80

19.92

33.53

degrees of freedom

17.0

25.5

23.0

29.0

p-value

0.9678

0.9978

0.6468

0.2568

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.

26

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

Expected

Birth

14 d

28 d

42 d

2 mo

3 mo

4 mo

5 mo

6 mo

7 mo

1

0.7

1.0

0.7

1.2

0.2

1.4

1.4

1.0

0.5

0.7

3

2.0

3.1

3.0

2.8

4.0

2.9

2.9

2.6

3.8

4.6

5

5.2

6.4

4.7

4.5

6.4

5.0

4.1

4.3

6.0

6.1

10

11.1

12.2

10.5

9.5

9.7

9.3

8.7

10.1

8.6

10.7

25

25.5

25.3

24.1

24.3

23.8

22.6

23.6

24.3

24.6

22.4

50

48.9

55.1

51.3

52.2

53.8

51.7

50.2

49.0

50.6

49.4

75

74.4

74.5

73.5

73.3

75.9

75.0

73.6

75.0

76.6

78.6

90

88.0

89.0

91.3

90.3

89.4

90.2

90.9

89.7

90.7

91.2

95

95.3

95.2

95.1

95.0

95.0

95.2

94.2

94.2

94.7

94.2

97

97.6

96.9

97.0

96.5

97.4

96.7

95.9

95.4

97.4

96.4

99

99.4

98.3

99.1

99.1

98.6

99.0

98.3

98.3

98.8

98.8

Expected

8 mo

9 mo

10 mo

11 mo

12 mo

14 mo

16 mo

18 mo

20 mo

22 mo

1

0.9

1.0

1.2

1.5

1.2

1.7

1.2

1.4

1.2

0.5

3

4.7

3.5

3.7

3.2

2.9

3.8

4.3

3.2

2.9

2.6

5

6.4

5.8

5.7

4.7

5.5

5.2

5.8

4.3

4.8

3.6

10

10.6

10.3

10.1

8.8

9.4

10.2

11.1

7.0

10.4

9.3

25

22.4

23.1

24.2

24.3

24.7

24.2

25.5

24.5

26.9

22.8

50

52.1

51.0

49.9

50.8

50.1

50.1

50.5

51.1

51.1

49.4

75

75.5

77.9

72.8

72.3

75.5

72.9

75.5

74.1

75.6

74.5

90

91.0

91.2

89.4

91.4

90.6

89.1

92.5

91.7

90.8

90.5

95

96.0

95.7

95.8

95.1

96.2

93.8

95.9

95.5

95.6

95.1

97

97.2

96.2

96.8

97.2

97.4

97.6

96.9

97.5

97.3

97.1

99

99.1

98.0

98.8

98.9

99.0

99.5

98.6

99.1

99.2

99.6

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)

Expected

24 mo

28 mo

34 mo

40 mo

46 mo

52 mo

58 mo

64 mo

70 mo

Overall

1

1.2

0.4

1.3

1.3

0.8

1.2

0.4

1.3

0.7

1.0

3

4.0

3.1

2.6

2.1

1.9

3.9

3.2

3.4

2.4

3.2

5

5.2

4.8

5.5

4.6

4.6

5.5

5.7

4.2

5.1

5.1

10

11.5

10.2

10.4

10.9

9.2

10.3

11.5

9.1

8.5

10.0

25

25.3

22.7

24.1

25.9

22.8

22.3

26.7

26.1

22.4

24.3

50

50.9

47.7

49.9

55.2

50.5

48.9

52.4

52.2

46.9

50.8

75

75.5

71.5

74.8

75.2

74.2

75.1

75.3

76.0

71.1

74.7

90

91.2

89.4

89.5

89.9

91.4

91.7

91.1

88.2

87.1

90.3

95

94.8

95.0

94.4

94.7

95.8

96.3

96.0

94.5

95.2

95.2

97

97.6

96.7

96.2

96.2

97.3

98.0

97.2

96.4

98.0

97.0

99

99.5

98.8

97.7

97.9

98.7

99.4

99.2

99.2

100.0

98.9

27

Note: Group labels correspond to the age intervals in Table 16.

60

80

90

Fitted

50

Empirical

0 2 4 6 8 10 12 14 16 18 20 22 24

Age (months)

97th 90th

28

50th

Length (cm)

70

10th 3rd

Length/height-for-age, boys

Figure 7 3rd, 10th, 50th, 90th, 97th smoothed centile curves and empirical values: length-for-age for boys

from birth to 24 months

50

60

90

Fitted Empirical

0 2 4 6 8 10 12 14 16 18 20 22 24

Age (months)

95th

Length/height-for-age, boys

75th 50th 25th

Length (cm)

70

80

5th

Figure 8 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: length-for-age for boys

29

from birth to 24 months

Height (cm)

80

90

110

120

Fitted Empirical

97th 90th

30

50th

100

10th 3rd

Length/height-for-age, boys

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

Height (cm)

80

90

110

120

Fitted Empirical

95th

Length/height-for-age, boys

75th 50th 25th

100

5th

24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72

Age (months)

Figure 10 5th, 25th, 50th, 75th, 95th smoothed centile curves and empirical values: height-for-age for boys

31

from 24 to 71 months

32 Length/height-for-age, boys

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

14) 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.

Length (cm)

70

60

80

90

Charts

Length/height-for-age, boys

3

2

1

0

-1

-2

-3

50

0 2 4 6 8 10 12 14 16 18 20 22 24

Age (months)

33

Figure 11 WHO length-for-age z-scores for boys from birth to 24 months

34

3

120

2

1

110

0

Height (cm)

100

-1

-2

90

-3

Length/height-for-age, boys

80

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

50

60

80

90

0 2 4 6 8 10 12 14 16 18 20 22 24

Age (months)

35

Figure 13 WHO length-for-age percentiles for boys from birth to 24 months

97th 85th

Length/height-for-age, boys

50th

Length (cm)

70

15th 3rd

Length/height-for-age, boys

Height (cm)

100

80

110

120

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

97th 85th

36

50th

90

15th 3rd

Length/height-for-age, boys

Tables

Table 18 Length-for-age for boys, age in weeks

37

Percentiles (length in cm)

Week

L

M

S

SD

1st

3rd

5th

15th

25th

50th

75th

85th

95th

97th

99th

0

1

49.8842

0.03795

1.8931

45.5

46.3

46.8

47.9

48.6

49.9

51.2

51.8

53.0

53.4

54.3

1

1

51.1152

0.03723

1.9030

46.7

47.5

48.0

49.1

49.8

51.1

52.4

53.1

54.2

54.7

55.5

2

1

52.3461

0.03652

1.9117

47.9

48.8

49.2

50.4

51.1

52.3

53.6

54.3

55.5

55.9

56.8

3

1

53.3905

0.03609

1.9269

48.9

49.8

50.2

51.4

52.1

53.4

54.7

55.4

56.6

57.0

57.9

4

1

54.3881

0.03570

1.9417

49.9

50.7

51.2

52.4

53.1

54.4

55.7

56.4

57.6

58.0

58.9

5

1

55.3374

0.03534

1.9556

50.8

51.7

52.1

53.3

54.0

55.3

56.7

57.4

58.6

59.0

59.9

6

1

56.2357

0.03501

1.9688

51.7

52.5

53.0

54.2

54.9

56.2

57.6

58.3

59.5

59.9

60.8

7

1

57.0851

0.03470

1.9809

52.5

53.4

53.8

55.0

55.7

57.1

58.4

59.1

60.3

60.8

61.7

8

1

57.8889

0.03442

1.9925

53.3

54.1

54.6

55.8

56.5

57.9

59.2

60.0

61.2

61.6

62.5

9

1

58.6536

0.03416

2.0036

54.0

54.9

55.4

56.6

57.3

58.7

60.0

60.7

61.9

62.4

63.3

10

1

59.3872

0.03392

2.0144

54.7

55.6

56.1

57.3

58.0

59.4

60.7

61.5

62.7

63.2

64.1

11

1

60.0894

0.03369

2.0244

55.4

56.3

56.8

58.0

58.7

60.1

61.5

62.2

63.4

63.9

64.8

12

1

60.7605

0.03348

2.0343

56.0

56.9

57.4

58.7

59.4

60.8

62.1

62.9

64.1

64.6

65.5

13

1

61.4013

0.03329

2.0440

56.6

57.6

58.0

59.3

60.0

61.4

62.8

63.5

64.8

65.2

66.2

38

Table 18 Length-for-age for boys, age in weeks (continued)

Length/height-for-age, boys

Z-scores (length in cm)

Week

L

M

S

SD

-3 SD

-2 SD

-1 SD

Median

1 SD

2 SD

3 SD

0

1

49.8842

0.03795

1.8931

44.2

46.1

48.0

49.9

51.8

53.7

55.6

1

1

51.1152

0.03723

1.9030

45.4

47.3

49.2

51.1

53.0

54.9

56.8

2

1

52.3461

0.03652

1.9117

46.6

48.5

50.4

52.3

54.3

56.2

58.1

3

1

53.3905

0.03609

1.9269

47.6

49.5

51.5

53.4

55.3

57.2

59.2

4

1

54.3881

0.03570

1.9417

48.6

50.5

52.4

54.4

56.3

58.3

60.2

5

1

55.3374

0.03534

1.9556

49.5

51.4

53.4

55.3

57.3

59.2

61.2

6

1

56.2357

0.03501

1.9688

50.3

52.3

54.3

56.2

58.2

60.2

62.1

7

1

57.0851

0.03470

1.9809

51.1

53.1

55.1

57.1

59.1

61.0

63.0

8

1

57.8889

0.03442

1.9925

51.9

53.9

55.9

57.9

59.9

61.9

63.9

9

1

58.6536

0.03416

2.0036

52.6

54.6

56.6

58.7

60.7

62.7

64.7

10

1

59.3872

0.03392

2.0144

53.3

55.4

57.4

59.4

61.4

63.4

65.4

11

1

60.0894

0.03369

2.0244

54.0

56.0

58.1

60.1

62.1

64.1

66.2

12

1

60.7605

0.03348

2.0343

54.7

56.7

58.7

60.8

62.8

64.8

66.9

13

1

61.4013

0.03329

2.0440

55.3

57.3

59.4

61.4

63.4

65.5

67.5

Length/height-for-age, boys

Table 19 Length-for-age for boys, age in years and months

39

Percentiles (length in cm)

Year: Month

Month

L

M

S

SD

1st

3rd

5th

15th

25th

50th

75th

85th

95th

97th

99th

0: 0

0

1

49.8842

0.03795

1.8931

45.5

46.3

46.8

47.9

48.6

49.9

51.2

51.8

53.0

53.4

54.3

0: 1

1

1

54.7244

0.03557

1.9465

50.2

51.1

51.5

52.7

53.4

54.7

56.0

56.7

57.9

58.4

59.3

0: 2

2

1

58.4249

0.03424

2.0005

53.8

54.7

55.1

56.4

57.1

58.4

59.8

60.5

61.7

62.2

63.1

0: 3

3

1

61.4292

0.03328

2.0444

56.7

57.6

58.1

59.3

60.1

61.4

62.8

63.5

64.8

65.3

66.2

0: 4

4

1

63.8860

0.03257

2.0808

59.0

60.0

60.5

61.7

62.5

63.9

65.3

66.0

67.3

67.8

68.7

0: 5

5

1

65.9026

0.03204

2.1115

61.0

61.9

62.4

63.7

64.5

65.9

67.3

68.1

69.4

69.9

70.8

0: 6

6

1

67.6236

0.03165

2.1403

62.6

63.6

64.1

65.4

66.2

67.6

69.1

69.8

71.1

71.6

72.6

0: 7

7

1

69.1645

0.03139

2.1711

64.1

65.1

65.6

66.9

67.7

69.2

70.6

71.4

72.7

73.2

74.2

0: 8

8

1

70.5994

0.03124

2.2055

65.5

66.5

67.0

68.3

69.1

70.6

72.1

72.9

74.2

74.7

75.7

0: 9

9

1

71.9687

0.03117

2.2433

66.8

67.7

68.3

69.6

70.5

72.0

73.5

74.3

75.7

76.2

77.2

0:10

10

1

73.2812

0.03118

2.2849

68.0

69.0

69.5

70.9

71.7

73.3

74.8

75.6

77.0

77.6

78.6

0:11

11

1

74.5388

0.03125

2.3293

69.1

70.2

70.7

72.1

73.0

74.5

76.1

77.0

78.4

78.9

80.0

1: 0

12

1

75.7488

0.03137

2.3762

70.2

71.3

71.8

73.3

74.1

75.7

77.4

78.2

79.7

80.2

81.3

1: 1

13

1

76.9186

0.03154

2.4260

71.3

72.4

72.9

74.4

75.3

76.9

78.6

79.4

80.9

81.5

82.6

1: 2

14

1

78.0497

0.03174

2.4773

72.3

73.4

74.0

75.5

76.4

78.0

79.7

80.6

82.1

82.7

83.8

1: 3

15

1

79.1458

0.03197

2.5303

73.3

74.4

75.0

76.5

77.4

79.1

80.9

81.8

83.3

83.9

85.0

1: 4

16

1

80.2113

0.03222

2.5844

74.2

75.4

76.0

77.5

78.5

80.2

82.0

82.9

84.5

85.1

86.2

1: 5

17

1

81.2487

0.03250

2.6406

75.1

76.3

76.9

78.5

79.5

81.2

83.0

84.0

85.6

86.2

87.4

1: 6

18

1

82.2587

0.03279

2.6973

76.0

77.2

77.8

79.5

80.4

82.3

84.1

85.1

86.7

87.3

88.5

1: 7

19

1

83.2418

0.03310

2.7553

76.8

78.1

78.7

80.4

81.4

83.2

85.1

86.1

87.8

88.4

89.7

1: 8

20

1

84.1996

0.03342

2.8140

77.7

78.9

79.6

81.3

82.3

84.2

86.1

87.1

88.8

89.5

90.7

1: 9

21

1

85.1348

0.03376

2.8742

78.4

79.7

80.4

82.2

83.2

85.1

87.1

88.1

89.9

90.5

91.8

1:10

22

1

86.0477

0.03410

2.9342

79.2

80.5

81.2

83.0

84.1

86.0

88.0

89.1

90.9

91.6

92.9

1:11

23

1

86.9410

0.03445

2.9951

80.0

81.3

82.0

83.8

84.9

86.9

89.0

90.0

91.9

92.6

93.9

2: 0

24

1

87.8161

0.03479

3.0551

80.7

82.1

82.8

84.6

85.8

87.8

89.9

91.0

92.8

93.6

94.9

40

Table 19 Length-for-age for boys, age in years and months (continued)

Length/height-for-age, boys

Z-scores (length in cm)

Year: Month

Month

L

M

S

SD

-3 SD

-2 SD

-1 SD

Median

1 SD

2 SD

3 SD

0: 0

0

1

49.8842

0.03795

1.8931

44.2

46.1

48.0

49.9

51.8

53.7

55.6

0: 1

1

1

54.7244

0.03557

1.9465

48.9

50.8

52.8

54.7

56.7

58.6

60.6

0: 2

2

1

58.4249

0.03424

2.0005

52.4

54.4

56.4

58.4

60.4

62.4

64.4

0: 3

3

1

61.4292

0.03328

2.0444

55.3

57.3

59.4

61.4

63.5

65.5

67.6

0: 4

4

1

63.8860

0.03257

2.0808

57.6

59.7

61.8

63.9

66.0

68.0

70.1

0: 5

5

1

65.9026

0.03204

2.1115

59.6

61.7

63.8

65.9

68.0

70.1

72.2

0: 6

6

1

67.6236

0.03165

2.1403

61.2

63.3

65.5

67.6

69.8

71.9

74.0

0: 7

7

1

69.1645

0.03139

2.1711

62.7

64.8

67.0

69.2

71.3

73.5

75.7

0: 8

8

1

70.5994

0.03124

2.2055

64.0

66.2

68.4

70.6

72.8

75.0

77.2

0: 9

9

1

71.9687

0.03117

2.2433

65.2

67.5

69.7

72.0

74.2

76.5

78.7

0:10

10

1

73.2812

0.03118

2.2849

66.4

68.7

71.0

73.3

75.6

77.9

80.1

0:11

11

1

74.5388

0.03125

2.3293

67.6

69.9

72.2

74.5

76.9

79.2

81.5

1: 0

12

1

75.7488

0.03137

2.3762

68.6

71.0

73.4

75.7

78.1

80.5

82.9

1: 1

13

1

76.9186

0.03154

2.4260

69.6

72.1

74.5

76.9

79.3

81.8

84.2

1: 2

14

1

78.0497

0.03174

2.4773

70.6

73.1

75.6

78.0

80.5

83.0

85.5

1: 3

15

1

79.1458

0.03197

2.5303

71.6

74.1

76.6

79.1

81.7

84.2

86.7

1: 4

16

1

80.2113

0.03222

2.5844

72.5

75.0

77.6

80.2

82.8

85.4

88.0

1: 5

17

1

81.2487

0.03250

2.6406

73.3

76.0

78.6

81.2

83.9

86.5

89.2

1: 6

18

1

82.2587

0.03279

2.6973

74.2

76.9

79.6

82.3

85.0

87.7

90.4

1: 7

19

1

83.2418

0.03310

2.7553

75.0

77.7

80.5

83.2

86.0

88.8

91.5

1: 8

20

1

84.1996

0.03342

2.8140

75.8

78.6

81.4

84.2

87.0

89.8

92.6

1: 9

21

1

85.1348

0.03376

2.8742

76.5

79.4

82.3

85.1

88.0

90.9

93.8

1:10

22

1

86.0477

0.03410

2.9342

77.2

80.2

83.1

86.0

89.0

91.9

94.9

1:11

23

1

86.9410

0.03445

2.9951

78.0

81.0

83.9

86.9

89.9

92.9

95.9

2: 0

24

1

87.8161

0.03479

3.0551

78.7

81.7

84.8

87.8

90.9

93.9

97.0

Length/height-for-age, boys

Table 20 Height-for age for boys, age in years and months

41

Percentiles (height in cm)

Year: Month

Month

L

M

S

SD

1st

3rd

5th

15th

25th

50th

75th

85th

95th

97th

99th

2: 0

24

1

87.1161

0.03507

3.0551

80.0

81.4

82.1

83.9

85.1

87.1

89.2

90.3

92.1

92.9

94.2

2: 1

25

1

87.9720

0.03542

3.1160

80.7

82.1

82.8

84.7

85.9

88.0

90.1

91.2

93.1

93.8

95.2

2: 2

26

1

88.8065

0.03576

3.1757

81.4

82.8

83.6

85.5

86.7

88.8

90.9

92.1

94.0

94.8

96.2

2: 3

27

1

89.6197

0.03610

3.2353

82.1

83.5

84.3

86.3

87.4

89.6

91.8

93.0

94.9

95.7

97.1

2: 4

28

1

90.4120

0.03642

3.2928

82.8

84.2

85.0

87.0

88.2

90.4

92.6

93.8

95.8

96.6

98.1

2: 5

29

1

91.1828

0.03674

3.3501

83.4

84.9

85.7

87.7

88.9

91.2

93.4

94.7

96.7

97.5

99.0

2: 6

30

1

91.9327

0.03704

3.4052

84.0

85.5

86.3

88.4

89.6

91.9

94.2

95.5

97.5

98.3

99.9

2: 7

31

1

92.6631

0.03733

3.4591

84.6

86.2

87.0

89.1

90.3

92.7

95.0

96.2

98.4

99.2

100.7

2: 8

32

1

93.3753

0.03761

3.5118

85.2

86.8

87.6

89.7

91.0

93.4

95.7

97.0

99.2

100.0

101.5

2: 9

33

1

94.0711

0.03787

3.5625

85.8

87.4

88.2

90.4

91.7

94.1

96.5

97.8

99.9

100.8

102.4

2:10

34

1

94.7532

0.03812

3.6120

86.4

88.0

88.8

91.0

92.3

94.8

97.2

98.5

100.7

101.5

103.2

2:11

35

1

95.4236

0.03836

3.6604

86.9

88.5

89.4

91.6

93.0

95.4

97.9

99.2

101.4

102.3

103.9

3: 0

36

1

96.0835

0.03858

3.7069

87.5

89.1

90.0

92.2

93.6

96.1

98.6

99.9

102.2

103.1

104.7

3: 1

37

1

96.7337

0.03879

3.7523

88.0

89.7

90.6

92.8

94.2

96.7

99.3

100.6

102.9

103.8

105.5

3: 2

38

1

97.3749

0.03900

3.7976

88.5

90.2

91.1

93.4

94.8

97.4

99.9

101.3

103.6

104.5

106.2

3: 3

39

1

98.0073

0.03919

3.8409

89.1

90.8

91.7

94.0

95.4

98.0

100.6

102.0

104.3

105.2

106.9

3: 4

40

1

98.6310

0.03937

3.8831

89.6

91.3

92.2

94.6

96.0

98.6

101.3

102.7

105.0

105.9

107.7

3: 5

41

1

99.2459

0.03954

3.9242

90.1

91.9

92.8

95.2

96.6

99.2

101.9

103.3

105.7

106.6

108.4

3: 6

42

1

99.8515

0.03971

3.9651

90.6

92.4

93.3

95.7

97.2

99.9

102.5

104.0

106.4

107.3

109.1

3: 7

43

1

100.4485

0.03986

4.0039

91.1

92.9

93.9

96.3

97.7

100.4

103.1

104.6

107.0

108.0

109.8

3: 8

44

1

101.0374

0.04002

4.0435

91.6

93.4

94.4

96.8

98.3

101.0

103.8

105.2

107.7

108.6

110.4

3: 9

45

1

101.6186

0.04016

4.0810

92.1

93.9

94.9

97.4

98.9

101.6

104.4

105.8

108.3

109.3

111.1

3:10

46

1

102.1933

0.04031

4.1194

92.6

94.4

95.4

97.9

99.4

102.2

105.0

106.5

109.0

109.9

111.8

3:11

47

1

102.7625

0.04045

4.1567

93.1

94.9

95.9

98.5

100.0

102.8

105.6

107.1

109.6

110.6

112.4

4: 0

48

1

103.3273

0.04059

4.1941

93.6

95.4

96.4

99.0

100.5

103.3

106.2

107.7

110.2

111.2

113.1

42

Table 20 Height-for age for boys, age in years and months (continued)

Length/height-for-age, boys

Percentiles (height in cm)

Year: Month

Month

L

M

S

SD

1st

3rd

5th

15th

25th

50th

75th

85th

95th

97th

99th

4: 1

49

1

103.8886

0.04073

4.2314

94.0

95.9

96.9

99.5

101.0

103.9

106.7

108.3

110.8

111.8

113.7

4: 2

50

1

104.4473

0.04086

4.2677

94.5

96.4

97.4

100.0

101.6

104.4

107.3

108.9

111.5

112.5

114.4

4: 3

51

1

105.0041

0.04100

4.3052

95.0

96.9

97.9

100.5

102.1

105.0

107.9

109.5

112.1

113.1

115.0

4: 4

52

1

105.5596

0.04113

4.3417

95.5

97.4

98.4

101.1

102.6

105.6

108.5

110.1

112.7

113.7

115.7

4: 5

53

1

106.1138

0.04126

4.3783

95.9

97.9

98.9

101.6

103.2

106.1

109.1

110.7

113.3

114.3

116.3

4: 6

54

1

106.6668

0.04139

4.4149

96.4

98.4

99.4

102.1

103.7

106.7

109.6

111.2

113.9

115.0

116.9

4: 7

55

1

107.2188

0.04152

4.4517

96.9

98.8

99.9

102.6

104.2

107.2

110.2

111.8

114.5

115.6

117.6

4: 8

56

1

107.7697

0.04165

4.4886

97.3

99.3

100.4

103.1

104.7

107.8

110.8

112.4

115.2

116.2

118.2

4: 9

57

1

108.3198

0.04177

4.5245

97.8

99.8

100.9

103.6

105.3

108.3

111.4

113.0

115.8

116.8

118.8

4:10

58

1

108.8689

0.04190

4.5616

98.3

100.3

101.4

104.1

105.8

108.9

111.9

113.6

116.4

117.4

119.5

4:11

59

1

109.4170

0.04202

4.5977

98.7

100.8

101.9

104.7

106.3

109.4

112.5

114.2

117.0

118.1

120.1

5: 0

60

1

109.9638

0.04214

4.6339

99.2

101.2

102.3

105.2

106.8

110.0

113.1

114.8

117.6

118.7

120.7

Length/height-for-age, boys

Table 20 Height-for-age for boys, age in years and months (continued)

43

Z-scores (height in cm)

Year: Month

Month

L

M

S

SD

-3 SD

-2 SD

-1 SD

Median

1 SD

2 SD

3 SD

2: 0

24

1

87.1161

0.03507

3.0551

78.0

81.0

84.1

87.1

90.2

93.2

96.3

2: 1

25

1

87.9720

0.03542

3.1160

78.6

81.7

84.9

88.0

91.1

94.2

97.3