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 23 months).However,this report presents only the standards based on length or height and weight.Observers working in pairs collected anthropometric data.Each observer independently measured and recorded a complete set of measurements,after which the two compared their readings.If any pair of readings exceeded the maximum allowable difference for a given variable (e.g.weight,100 g;length/height,7 mm),both observers once again independently measured and recorded a second and,if necessary,a third set of readings for the variable(s)in question (de Onis et al.2004c). All study sites used identical measuring equipment.Instruments needed to be highly accurate and precise,yet sturdy and portable to enable them to be carried back and forth on home visits.Length was measured with the portable Harpenden Infantometer(range 30-110 cm,with digit counter readings precise to 1 mm).The Harpenden Portable Stadiometer(range 65-206 cm,digit counter reading)was used for measuring adult and child heights.Portable electronic scales with a taring capability, calibrated to 0.1 kg (i.e.UNICEF Electronic Scale 890 or UNISCALE),were used to measure weight. Length and height were recorded to the last completed unit rather than to the nearest unit.To correct for the systematic negative bias introduced by this practice,0.05 cm (i.e.half of the smallest measurement unit)was added to each measurement before analysis.This correction did not apply to weight,which was rounded off to the nearest 100 g.Full details of the instruments used and how measurements were taken are provided elsewhere(de Onis et al.,2004c). 2.3 Sample description The total sample size for the longitudinal and cross-sectional components from all six sites was 8440 children.A total of 1743 children were enrolled in the longitudinal sample,six of whom were excluded for morbidities affecting growth(4 cases of repeated episodes of diarrhoea,1 case of repeated episodes of malaria,and 1 case of protein-energy malnutrition)leaving a sample of 1737 children (894 boys and 843 girls).Of these,the mothers of 882 children(428 boys and 454 girls) complied fully with the MGRS infant-feeding and no-smoking criteria and completed the follow-up period of 24 months (96%of compliant children completed the 24-month follow-up)(Table 1).The other 855 children contributed only birth measurements,as they either failed to comply with the study's infant-feeding and no-smoking criteria or dropped out before 24 months.The reason for using these measurements was to increase the sample size at birth to minimize the left-edge effect.The size at birth of these 855 children was similar to that of the compliant sample (Table 2).The total number of records for the longitudinal component was 19 900. Table 1 Total sample and number of compliant children in the longitudinal component Site N Compliant Bovs 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 All 1737 428 454 882 a Compliant with infant-feeding and no-smoking criteria and completed the 24-month follow-up
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). 2.3 Sample description The total sample size for the longitudinal and cross-sectional components from all six sites was 8440 children. A total of 1743 children were enrolled in the longitudinal sample, six of whom were excluded for morbidities affecting growth (4 cases of repeated episodes of diarrhoea, 1 case of repeated episodes of malaria, and 1 case of protein-energy malnutrition) leaving a sample of 1737 children (894 boys and 843 girls). Of these, the mothers of 882 children (428 boys and 454 girls) complied fully with the MGRS infant-feeding and no-smoking criteria and completed the follow-up period of 24 months (96% of compliant children completed the 24-month follow-up) (Table 1). The other 855 children contributed only birth measurements, as they either failed to comply with the study's infant-feeding and no-smoking criteria or dropped out before 24 months. The reason for using these measurements was to increase the sample size at birth to minimize the left-edge effect. The size at birth of these 855 children was similar to that of the compliant sample (Table 2). The total number of records for the longitudinal component was 19 900. Table 1 Total sample and number of compliant children in the longitudinal component Complianta Site N 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 All 1737 428 454 882 a Compliant with infant-feeding and no-smoking criteria and completed the 24-month follow-up
Methodology Table 2 Comparison of mean size at birth for compliant newborns and those that contributed only birth measurements Non-compliant Measurement Compliant" N=882 N=855 Weight(g) 3325 3306 Length(cm) 49.6 49.5 Head circumference (cm) 34.1 34.2 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 2.4 Data cleaning procedures and exclusions Data cleaning The MGRS data management protocol (Onyango et al,2004)was designed to create and manage a large databank of information collected from multiple sites over a period of several years.Data collection and processing instruments were prepared centrally and used in a standardized fashion across sites.The data management system contained internal validation features for timely detection of data errors and its standard operating procedures stipulated a method of master file updating and correction that maintained a clear trail for data-auditing purposes.Each site was responsible for collecting,entering,verifying and validating data,and for creating site-level master files.Data from
Methodology 5 Table 2 Comparison of mean size at birth for compliant newborns and those that contributed only birth measurements Measurement Complianta N=882 Non-compliant N=855 Weight (g) 3325 3306 Length (cm) 49.6 49.5 Head circumference (cm) 34.1 34.2 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 2.4 Data cleaning procedures and exclusions Data cleaning The MGRS data management protocol (Onyango et al., 2004) was designed to create and manage a large databank of information collected from multiple sites over a period of several years. Data collection and processing instruments were prepared centrally and used in a standardized fashion across sites. The data management system contained internal validation features for timely detection of data errors and its standard operating procedures stipulated a method of master file updating and correction that maintained a clear trail for data-auditing purposes. Each site was responsible for collecting, entering, verifying and validating data, and for creating site-level master files. Data from
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 13368 98.6 Lower 11 0.1 Excluded 2 0.1 13 0.1 Upper 56 0.6 116 2.7 172 1.3 Total 9300 100.0 4253 100.0 13553 100.0 Girls LS 9% CS % Total 9% Included 9740 99.6 3886 97.2 13626 98.9 7 Excluded Lower 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 13781 100.0 LS,Longitudinal study:CS,Cross-sectional study
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 indepth 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 crosssectional 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 cutoffs. In total, only a small proportion of observations were excluded for unhealthy weight-forlength/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 Lower 11 0.1 2 0.1 13 0.1 Excluded 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 Lower 7 0.1 3 0.1 10 0.1 Excluded 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 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 13623 13362 26985 Weight-for-age 14056 13797 27853 Length/height-for-age 13783 13551 27334 BMI-for-age 13623 13362 26985 2.5 Statistical methods for constructing the growth curves The construction of the growth curves followed a careful,methodical process.This involved: detailed examination of existing methods,including types of distributions and smoothing techniques,in order to identify the best possible approach; selection of a software package flexible enough to allow comparative testing of alternative methods and the actual generation of the curves: systematic application of the selected approach to the data to generate the models that best fit the data. A group of statisticians and growth experts met at WHO/HQ to review possible choices of methods and to define a strategy and criteria for selecting the most appropriate model for the MGRS data (Borghi et al.,2006).As many as 30 construction methods for attained growth curves were examined. The group recommended that methods based on selected distributions be compared and combined with two smoothing techniques for fitting parameter curves to further test and provide the best possible approach to constructing the WHO child growth standards. Choice of distribution.Five distributions were identified for detailed testing:Box-Cox power exponential (Rigby and Stasinopoulos,2004a),Box-Cox t(Rigby and Stasinopoulos,2004b),Box- Cox normal (Cole and Green,1992),Johnson's SU (Johnson,1949),and modulus-exponential-normal (Royston and Wright,1998).The first four distributions were fitted using GAMLSS (Generalized Additive Models for Location,Scale and Shape)software (Stasinopoulos et al.,2004)and the last using the "xriml"module in STATA software (Wright and Royston,1996).The comparison was done by age group,without considering the smoothing component.The Box-Cox-power-exponential(BCPE) distribution with four parameters-u (for the median),o(coefficient of variation),v (Box-Cox transformation power)and t(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 v=1 and t=2,and when v1 and t=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 t(Rigby and Stasinopoulos,2004a)
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 2.5 Statistical methods for constructing the growth curves The construction of the growth curves followed a careful, methodical process. This involved: • detailed examination of existing methods, including types of distributions and smoothing techniques, in order to identify the best possible approach; • selection of a software package flexible enough to allow comparative testing of alternative methods and the actual generation of the curves; • systematic application of the selected approach to the data to generate the models that best fit the data. A group of statisticians and growth experts met at WHO/HQ to review possible choices of methods and to define a strategy and criteria for selecting the most appropriate model for the MGRS data (Borghi et al., 2006). As many as 30 construction methods for attained growth curves were examined. The group recommended that methods based on selected distributions be compared and combined with two smoothing techniques for fitting parameter curves to further test and provide the best possible approach to constructing the WHO child growth standards. Choice of distribution. Five distributions were identified for detailed testing: Box-Cox power exponential (Rigby and Stasinopoulos, 2004a), Box-Cox t (Rigby and Stasinopoulos, 2004b), BoxCox 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) ν Y having a shifted and scaled (truncated) power exponential (or Box-Tiao) distribution with parameter τ (Rigby and Stasinopoulos, 2004a)
Methodology Apart from other theoretical advantages,the BCPE presents as good or better goodness-of-fit than the modulus-exponential-normal or the SU distribution. Choice of smoothing technique.The expert group recommended two smoothing techniques for comparison:cubic splines and fractional polynomials (Borghi et al.,2006).Using the GAMLSS software,the two techniques were compared for smoothing length/height-for-age,weight-for-age and weight-for-length/height curves.For the fractional polynomials,a function in GAMLSS was used that estimates the best set of powers among {-2,-1,-0.5,0,0.5,1,2,3)within the choices of polynomials with the same number of terms.The best fractional polynomial for 1,2 or 3 terms was fitted for each parameter curve.A number of combinations were tried among the different parameter curves, considering the Akaike Information Criterion (Akaike,1974),AIC,defined as: AIC =-2L+2p, 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(u)=n1,df(a)=n2,df(v)=n3,df(t)=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)
8 Methodology Apart from other theoretical advantages, the BCPE presents as good or better goodness-of-fit than the modulus-exponential-normal or the SU distribution. Choice of smoothing technique. The expert group recommended two smoothing techniques for comparison: cubic splines and fractional polynomials (Borghi et al., 2006). Using the GAMLSS software, the two techniques were compared for smoothing length/height-for-age, weight-for-age and weight-for-length/height curves. For the fractional polynomials, a function in GAMLSS was used that estimates the best set of powers among {-2, -1, -0.5, 0, 0.5, 1, 2, 3} within the choices of polynomials with the same number of terms. The best fractional polynomial for 1, 2 or 3 terms was fitted for each parameter curve. A number of combinations were tried among the different parameter curves, considering the Akaike Information Criterion (Akaike, 1974), AIC, defined as: AIC = −2L + 2 p, where L is the maximized likelihood and p is the number of parameters (or the total number of degrees of freedom). According to this criterion, the best model is the one with the smallest AIC value. The cubic spline smoothing technique offered more flexibility than fractional polynomials in all cases. For the length/height-for-age and weight-for-age standards, a power transformation applied to age prior to fitting was necessary to enhance the goodness of fit by the cubic spline technique. Choice of method for constructing the curves. In summary, the BCPE method, with curve smoothing by cubic splines, was selected as the approach for constructing the growth curves. This method is included in a broader methodology, the GAMLSS (Rigby and Stasinopoulos, 2005), which offers a general framework that includes a wide range of known methods for constructing growth curves. The GAMLSS allows for modeling the mean (or median) of the growth variable under consideration as well as other parameters of its distribution that determine scale and shape. Various kinds of distributions can be assumed for each growth variable of interest, from normal to skewed and/or kurtotic distributions. Several smoothing terms can be used in generating the curves, including cubic splines, lowess (locally weighted least squares regression), polynomials, power polynomials and fractional polynomials. The simplified notation to describe a particular model within the class of the BCPE method is: BCPE(x=x, df(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)