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 Table of Contents  
Year : 2014  |  Volume : 58  |  Issue : 2  |  Page : 92-99  

Construction of national standards of growth curves of height and weight for children using cross-sectional data

1 PhD Scholar, International Institute for Population Sciences, Mumbai, Maharashtra, India
2 Professor, Department of Mathematical Demography and Statistics, International Institute for Population Sciences, Deonar, Mumbai, Maharashtra, India

Date of Web Publication12-May-2014

Correspondence Address:
Rachana Patel
Q.N. E-5, NTRO, Behind SSB Complex, Ayan Nagar, New Delhi - 110 047
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0019-557X.132281

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Objectives: Growth curves are the most important tools for the assessment of growth of children, which could further helps to develop preventive interventions. Geographical and physical differences necessitate using national growth curves. This study aims to construct growth curves using anthropometric measurements namely weight and height for Indian children using cross-sectional data from National Family and Health Surveys. Materials and Methods: Box-Cox power exponential, a flexible distribution, was used that offers to adjust kurtosis and improves the estimation of extreme percentiles. LMS-methods that fit skewed data adequately and generate fitted curves that follow closely the empirical data, with maximum penalized likelihood, Akaike information criteria (AIC) and generalized AIC with penalty 3 were used to construct the growth curves. Before fittings this model factors which influence the nutritional status of children were examined, similar to World Health Organization (WHO) (2006) factors, namely standard infant feeding practices, sanitation, non-smoking mothers additionally poverty (household consumable assets based). Results: Model fitted in LMS-model and standard based on height and weight for children aged 0-60 months was obtained after iteration for degrees of freedom for the parameters. Growth curves for mean Z-scores and percentiles were constructed for both sexes and significant lower values were noticeably found to be set as growth-standard compared to WHO-standards. Conclusion: Study showed the prospect of constructing regional/national growth curve and their need for the assessment of children's growth, which could help to identify undernourished-children at national level. There is an urgent need to collect longitudinal data of children to fit the growth curve of children in India.

Keywords: Anthropometric, Cubic-spline, Growth-curve, Percentiles, Wealth-score, Z-scores

How to cite this article:
Patel R, Unisa S. Construction of national standards of growth curves of height and weight for children using cross-sectional data. Indian J Public Health 2014;58:92-9

How to cite this URL:
Patel R, Unisa S. Construction of national standards of growth curves of height and weight for children using cross-sectional data. Indian J Public Health [serial online] 2014 [cited 2019 Jun 17];58:92-9. Available from:

   Introduction Top

Growth curves are among the most commonly used tools for assessing the general wellbeing of infants and children and the communities in which they live. Physical structure of the human body in different countries differs according to the geographical location therefore considering different regional growth pattern; the assessment of nutritional aspects for national policies should adopt parameters at national level. The choice of the reference population to assess nutritional status has a significant impact on the proportion of children identified as being malnourished and has important programmatic implications. [1] Until 2006, the most commonly used reference population was the U.S. National Center for Health Statistics (NCHS) standard, which was recommended at that time by the World Health Organization (WHO). [2] The WHO standards (2006), a new international reference population, was developed to replace NCHS which adopted a perspective approach, describing how health children should grow and was based on children around the world who are raised in healthy environments, whose mothers do not smoke, and who are fed with recommended feeding practices. [3],[4] WHO standards (2006) were prepared based on multicenter sampling and India shared approximately 22% of that children sample. [5]

A study in China compared the WHO Child growth standard with their children, which observed Chinese children are ranked below the international standards at the age of five and above in all anthropometric indices. [6] Another study compared the WHO child growth standards with US CDC 2000 which reflected heavier and shorter children in CDC than the WHO. [7] Studies in European and Asian countries showed that the height and weight curves of children aged below 5 years were different from WHO and NCHS growth standards. A WHO expert consultation also concentrated on the debate about interpretation of recommended body mass index (BMI) cut-off points for determining the nutritional status in Asian populations and examined scientifically that suggests that Asian populations have different associations between BMI, percentage of body fat, and health risks than do European populations. It was said to propose methods by which countries could make decisions about the definitions of increased risk for their population. [8] Some countries like China and Iran have paid great attention to the regular collection of anthropometric data on children <5 years of age for growth monitoring and encouraging to construct growth curves in most significant and statistical way. [9] International standards help to compare growth across the countries. But as long as nationwide standard is appropriate - in terms of inclusion and exclusion criteria as well as modeling the collected data - the need for an international standard is debatable. Considering the epidemiological changes and existing genetic differences and different children's weight and height growth patterns, it seems that the global standard for the children's growth, including the WHO (2006) standards, may not be applicable to all the populations and it necessitated country specific standards.

Geographical-physical similarities and population distribution characteristics probably make national growth curves applicable to children in India. Well-defined influential factor was applied in this study design to achieve the aim and construction of child growth curves followed a careful rigorous methodological process. For choosing standard reference population from such a cross-sectional data was logical and socioeconomic criterion such as maternal, child and household factors were taken into account. The method of iteration has been adopted for choosing the degree of freedom (df) for smoothing all parameters (mean, standard deviation [SD] and skewness where kurtosis are assumed as constant) and selecting the best model for growth curves.

Available methods in India and comparison

In India, Integrated Child Development Scheme uses Indian Academy of Pediatrics (IAP), 1972 classification for growth monitoring and identifying severely malnourished children aged up to 5 years for supplementary food program. [10] A drawback of IAP classification is that it is arbitrary and underestimates severely malnourished children. IAP classification fixes 60% of median (standard weight) as the cut off points for severe malnutrition. However, international organizations even National Family and Health Surveys (NFHS) had used NCHS standards since 1992-1999 and later used WHO (2006) standards based on SD classifications. Even if we compare these two classifications, NCHS (1977) gives significant difference in prevalence (ranges 5-10%) for underweight and stunted (ranges 5-15) children [Figure 1] and [Figure 2] across the age compared to WHO-standards. [11] Since, the different classification showed different prevalence so again it becomes the necessity to adopt more relevant to the study population.
Figure 1: Difference in prevalence of underweight and stunted children between National Centre for Health Statistics and World Health Organization classification

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Figure 2: Difference in prevalence of underweight and stunted children between National Centre for Health Statistics and World Health Organization classification

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   Materials and Methods Top

Cross-sectional data

For individual applications in screening high-risk children, cut-off points should be locally identified by taking into account: the population-specific prevalence and nature of malnutrition; The cut-off point below which children are shown to respond to specific interventions. [12] Rich cross sectional data from three rounds of National Family and Health Survey (NFHS 1992-1993, 1998-1999, 2005-2006) available on anthropometric measures namely height/length (cm) and weight (kg) of children are used for this analysis. Data were collected from a probability sample which represents 99% of India's population. NFHS collected a complete birth history, including sex and date of birth of each child below age 5 years, from each ever-married woman in the sample from all the states. Importantly, information on their weight and height are also measured, including a number of maternal and household characteristics relating to the care of each child. Interviewers followed United Nations Guidelines to measure the weight and height of children. [13]

Of the total 133,540 appended children aged 0-5 years data NFHS-I, II, and III contribute 37%, 25%, and 39%, respectively for the further procedure of the reference population. Since the criterion and method of anthropometric measurement on weight and height was same in all NFHS, so it was assumed that growth pattern of healthy children from appended data, utilized for the reference population, could be same irrespective of static time. Anthropometry is an important instrument in the epidemiological assessment of health and nutritional status of populations of children and anthropometric values are compared across individual or populations in relation to a set of reference values. Two of the three measures of child nutrition (height-for-age and weight-for-age) are chosen to construct growth curves separately for girls and boys.

Selection of standard reference population

Growth references are different from the growth standards. Later is perspective and define how a population should grow given the optimal nutrition and optimal health. While former is descriptive and are prepared from a population, which is thought to be growing in the best possible state of nutrition and health in a given community. This describes the growth of children "how children are growing" rather than "how they should be growing" at that time and region. The justification for use of a reference population is the empirical finding that well-nourished children in all populations follow very similar growth patterns. [14] Many factors can cause malnutrition, most of which are related to poor diet or severe and repeated infections, particularly in underprivileged populations. [15],[16] Concern for selecting reference population is very logical because standard population should cover all domains for a healthy environment as for children to grow up. Factors influence the nutritional status of children is examined which helped to select children with those characteristics for the reference population. Nutritionally well-off child population was identified and selections of those children belong to socioeconomically well-off household was prepared (i.e., children with standard breast feeding practices, belong to richest family, average size at birth, etc.) [Table 1]a based on literatures.
Table 1:

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Data range: Inclusion of economic status and identification of households with favorable conditions for growth

Except "income" variable all are directly asked in survey therefore wealth index taken as poverty indicator. It was established (Wilkinson theory) that poverty is directly related to child health. This variables indicator is associated with a household's relative position in the distribution of the underlying wealth factor and computation of wealth index was based on demographic health survey report.

One composite index was computed using principle component analysis in STATA (Stata 10) which gives score to each goods available in house accordingly and further distribution of under-nourished children examined by wealth deciles and other health factors. Data from three rounds of NFHS with same characteristics was selected for reference data to work with enough samples at each age. Since, study period of data collection was at three points of time 1992-1993, 1998-1999 and 2003-2004 (almost 13 years duration, each at 6 years of interval, data on weight, and height of children based on similar anthropocentric measurement) hence decided to choose same characteristics of children selected for the reference population to minimize the nuisance and biased result in growth pattern. Further, the procedure to choose reference data on height/weight of healthy children, who already had grown up in a healthy environment, by age was done. And criterion (factors) satisfied by each child given below is chosen [Table 1]a.

Sample size

At each age for both sexes (Weight-for-age and Height-for-age) mean, median, SD, skewness and kurtosis are calculated and fitted the normal distribution. To avoid the influence of unhealthy weights and height, observations falling between (median ± 3 SD) of the sample were included prior to constructing the standards and curve fitting assumed to be free from nuisance due to outliers; notably, (μ ± 3 σ) limits enclose 99.73% of the Normal Distribution. The total sample size for the reference population was 7679 (4206 boys:3473 girls) considering selected maternal-child factor and wealth index (d 10 ) [Table 1]b.

Statistical methods

Choice of distribution

Though normal probability distribution is based on applying statistical methodology; but, data do not always meet the necessary normal distribution assumptions. Therefore, researchers often transform non-normal data to a distribution that is approximately normal. The original height and weight distributions were slightly modified by a normalized procedure. [17] Reference populations used prior to the NCHS/WHO reference in the growth curves were generally not normalized. The Box-Cox method offers a simple method for choosing the most appropriate power transformation and easy to interpret. [18] WHO (2006) used Box-Cox power exponential (BCPE) distribution after examining several methods. Hence, for India also it is decided to use the same distribution and smoothing techniques.

The BCPE distribution provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). BCPE (μ, σ, υ, ζ) is flexible distribution that offers the possibility to adjust for kurtosis; the parameters, μ, σ, υ and ζ may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS (lambda-mu-sigma, i.e., skewness, median, coefficient of variation) method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. LMS method proposed by Rigby and Stasinopoulos, and implemented in the Generalized Additive Model for Location, Scale and Shape (GAMLSS) package in R software (R 2.11.0 for windows [32 bits]). [19],[20] Which is a general class of statistical models for a univariate response variable.

Choice of smoothing technique

For maximizing the penalized likelihood of data under GAMLSS, Rigby and Stasinopoulos and Cole and Green algorithms were used. [20] Smooth centile curves are drawn by modeling each of the four parameters of the distribution as a smooth nonparametric function of an explanatory variable. [7] Before fitting the model, age power transformation (λ) was searched then determined the best degrees of freedom for the parameter curves (f(λ) = ageλ). [3]

In order to draw centile and Z-score curves by the LMS (keeping kurtosis as constant) method, few steps was implemented in accordance with df was optimized. The sequence of steps is sensible because the M curve describes the most important variation, while the influence of S and L is relatively small.

Selecting the best model

This study used the cubic splines for curve smoothing and in order to select the best model for μ parameter, the best model is the one with the smallest Akaike information criterion (AIC) value, defined as: AIC = −2L + 2p, where L is the penalized maximum likelihood and p is the number of parameters (or the total number of degrees of freedom); [21] to determine the best model for σ, υ and τ, we had used the generalized AIC with a penalty equal 3 (GAIC [3]) as defined in Rigby and Stasinopoulos: GAIC = −2L + 3p. [19] The best model was the one with smallest AIC or GAIC value. The simplified notation to describe a particular model within the class of the BCPE method is: BCPE (x = x, df(μ) = n 1 , df(σ) = n 2 , df(ν) = n 3 , df(τ) = n 4 ), Where df(·) are degrees of freedom for the cubic splines smoothing the respective parameter curve and x is age (or transformed age) of weight or height.

   Results Top

Centile curves (3 rd , 10 th , 25 th , 50 th , 75 th , 90 th , and 97 th ) and Z-score curves (−3 to +3) for weight-for-age and height-for-age were generated using the LMS method for weight-for-age and height-for-age. The weight-for-age standards had the best fit compared to the height-for-age. The results from fitting the height curve showed misfits in parameters (μ, σ, υ, τ) of distribution for a few younger age groups for boys and girls while weight-for-age curves fitted significantly good for both sexes. These were shown by sex in [Figure 3], [Figure 4], [Figure 5] and [Figure 6]. The fitted models are as below:
Figure 3: Fitted curve: Weight-for-age: 0-60 months

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Figure 4: Fitted curve: Weight-for-age: 0-60 months

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Figure 5: Fitted curve: Length/height-for-age: 0-60 months

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Figure 6: Fitted curve: Length/height-for-age: 0-60 months

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  1. BCPE (x = age 0.25 , df(μ) = 10, df(σ) = 9, df(υ) = 1, df(τ) = 2); for boys
  2. BCPE (x = age 0.25 , df(μ) = 10, df(σ) = 9, df(υ) =2, df(τ) = 2); for girls.


  1. BCPE (x = age 0.30 , df(μ) = 11, df(σ) = 9, df(υ) = 0, df(τ) = 2); for boys
  2. BCPE (x = age 0.30 , df(μ) = 9, df(σ) = 8, df(υ) = 0, df(τ) = 2); for girls.

The dispersion in height data for age <12 months is more as compared to weight data. Almost similar model fitting is followed by both boys and girls in developing the growth curves. Height-for-age standard followed a normal distribution where Weight-for-age standard required the modeling of skewness, but not kurtosis. Percentiles and Z-scores curves for boys and girls aged 0-60 were generated for height-for-age and weight-for-age. Differently lower values for weight of girls were noticeably found compared to boys.

Comparison of Z-score and centile curves for weight-for-age for India and WHO are shown in [Figure 7] and [Figure 8] separately for boys and girls. Obtained curves for India showed the lower values for both Z-scores and centiles curves compared to WHO-values. At younger ages (age group) almost similar value are observed in both Indian and WHO growth curves, however, in later ages (age 11 months onwards) significant difference was appeared. Relatively heavier children are in WHO standard than that of Indian growth curve for median Z-scores and centiles. Similarly, Comparisons of Z-score curves for height-for-age (24-60 months) were done and [Figure 9] and [Figure 10] showed that growth pattern is quite different. Since birth, median Z-scores for height in the Indian children rapidly declined towards the WHO median by age 12 months and range of Z = 2, 3 has increased than WHO. Slope of growths for the boys in age 24-60 are similar for both population; however, the values for Indian children are lower compared to WHO while growth gradient is faster for Indian girls, but they are very shorter in all ages except for few older ages than WHO-standard.
Figure 7: Comparisons of weight-for-age Z-scores curves for Indian children with World Health Organization data

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Figure 8: Comparisons of weight-for-age Z-scores curves for Indian children with World Health Organization data

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Figure 9: Comparisons of height-for-age Z-scores curves for Indian children with World Health Organization data (24-60 months)

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Figure 10: Comparisons of height-for-age Z-scores curves for Indian children with World Health Organization data (24-60 months)

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   Discussion and Conclusion Top

The mean of this study was to construct new growth curve for girls and boys aged 0-60 months separately in reference to the growth of healthy children in Indian environment. Comparison of constructed curve for India with WHO curve revealed, significant differences between growth patterns of Indian children was found. The values of constructed growth chart in this study are more close to Khadilkar et al. (2007) for age 24 months and above while WHO reference are heavier; however, almost similar pattern of centile curves was observed in earlier ages, since birth (0-24 months) to age 24 months. [22] Similar to the recent multicentric study of preschool Indian children the Mean Z-scores for height, weight, BMI, and weight for height was found below to the WHO 2006 standards. [23]

Previous study by Mercedes de Onis et al. (2001) also found that the earlier NCHS reference data, proposed by WHO (1977, 1979), seem inadequate for Indian children. [24] Similar differences had been observed in studies from other countries. [8],[25] Comparisons of Indian children aged <5-year-old with NCHS showed a significant deviation from WHO pattern (NFHS 2005-2006). A study conducted on infants' growth pattern showed that height and weight of children under 2 years were generally lower than those of NCHS. [26]

Inconsistency with the growth pattern of Indian children estimates may be misleading. Therefore, constructing national standard curves seem to be of high priority in health policies for nutritional and medical interventions like supplementary feeding, foods to the vulnerable group, underprivileged children, etc. to identify the population at risk of malnutrition at local level and that could be much more helpful than using international norms or curves. This study explored the prospect of regional/national growth curves construction and their importance for evaluating children's growth and risk assessment.

Constructing similar curves using longitudinal studies and regular updating to account the secular trends is recommended. Concerns raise with regard not only to have separate national standards for each country, but also the standards of any country should be functionally updated based on socioeconomical developments and their effects on growth and development of children. Because of the nature of cross-sectional studies as in this study, obtained curves need to be confirmed by longitudinal data with more representative samples across the country.

There are certain advantages as well as limitations. First of all, data regarding general health condition and nutritional practices were available and obtained curves are regarded as reliable considering the sample size and healthy condition of the recruited children. Secondly, there is enough data regarding feeding practice of children younger than 2 years of age, other child factor, maternal factors and household factors which is easy to include in the data for selecting the reference population. As for limitations, the data used in this study are cross-sectional and obviously of less validity compared to longitudinal data. Data quality may be debatable for the utilization of growth curves. Despite this, the curves are prepared by using well-known methods and based on a data set of a representative sample of India children maybe preferred over those prepared by using data of other populations. Therefore, we recommend using our local curves instead of international ones until longitudinal data supposed to prepare.

   Acknowledgments Top

The author would like to thank Professor P. Arokiasamy for valuable discussions, comments on the work and help in researching resources, NFHS office assistance for the requirement of data.

   References Top

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  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10]

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