Distribution of Body Mass Index of Indian Women: A Study Based on NFHS-2 and NFHS-3

World Health Organization recommended Body Mass Index (BMI) as a measure of nutritional status of adults. This study investigates the distribution of BMI and its changes among Indian women in the age-group 15-49 years based on sampled data of 83,646 and 111,983 women from the National Family Health Survey-2 (NFHS-2) and NFHS-3 respectively. Background characteristics (BC) specific distributional changes in BMI are demonstrated by (i) fitting an appropriate probability distributions (ii) partial sum based on percentiles of distribution and (iii) test of equality of percentiles of distribution of BMI from NFHS-2 and NFHS-3. Relative measures R1 and R2 are defined to demonstrate burden of underweight and obesity. Changes in the prevalence of underweight, obesity and annual gain in mean BMI for synthetic cohort by age-groups are presented. Rapid increments are observed in mean and higher percentiles of BMI among married women, women in the higher age-groups, and women from south zone of India. High prevalence of underweight is observed among rural women (40.6%) and women from low standard of living (49.7%). Double burden of underweight and obesity is reported among older, rich and highly educated women and women from Christian and Sikh religions. Tests of equality of percentiles of BMI are rejected ( for many BC. Results may be useful for making health policy for Indian women. India need to address women health issues afflicting the underweight from poor class and obesity from the rich class. Ramkrishna L. Shinde and Yashwant P. Patil 120 ISSN-2424-6271 IASSL


Introduction
The Body Mass Index (BMI) or Quetelet Index is a statistical measure of the weight of a person scaled according to height. The BMI of a person is the ratio of person's weight in kilograms to the square of the height in meters (kg/m 2 ). Researchers have demonstrated the population based changes in BMI through the change in mean BMI or point estimates such as prevalence of obesity to summarize changes in overall distribution (Headley et al, 2004;Flegal et al., 2010;Ogden et al., 2014). The implicit assumption in most of the studies was that the distribution of BMI or the dispersion in the population has remained constant, with the entire distribution moving typically to right, allowing summaries of population change by examining a single parameter. Previous research had showed greater increases in the upper deciles of the BMI distribution accompanied by increases in the variance across United states for birth cohorts from 1882 to 1986 (Komlos & Brabee, 2011). There has also been evidence of grater increases in BMI at higher quantiles within socioeconomic and demographic groups (Ljungvall & Zimmerman, 2012). The prevalence and distribution of malnutrition in a society have implications for public health outcomes and policy formulation. Underweight people die at much higher rates, perhaps because of diseases related to being malnourished, while overweight and obese people also have higher rates of death and disease, mostly from causes such as diabetes, heart disease and cancer (Razaket al., 2013). This growing trend of body weight extremes is going to pose a major challenge for health care and policy leaders (Razaket al., 2013). While exploring the prevalence of BMI categories and changes in mean BMI are important for understanding population health, they do not capture the whole distribution of BMI. Understanding the actual distribution of BMI is important since mean values may hide differences in patterns at both the upper and lower ends of the distribution.
Major objective of this study is to investigate the distributional changes in BMI of Indian women from NFHS-2 to NFHS-3. For this study, we have used data from NFHS-2 and NFHS-3. These nationwide surveys were conducted in India during 1998-99 and 2005-06 respectively. We have demonstrated the changes in the distribution of BMI of Indian women for some selected background characteristics (BC) using different approaches.
The paper is organized as follows. Methodology is described in Section 2, which include different approaches for studying change in distribution of BMI and derived output Tables of analysis. The results extracted from output Tables of Section 2 are reported in Section 3. Discussion on results is also included in Section 3. In Section 4, we have given brief conclusion of the study.

Data from NFHS-2 and NFHS-3
In India, the National Family Health Survey (NFHS) program started in the early 1990s and it provides a nationally important source of representative data on population health for Indian states. NFHS program was initiated by the Ministry of Health and Family Welfare, Government of India. So far four rounds of NFHS are conducted namely NFHS-1 (1992-93), NFHS-2 (1998-99), NFHS-3 (2005-06) and NFHS-4 (2015-16). These are nationwide surveys conducted with a representative sample of households throughout the country. In NFHS-1 and NFHS-2 data were collected on women only. Data on height and weight of women were not collected in NFHS-1. In NFHS-2, information was collected from 91,196 households and interviewed 89,199 ever married women aged 15-49 years. Women who were pregnant at the time of survey, women who gave birth during the two months preceding the survey and women for whom there was no information on height and/or weight or for whom a BMI could not be estimated are excluded from the analysis. After omission cases of such women the total sample size from India during NFHS-2 became 83,646 ever married women. In NFHS-2, the response rate was 93.7% (IIPS, 2000 In this study, we considered some socio-economic and demographic variables as BC: age-group, formal educational level, religion, caste, type of residence, marital status, zone and standard of living index of the household of each respondent. These variables were also considered and discussed in detail by Patil and Shinde (2014).

Methods for studying change in distribution of BMI
To demonstrate the changes in the distribution of BMI of Indian women based on the survey data of NFHS-2 and NFHS-3, we have used following approaches: (i)prevalence rates and descriptive statistics of BMI (ii) longitudinal changes using synthetic cohorts based on age-groups (iii) fitting an appropriate probability distribution to BMI (iv) partial sums based on percentiles of distribution of BMI and (v) test of equality of percentiles of distribution of BMI from NFHS-2 and NFHS-3. In the following subsections we have explained these approaches briefly and presented the tables derived from analysis.

Prevalence of underweight and obesity in Indian women
Using the categorical groups based on ranges of BMI, we define following two measures and to assess burden of malnutrition (UW/OW/OB) on population. (1) (2) Interpretations based on values of and are as follows.  If then more than 50% of population belongs to NW. This case is rare under BC for Indian women (see Table 1).  If then more than 50% of population is under malnutrition (UW/OW/OB) status. This case is commonly observed for many BC.  If and then there is double burden of UW as well as obesity (OW/OB) and problem of obesity is of more concern than UW.  If and then problem of UW is of more concern than obesity (OW/OB).
The weighted and un-weighted prevalence percentages based on ranges of BMI of Indian women according to BC are presented in Table 1 for NFHS-2 and NFHS-3. The values of R 1 and R 2 based on weighted prevalence percentages are also presented in Table 1. Results are discussed in Section 3.

Descriptive statistics of BMI of Indian women
The weighted descriptive statistics (Mean, Standard Deviation (SD), some  percentiles, Coefficient of Skewness (β 1 ) and Kurtosis(β 2 )) of BMI for women according to various BC are presented in Table 2 for both surveys. Estimated annual percent gain in mean BMI during the period of NFHS-2 and NFHS-3 (in 7 years span) is calculated by using following formula. (3)

Synthetic cohort approach
We use synthetic cohort approach to examine longitudinal change in BMI between NFHS-2 and NFHS-3, by matching the age-group level representatives by their birth year. This technique has been widely used by econometricians and involves the creation of a 'pseudo panel' from a time series of independent surveys conducted using the same methodology and on the same reference population (Lean et al., 2013 andRobinson et al., 2013). This approach is also useful in epidemiological studies of under nutrition and obesity population. In this study, we have created synthetic cohorts to determine changes in mean BMI for same age-groups between 1998-99 (NFHS-2) and 2005-06 (NFHS-3). For the analysis, age-groups in six-year bands were used to facilitate comparisons between the different time periods. Five cohorts were defined for women, the youngest age-group was 15-21 years, and the oldest age-group was 36-42 years in NFHS-2 (1998-99). These cohorts were matched with the equivalent cohorts underNFHS-3(2005-06). That is, the cohort of women of age-group 15-21 years from NFHS-2 is matched with women aged 22-28 years from NFHS-3, age-group 22-28 years from NFHS-2 is matched with women aged 29-35 years from NFHS-3 and so on. Thus, we can estimate longitudinal change in BMI for age stratified groups. Mean BMI within period are determined for each synthetic cohort. Finally, in order to investigate age period effect in annual BMI change, change in mean BMI over seven years is annualize by assuming constant annual change within period by using equation (3). The results of change in prevalence of BMI categories and annual gain in mean BMI for synthetic cohort by age-groups are reported in Table 3 and Table 4 respectively.

Fitting of probability distribution to BMI
For many years, prior to year 2000, the distribution of BMI was assumed to follow a normal distribution or approximately a bell-shaped curve as this was similar case of measurements of weight and height. Penman and Johnson (2006) has made claim that normal distribution is not appropriate for BMI indicating that some positively skewed distribution may be a better fit. Hence, the distributions, exhibiting a positive degree of skewing in the right tail of the data, were fitted using one of the parameter estimation methods namely method of moments, maximum likelihood, least square, and L-moments by Easy-Fit software. The fitted distributions of BMI for various BC and their estimated parameters using Easy-Fit Software (Easy-Fit) are presented in Table 5 for NFHS-2 and NFHS-3.
We observed that commonly best fitted probability distributions of

Change in distribution of BMI by using partial sums on percentiles
In this section, we suggest using the partial sum plot to demonstrate changes in the distribution of BMI. Changes in distribution of BMI can be shown through the changes in partial sums of absolute difference between percentiles of BMI based on NFHS-2 and NFHS-3. We can compare these values of partial sums for different BC with the partial sums of total population or population under other BC. The partial sums for some BC and for some selected percentiles are reported in Table 6 and shown in Figure 2 (A, B, C and D). The numerical values from the Table 6 and Figure 2 more clearly indicate the magnitude of changes in the distribution of BMI of women from NFHS-2 to NFHS-3.

Change in distribution of BMI using test of equality of percentiles
Student's t-test and analysis of variance are frequently used to test the hypothesis that two or more distributions have same means. However, many random variables such as BMI having skewed distributions that are not readily transformed to symmetry, rendering the distributional assumptions that underlie use of these methods inappropriately. The non-parametric tests such as Wilcoxon, Kolmogorov-Smirnov, and median tests are used to test for differences in distributions (Siegel &Castellan, 1988). These tests are not designed to pin-point where the distributions are unequal or simultaneously test for differences in more than one distribution parameter. The t-test and variance-test are powerful for detecting differences in location and scale respectively. The t-test and variancetest have scope to test one parameter only. In these circumstances, it may be of greater interest to compare the distributions in terms of their percentiles rather than their means or an overall test of equivalence. A percentile profile is defined as a set of one or more percentiles. It may be more informative to compare two or more distributions by testing the hypothesis that their profiles of judiciously selected percentiles are equal (Zhang et al. 2014).
Zhang et al. (2014) had first described the procedure as a generalization of the median test. In median test, we test the equality of the 50 th percentile. Instead of testing the equality of only one percentile, the method is extended to simultaneously test multiple percentiles. The method is as follows: Let denote a continuous random variable (in our case is BMI) and let , , …, denote a set of percentiles that in some sense characterize the distribution of BMI across its range. Further let , …, represent a random sample of observations and let , …, represent the usual sample estimates of , , …, respectively. Suppose random samples are available from each of populations with percentiles , , …, , = , , …, . There is interest in testing the hypothesis that the percentile profiles are identical across the populations; that is to test H o : = = … = . The complete process of testing this hypothesis as an extension of median test was discussed in Zhang et al. (2014). We have conducted these tests for =2 (as we have two distributions of BMI one each for NFHS-2 and NFHS-3) and =5 (5 th , 25 th , 50 th , 75 th and 95 th percentiles). The -values of test of equality of percentiles of BMI for five percentiles and for five combined percentiles are reported in the Table 7.

Results and Discussion
The weighted and un-weighted prevalence according to different BC of Indian women during NFHS-2 and NFHS-3 are presented in Table 1 From Table 3, under synthetic cohort age-groups, we observed negative changes in the prevalence percentages for UW and NW, whereas positive changes are reported for OW and OB classes. High positive changes are reported for women from obese class. We noticed from Table 4 that an annual gain in mean BMI was highest (0.82%) for the age-group 22-28 under NFHS-2 with its cohort group 29-35 under NFHS-3. Also, as expected, annual gains in mean BMI were higher for cohort groups than same age groups.
Best fitted probability distributions for BMI of women under different BC were decided based on p-values of goodness of fit tests and ranks given by Easy-Fit software. These best fitted distributions are reported in Table 5. Changes in the distribution of BMI under different age-groups using best fitted distributions and their estimated parameters are demonstrated in Figure 1. Due to lack of space similar figures for other BC are not presented in this manuscript.
From Table 6 and Figure 2, we clearly observed the magnitude of changes in distribution of BMI in terms of percentiles of distribution. For urban women, women from older age-groups, women with secondary/higher education and women with high standard of living almost uniform changes in all percentiles are observed, whereas for other BC major changes are observed at higher percentiles of BMI. From Table 7 we notice that, tests of equality of percentiles of BMI showed significant difference in percentile of BMI for higher percentiles of NFHS-2 and NFHS-3 for many BC. Test of equality of percentiles can be accepted for all and combined percentiles for women from Sikh religion and women from West zone of India.
Our results suggest that, rapid increments are observed in mean and higher percentiles of BMI among married women, women in the higher age-groups, and women from south zone. This study shows a persistent problem of UW in India, with 35.2% and 35.6%of women population being UW in NFHS-2 and NFHS-3 respectively; at the same time the percentage of women who are overweight and obese has increased from 18.4% to 21.2%. This pattern of persisting problems of under nutrition along with a simultaneous rise in obesity was also seen in most of the low to middle income countries (Razaket al., 2013). Using a synthetic cohort approach we have quantified age-specific longitudinal change in BMI among Indian women during from NFHS-2 to NFHS-3. The positive changes in prevalence percentages according to BMI categories for all synthetic cohort age-groups are observed for OW/OB categories while negative changes for all synthetic cohort age-groups are observed for UW and NW categories of BMI. This shows the impact of ageing on weight gain among Indian women.
Concerning the prevalence of UW and obesity(OW/OB) there is urgent need to make more awareness of consequences of underweight and obesity among highly educated women and women from high standard of living. To overcome the problem of UW, the Indian government has passed the National Food Security Act, 2013 in September2013. As per the National Food Security Act 2013, all eligible households are entitled to get food grains (5 kg per person per month) at the subsidized prices. This Act will make access for sufficient and nutritious food for75% of rural and 50% of urban population of India including all poor. There are some more provisions for advancing food security as mentioned in the National Food Security Act 2013, which may also be helpful to improve the nutritional status of Indian women. These provisions include access to (a) safe and adequate drinking water and sanitation; (b) health care;(c) nutritional, health, and education support to adolescents; and (d) adequate pensions for senior citizens, persons with disability, and single women (National Food Security Act, 2013). More awareness programs to control obesity among Indian women are needed. Government may think of providing some incentives to employees for consistently maintaining their BMI under NW category.

Conclusion
In all age-groups except 15-19 years, the distribution BMI shifted to the right and become more right skewed and extent of shift is greatest for the older age-groups. Women with low standard of living the prevalence of underweight had increased from 46.9% to 49.7% during the period NFHS-2 to NFHS-3. Also, prevalence of obesity (OW/OB) among all women increased from 18.4% to 21.2%. For many BC major changes in higher percentiles of distribution of BMI are observed from NFHS-2 to NFHS-3. This shows the right shift of the distribution of BMI. As per NFHS-3, problem of obesity was still serious or started becoming serious among urban women, rich and highly educated women, women from south and north zone, women belonging to general and other caste category, and among married women.
The major limitation of this study is that, as the respondents are not same from NFHS-2 and NFHS-3, hence carrying out longitudinal study to demonstrate change in distribution of BMI based on synthetic cohorts may not be proper approach. However, we have used this approach because sample sizes are very large in both nationwide surveys, so the distribution of BMI was properly reflected. An advantage of this study is that the best fitted probability distributions can be used to plot cumulative distribution function of BMI under different BC. Also, in future, researchers can use these fitted probability distributions to study longitudinal changes in the distribution of BMI of Indian women.