Prevalence of Obesity and Trends of Body Mass Index in Azad Jammu and Kashmir

In the present study an attempt has been made to figure out the remarkable factors that were responsible for higher body mass index (BMI) and obesity as well as to observe the existing trends of BMI in Azad Jammu and Kashmir. The factors were age, sex, diabetes, blood pressure, total cholesterol, triglycerides, blood glucose and random glucose. The statistical analysis with both classical and Bayesian methodologies was carried out for the investigation of significant risk factors. The results showed that with the increase in age the BMI also increases i.e., respondents of age group > 60 have the highest percentage of 82.76% for BMI. Moreover, it was found that except sex and blood pressure all other factors had significant association with BMI. Additionally, four factors namely, age, diabetes, total cholesterol and triglycerides were selected for the development of the parsimonious model of BMI based on generalized linear model, step wise regression and Bayesian model averaging.


INTRODUCTION
Along with economic advancement and globalization the human beings have been facing many problems for few decades. The health related issues are believed to be the most concerning. Among these issues, obesity is considered as a major health problem in present days. Obesity rates have been increasing since last few decades. Excessive body fat is considered as a major issue for numerous diseases like diabetes, cancer and cardiovascular disorders. The prevalence of obesity and overweight have been reported to be continuously growing, not only in the Asian countries but in Western countries too. Obesity has been defined as a weight higher than 20% above what is considered to be normal according to standard age, height and weight tables. It can also be recognized by a formula known as the body mass index (BMI). The BMI may be defined as: The BMI is considered an alternative for direct measures of a body fat. Generally, BMI is not only cheap but also easy to manage method of screening for weight categories that may later cause swear health problems. The BMI numeric is not same for male and female as any other biologic phenomenon. World Health Organization (WHO) in 2000 has represented different guidelines on BMI for universal population and South Asia. For universal population, WHO has fixed worth 25 for normal BMI, 25 to 30 for morbidly obese and above 30 for obesity. In contrast, WHO sets comparatively firm BMI levels for South Asian countries, which put value 23 for common BMI, 23 to 27.5 for overweight and above 27.5 for obese? In contrast, the cut off levels for normal BMI presented by Chinese (2002) are as 18.5 kg/ m 2 ≤ BMI < 24 kg/m 2 means less than 18.5 is underweight and higher than 24 is overweight and obesity categories. In the current study the cut off values taken for BMI are set by Chinese.
However, the risk of obesity can be minimized by timely modifying specific factors which are considered to be associated with higher BMI. As Pakistan is 6 th most populous country and according to recent research it has been reported that one in four adults is overweight/obese. The BMI is a good proxy to catch obesity on population level. Many articles on obesity have been published not long time ago. Ogden et al. [1] described national estimates of the frequent obesity and its drifts among United States children and adolescents availing the third National Health and Nutrition Examination Survey (NHANES-III) data. Based on the statistical analysis, they inferred that the universality of overweight among children in the United States is getting increased, especially in Mexican American and Non-Hispanic black youngsters. Moreover, Nandram et al. [2] exclusively scrutinized the NHANES-III data and applied a Bayesian method which used small area estimation methods (Rao, 2003) with a spline regression to estimate the percentiles at each age (2 to19 years). Qasim et at. (2014) conducted a study in Bhimber, AJK to purpose the total Cholesterol, Triglycerides and BMI of unmarried males and females. Moreover, Mtambo [3] proposed spatio temporal quantile interval regression models for childhood stunting, overweight, and obesity in Republic of Congo from 2005 to 2012 based on Demographic and Health Survey datasets. He conclude that mother's BMI had significant nonlinear effects on childhood overweight and obesity. Yu et al. [4] reviewed both classical and modern statistical methods for BMI analysis, highlighting that most of the classical methods were simple and easy to implement but ignore the complexity of data and structure, whereas modern methods did take complexity into consideration but could be difficult to implement. Terada et al. [5] analyzed data of 7560 patients who underwent coronary artery bypass grafting using BMI of 18.5 to 24.9 as a reference. They concluded that a greater attention and intervention to control the risks associated with infection and length of stay in patients with BMI ≥40.0 might improve patient care quality and efficiency.
Additionally, Martin et al. [6] evaluated the association between exercise and BMI in adults and concluded that there was no association between hours of exercise per week and BMI. Similarly, Flegal et al. [7] estimated the prevalence of adult obesity from 2009 to 2010 NHANES-III data and compared adult obesity and the distribution of BMI with data from 1999 to 2008. They found that trends in BMI were similar to obesity trends.
Moreover, Nandram et al. [2], Tesfaye et al. [8], Nishida et al. [9], Moens et al. [10], Cole et al. [11], Paeratakul et al. [12], Mitchel et al. [13] and Li et al. [14] investigated the relation between BMI and different risk factors. However, Acquah et al. [15], Yang et al. [16] and Raftery et al. [17] applied both classical and Bayesian methods to identify the significant risk factors of BMI. Based on the abovementioned details, the major objectives of the study are to: Including this introduction section, the rest of the article unfolds as follows. Section 2 contains the materials and methods whereas Section 3 comprises results and discussion. Section 4 designates the parsimonious model for BMI and Section 5 quantifies the summary and discussion.

About the Data
The existent study conducted in Muzaffarabad, AJK. In which 300 respondents took part. The data was collected in collaboration with City Diagnostic Laboratory Muzaffarabad, Azad Jammu and Kashmir (AJK). Whereas, all the respondents have the ages between 20 to 81 year. About nine variables (factors) were observed against each respondent. The variables are age(AGE), sex(SEX), BMI, diabetes(DB), total cholesterol(TC), triglycerides(TG), blood pressure(BP), blood glucose(BG) and random glucose(RG). In parenthesis, the notation used for each variable during the statistical analysis has been given. Except age all the factors are binary such that they have only two categories i.e., 0 and 1. While '0' represents the normal value and 1 represents the abnormal. Whereas, age has been divided into three categories (20-40, 41-60, 61-81). BMI has been taken as the outcome variable and it has been coded as 0 and 1, representing 0 as less than 24kg/m 2 and 1 as higher than 24kg/m 2 .

Statistical Methods
The statistical techniques applied in the current study are bivariate analysis (Chi-Square and Fisher Exact), Generalized Linear models, Stepwise Logistic Regression, Bayesian Logistic Regression and Bayesian Model Averaging. Different models and the corresponding odds ratios have also been computed to check the association between different risk factors and the outcome variable. The significance level selected was 0.05.

RESULTS AND DISCUSSION
The resulting distribution of BMI (whether 0 or 1) across all different factors is presented in Table  1. and Fig. 1. It is observed that respondents of age group > 60 have the highest percentage of 82.76% for BMI. While those belong to age group < 41 have lowest percentage of 20.29% for BMI. Additionally, it is also noticed that male respondents have higher percentage of 44.03% than of female respondents (41.57%) for higher BMI.
Moreover, it has also been observed diabetic and nondiabetic respondents have a significant difference between their percentages i.e., 66.67% and 40.29% respectively. Also, it is noted that respondents who have high level of TC have higher occurrence (70.24%) of higher BMI than those who have normal cholesterol level (31.94%). A matching trend has also been observed for TG, BG and RG. Furthermore, those who were suffering from high BP had higher percentage (42.86%) of BMI. all this discription is shown in Fig. 1. In which x-axis represents the risk factors whereas, y-axis denotes the percentages of the coressponding risk factors.

Bivariate Analysis
To find out the association between BMI and other risk factors, bivariate analysis was carried out. Goodness of fit statistics such as, Pearson Chi-square test, Fisher tests and odds ratio (OR) with 95% confidence interval (CI) were calculated and presented in Table 2. P-values (<0.05) of Chi-square and Fisher statistics depict that BMI has a significant relation with all variables except SEX and BP. While the results computed from OR (under 95% CI) show that BMI has a significant relation with all risk factors such that, all the values of odds ratios are greater than 1. Moreover, it can be seen clearly that the respondents belong to the age group > 61 has higher prevalence of obesity (OR=18.43) as compare to respondents having age 41 to 60 (OR=5.2). The diabetic respondents have the odds of being obese 19.5% greater than the nondiabetic respondents. Also, the subjects having abnormal level of TC have the higher odds of obesity than those having normal level of TC. A similar trend was observed for the TG, BG and RG levels. The graphs of ORs along with 95% confidence interval (CI) for eight independent variables are given in Fig. 2. and 3. respectively.

SELECTION OF THE PARSIMONIOUS MODEL
To develop the parsimonious model for BMI generalized linear model, step wise logistic regression and Bayesian models have been applied to identify the significant risk factors. In which the BMI is considered as a dichotomous dependent variable and rest of variables have been treated as independent. The results of these models have been summarized in the following subsections.

Generalized Linear Model
The results obtained by applying generalized linear model (GLM) are shown in Table 3

Stepwise Logistic Regression
For the best fitted parsimonious model, we have also applied the stepwise regression model to BMI dataset and results are presented in Tables  4-5. Table 4 has shown all the steps of stepwise regression. Whereas, Table 4 and 5 are showing the final model analysis including odds ratios for each explanatory variable. From Table 4, it can be seen clearly that in stepwise regression model, variables are being dropped one by one on the basis of AIC value. That is, a variable with lowest AIC value has to be dropped from the selected regression equation. Moreover, the negative sign indicates the inclusion of variables in the model and vice versa. So, it is selecting four significant variables for BMI namely, AGE, SEX, TG and BG. All having negative sign in the final step. As the model 5 has the lowest AIC value so it has been selected as the final model. From Table 6, it can be seen that the age group > 61 has higher odds of obesity as its odds ratio is greater. Additionally, it is observed that the diabetic subjects have odds of being obese 2.09 times more than odds non-diabetic. Similarly, the odds of respondents having normal level of TG is 2.10 times less than the respondents having non normal level. A similar pattern has been observed for the risk factor TC.

Bayesian Logistic Regression Model
The Bayesian logistic regression model has been applied to the observed data by taking student t distribution as a prior distribution with 6 DF. To get efficient number of sample size based on Monte Carlo simulation technique, the results of posterior logistic regression model are presented in Table 7. There are 9 predictors including intercept in the model. It can be observed that the estimates of coefficients of Bayesian logistic regression model are approximately similar to the estimates derived from the generalized linear model. In Bayesian analysis we use credible intervals to assess the significance of the estimated coefficients of the predictors. Where the required credible interval is obtained by 2.5 and 97.5 percentiles values. The 2.5 and 97.5 percentiles are also given in the Table 6. Which shows that 95% of the sampled values fall between the credible interval values.
Moreover, the values of Monte Carlo Standard Error (MCSE) must be less than the 5% of the value of the standard deviation (SD) of the predictor's parameters [18]. In our study, it is very close to zero which means it is less than the 5% of the parameters' SD. Additionally, =1, indicates the convergence of Markove Chain Monte Carlo (MCMC) simulation results. Additionally, the graphs in Fig. 5 are displaying distribution of the estimates of the parameters through the Bayesian logistic regression model. It is observed that these graphs are much alike to the distribution of estimates of the parameters measured through the generalized linear model. Moreover, the four variables (Age, DB, TC and TG) who have the positive influence on BMI are same as identified by the stepwise regression analysis. Moreover, Fig. 6. is representing the number of MCMC logit posterior sample obtained through the iteration technique. About 10000 times iteration have been run to acquire the convergence.     predictors, namely AGE, TC and TG are being included in our final model. As the peaks of the DB and BG curves are too low that is approximately equal to zero, so we are not including DB and BG in our final model. It is also noticed that these variables (AGE, TC and TG) are similar to the variables obtained through the stepwise regression. But in stepwise regression model, DB is also included.

Bayesian Model Averaging (BMA)
To develop the best fitted parsimonious model with significant predictors via Bayesian approach, BMA for logistic regression model has been applied to the observed BMI dataset. Unlike stepwise regression, BMA does not take different steps to exclude non-significant factors but takes different models with different predictors and gives the final models with significant predictors for a dichotomous outcome variable. In the present study, BMI has been selected as an outcome variable while all other variables are taken as predictors. The results of BMA for posterior logistic regression models are presented in Table 8. and Fig. 7. About 14 models have been selected and 5 best models are presented.

Parsimonious Models Obtained by Different Criterion
We have applied different techniques to develop the parsimonious models for BMI. The proposed models are presented in Table 9. From Table 9, it has been seen that the estimated intercept coefficients of all three models are negative.

Comparison of Odds Ratios
The ORs calculated through different methodologies are presented in Table 10. It can be observed that ORs of only four significant factors are presented for the stepwise regression model, whereas, for all other techniques the ORs of those factors are also displayed which are statistically insignificant. Moreover, bringing light to the overall results of Table 10. it can be clearly seen that there is negligible difference between the ORs of bivariate analysis, Generalized Linear model and Bayesian Logistic regression analysis. Whereas, the ORs of Stepwise regression are different from other methods.

MCMClogit Posterior Sample
Iteration number

CONCLUSION
In modern era, obesity has become one of the basic health problems. The basic purpose to conduct this study is to explore the risk factors related to higher BMI and obesity.
The secondary data used in the present study has been collected from City Diagnostic Lab, Muzaffarabad, AJK . There are nine variables including the outcome variable. The variables are age(AGE), sex(SEX), body mass index(BMI), diabetes(DB), total cholesterol(TC), triglycerides(TG), blood pressure(BP), blood glucose(BG) and random glucose(RG). In parenthesis, the notation used for each variable during the statistical analysis has been given. Initially, all the variables are coded then different statistical methods have been applied to find out different risk factors for the outcome variable (BMI) and their association with BMI.
Bivariate analysis has been carried out at first and the relative p-values for Chi-square and Fisher Exact tests have been calculated. It has been observed that sex and BP are found to be insignificant as their p-values are exceeding 0.05. Moreover, the ORs have also been computed. All the variables showed the positive association with BMI as the values of ORs were greater than 1. The Generalized Linear model analysis carried out by taking logit as a link function. The p-values calculated for all predictor variables showed that only age and TG is having a significant relation with BMI. The similar results have been obtained through Bayesian Logistic regression analysis and it has been noticed that Bayesian Analysis provided more stable results as the values of standard error for estimated coefficients were lower than that calculated via Generalized Linear Model.
Stepwise regression approach has also been used to find out the parsimonious model. A parsimonious model is one that neither underfits nor overfits i.e., having a reasonable set of independent variables. Four predictor variables

CONSENT
As per international standard or university standard, respondents' written consent has been collected and preserved by the author(s).

ETHICAL APPROVAL
As per international standard or university standard written ethical approval has been collected and preserved by the author(s).