The Interactive Association of Body Mass Index and Waist Circumference with Body Fat Using Beta Regression

Abstract

Abstract Background: The relationship of body mass index (BMI) and waist circumference (WC) with body fat rate (BFR) was analyzed frequently using linear model with normal distribution assumption. We aimed to investigate the association between of them using beta regression more applicable to BFR data to gain a deeper understanding of the best predictors of BFR.Methods: We analyzed 1087 middle-aged or elderly people from the Lanzhou rural cardiovascular and cerebrovascular disease and risk factor study. The location submodel (LSM) of the multivariate beta regression was used to evaluate the effect or interactions of BMI and WC on BFR while its precision submodel (PSM) was fitted synchronously to evaluate the impact of all entered factors on the variance of BFR. Results: Overall, the BFR had a mean of 0.28 with a standard deviation of 0.07. LSM of the multivariate beta regression showed that overweight (OWBMI) or general obesity (GOBMI) increased the likelihood of BFR increase by 18% (95%CI: 15%~22%) or 36% (95%CI: 31%~42%) respectively but central obesity (COWC) only by 12% (95%CI: 9%~16%). Moreover, there existed the interactions of BMI and WC on BFR and the results showed that compared to normal or underweight with BMI and non-central obesity, OWBMI+COWC could increase the likelihood of BFR increase by 33% (95%CI: 28%~37%) and GOBMI+COWC had a 54% (95%CI: 48%~61%) increase the likelihood of BFR increase. In addition, PSM showed that the variance of BFR decreased in some cases.Conclusion: In the beta regression BFR could be predicted with BMI or WC but BMI better and the combination of BMI and WC could increase their individual predictive performance.