Bayesian Logistic Regression Model on Risk Factors of Type 2 Diabetes Mellitus

Abstract

This research evaluates the risk of diabetes among 581 men and women with factors such as age, ethnicity, gender, physical activity, hypertension, body mass index, family history of diabetes, and waist circumference by applying the logistic regression model to estimate the coefficients of these variables. Significant variables determined by the logistic regression model were then estimated using the Bayesian logistic regression (BLR) model. A flat non-informative prior, together with a non- informative non- flat prior distribution were used. These results were compared with those from the frequentist logistic regression (FLR) based on the significant factors. It was shown that the Bayesian logistic model with the non-informative flat prior distribution and frequentist logistic regression model yielded similar results, while the non-informative  non-flat model showed a different result compared to the (FLR) model. Hence, non-informative but not perfectly flat prior yielded better model than the maximum likelihood estimate (MLE) and Bayesian with the flat prior.

Keywords: Bayesian approach,  Binary  logistic regression,  Parameter estimate,  Prior,  MCMC.