Bayesian Analysis of Binary Data Using Skewed Logit Models

Abstract

The logistic regression is one of the most widely used models for binary response data in medical and epidemiologic studies. However, in some applications, the overall fit can be improved significantly by the use of a noncanonical link and in particular by an asymmetric link. In this paper, we consider a skewed logit model for analyzing binary response data with presence of covariates. Using a Bayesian approach, we propose informative priors using historical data from a similar previous study. We use various Bayesian methods for model comparison and model adequacy. More specifically, we use conditional predictive ordinates (CPO) to develop the pseudo-Bayes factor and Bayesian standardized residuals. In addition, we propose Bayesian latent residuals for assessing choices of link functions. Data sets from a prostate cancer study are used to demonstrate the methodology as well as the role of informative priors in model comparison and model adequacy.