Bayes variable selection for semicontinuous outcome regression

Abstract

In biomedical research, semi-continuous data (mixture of zeros and continuously distributed positive values) frequently arise. Regression analysis for such semi-continuous outcome variable is challenging because of the inappropriateness of the normal error assumption. One naive approach is to fit a normal regression with log-transformed outcome variable. This method is easy to implement but is not flexible enough to account for large proportion of zeros. A two-part model has been developed allowing for more flexibility where two regressions model the binary part and the continuous part of the data separately. Alternatively, a truncated normal regression is applicable, which assumes an underlying latent variable exists and follows a normal regression, and it can be extended to zero-inflated truncated normal model. In this research, we compare 4 different methods for semi-continuous outcome regression in various scenarios via simulation studies and examine how inferences are affected by different model specifications. In all methods, we conduct Bayesian inference and develop MCMC algorithms for posterior sampling where the Stochastic Search Variable Selection (SSVS) structure for the regression coefficients is incorporated facilitating variable selection. We apply the 4 methods to a motivating example data to investigate the relationship between impulsivity and hazardous drinking in young adulthood.