Bayesian Inference on Bivariate Semi-continuous Mixed-effects Models with Application to Longitudinal Substance Use Data

Abstract

Multivariate (bivariate) correlated data encountered frequently in longitudinal studies are often analyzed using a multivariate linear mixed-effects model with normality assumption. Semi-continuous data in the form of a mixture of high proportion of zeros and right-skewed positive values bring special challenges to the field of multivariate modeling. In this paper, we propose a Bayesian approach to analyze bivariate semi-continuous outcomes by jointly modeling a generalized logistic mixed-effects model on zero-inflation in either response and a bivariate linear mixed-effects model (BLMM) on the positive values given both responses occurred through a correlated random-effects structure. Multivariate skew distributions including skew-t and skew-normal distributions are used to relax the normality assumption in BLMM. The proposed models are illustrated with an application to the correlated alcohol and drug uses data from a longitudinal observational study. A simulation study is conducted to evaluate the performance of the proposed models.