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

This is the authors' abstract. We don't add key points for this paper.

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 randomeffects 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.