A Multi-level Two-part Random Effects Model, with Application to an Alcohol-dependence Study

Two-part random effects models (J. Am. Statist. Assoc. 2001; 96:730-745; Statist. Methods Med. Res. 2002; 11:341-355) have been applied to longitudinal studies for semi-continuous outcomes, characterized by a large portion of zero values and continuous non-zero (positive) values. Examples include repeated measures of daily drinking records, monthly medical costs, and annual claims of car insurance. However, the question of how to apply such models to multi-level data settings remains. In this paper, we propose a novel multi-level two-part random effects model. Distinct random effects are used to characterize heterogeneity at different levels. Maximum likelihood estimation and inference are carried out through Gaussian quadrature technique, which can be implemented conveniently in freely available software-aML. The model is applied to the analysis of repeated measures of the daily drinking record in a randomized controlled trial of topiramate for alcohol-dependence treatment.