Two-stage model for time varying effects of zero-inflated count longitudinal covariates with applications in health behaviour research

Summary: This study proposes a two-stage approach to characterize individual developmental trajectories of health risk behaviours and to delineate their time varying effects on short-term or long-term health outcomes. Our model can accommodate longitudinal covariates with zero-inflated counts and discrete outcomes. The longitudinal data of a well-known study of youths at high risk of substance abuse are presented as a motivating example to demonstrate the effectiveness of the model in delineating critical developmental periods of prevention and intervention. Our simulation study shows that the performance of the model proposed improves as the sample size or number of time points increases. When there are excess 0s in the data, the regular Poisson model cannot estimate either the longitudinal covariate process or its time varying effect well. This result, therefore, emphasizes the important role that the model proposed plays in handling zero inflation in the data.