Modeling Longitudinal Count Data with Excess Zeros and Time-Dependent Covariates: Application to Drug Use

When longitudinal count response data are collected, mixed Poisson regression models can give appropriate subject-specific analysis results.  When count responses show an excess of zeros, either a zero-inflated Poisson (ZIP) or hurdle mixture model can be employed to account for the inflation of zero counts.  Recently researchers have begun to consider models for data with a combination of excess zeros and longitudinal observation.  However, the performance of such models has not been considered for the case of longitudinal data with time-dependent covariates.  Presence of time-dependent covariates has been shown to affect the efficiency of hypothesis tests for longitudinal data.  

In this paper a comparison is made between a mixed ZIP model and a mixed hurdle model for longitudinal count data with excess zeros and time-dependent covariates.  Consideration is given to results of hypothesis tests, parameter estimates, and parameter interpretations.  An example longitudinal data set is modeled using instances of recreational drug use over a fixed period, a count response that commonly shows excess zeros.  Time-dependent covariates include the social environment and the level of drug craving during data collection.  The drug under consideration has recently been legalized in the region of data collection and recreational usage is of great interest for public policy.  Based on researcher interpretations, the mixed ZIP model is selected for the analysis, but benefits of both models are discussed.