Distribution-free Inference of Zero-inated Binomial Data for Longitudinal Studies

Count reponses with structural zeros are very common in medical and psychosocial research, especially in alcohol and HIV research, and the zero-inflated poisson (ZIP) and zero-inflated negative binomial (ZINB) models are widely used for modeling such outcomes. However, as alcohol drinking outcomes such as days of drinkings are counts within a given period, their distributions are bounded above by an upper limit (total days in the period) and thus inherently follow a binomial or zero-inflated binomial (ZIB) distribution, rather than a Poisson or zero-inflated Poisson (ZIP) distribution, in the presence of structural zeros. In this paper, we develop a new semiparametric approach for modeling zero-inflated binomial (ZIB)-like count responses for cross-sectional as well as longitudinal data. We illustrate this approach with both simulated and real study data.