Distribution-free inference of zero-inflated binomial data for longitudinal studies

Count responses 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 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 ZIP distribution, in the presence of structural zeros. In this paper, we develop a new semiparametric approach for modeling ZIB-like count responses for cross-sectional as well as longitudinal data. We illustrate this approach with both simulated and real study data.