Semiparametric analysis of zero-inflated recurrent events with a terminal event

Recurrent event data frequently arise in longitudinal studies and observations on recurrent events could be terminated by a major failure event such as death. In many situations, there exist a large fraction of subjects without any recurrent events of interest. Among these subjects, some are unsusceptible to recurrent events, while others are susceptible but have no recurrent events being observed due to censoring. In this article, we propose a zero-inflated generalized joint frailty model and a sieve maximum likelihood approach to analyze zero-inflated recurrent events with a terminal event. The model provides a considerable flexibility in formulating the effects of covariates on both recurrent events and the terminal event by specifying various transformation functions. In addition, Bernstein polynomials are employed to approximate the unknown cumulative baseline hazard (intensity) function. The estimation procedure can be easily implemented and is computationally fast. Extensive simulation studies are conducted and demonstrate that our proposed method works well for practical situations. Finally, we apply the method to analyze myocardial infarction recurrences in the presence of death in a clinical trial with cardiovascular outcomes.