Bayesian modelling of zero-inflated recurrent events and dependent termination with compound Poisson frailty model

The recurrent event data are encountered in many longitudinal studies. In many situations, there are a nonsusceptible fraction of subjects without any recurrent events, manifesting heterogeneity in risk among study participants. The frailty models have been widely used to account for this heterogeneity that does not rely on self-reported survival data. Frailty is commonly modelled with a gamma distribution because of mathematical convenience, not based on biological reasons. One model that accommodates zero inflation and a continuous frailty is based on the compound Poisson model. On the other hand, dependent termination may occur, which could be correlated with the recurrent events. In this paper, we consider a joint model of recurrent event process and dependent termination under a Bayesian framework in which a shared compound Poisson frailty is used to account the association between the intensity of the recurrent event process and the hazard of the dependent termination. In addition, the proportion of participants insusceptible to the event is estimated. We assess model performance via simulation and apply the model to data from a cohort of achalasia patients. Simulation results suggest that misspecifying frailty distributions such as the gamma distribution when faced with zero-inflated recurrent events may introduce bias in regression coefficients estimation.