  Recurrent event data are common in clinical studies when participants are
followed longitudinally, and are often subject to a terminal event. With the
increasing popularity of large pragmatic trials with a heterogeneous source
population, participants are often nested in clinics and can be either
susceptible or structurally unsusceptible to the recurrent process. These
complications require new modeling strategies to accommodate potential
zero-event inflation as well as hierarchical data structures in both the
terminal and non-terminal event processes. In this paper, we develop a Bayesian
semi-parametric model to jointly characterize the zero-inflated recurrent event
process and the terminal event process. We use a point mass mixture of
non-homogeneous Poisson processes to describe the recurrent intensity and
introduce shared random effects from different sources to bridge the
non-terminal and terminal event processes. To achieve robustness, we consider
nonparametric Dirichlet processes to model the residual of the accelerated
failure time model for the survival process as well as the cluster-specific
frailty distribution, and develop a Markov Chain Monte Carlo algorithm for
posterior inference. We demonstrate the superiority of our proposed model
compared with competing models via simulations and apply our method to a
pragmatic cluster randomized trial for fall injury prevention among the
elderly.
