Bayesian Threshold Regression Model with Random Effects for Recurrent Events

Abstract

It is of practical importance to extend time-to-event models in order to be applicable in situations with recurrent events on the same individual or machine. The model proposed here extends in this direction a threshold regression model with random individual effects, in which event times are modeled as realizations of the first hitting times of an underlying Wiener process, leading to Inverse Gaussian distributions of times between events. In our approach, the parameters of the distribution of an event time may depend on features of the process (such as number of previous events and total elapsed time) as well as on measured, possibly time varying, covariates and the individuals’ random effects. A Bayesian approach is adopted for model estimation using an improved MCMC algorithm, which guarantees a proper choice of proposal distribution at any step of the hybrid Gibbs sampler when this is required. Model fitting is investigated using simulated data and the model is applied to a set of real data on drug users who made repeated contacts with treatment services.