Dynamic Frailty and Change Point Models for Recurrent Events Data

We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity function. The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline intensity uses an unknown grid for the piecewise constant function. Implementation of Bayesian inference using a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is developed to handle the change of the dimension in the parameter space for models with a random number of change points. A data set provided by Grubbs et al. (1991) with recurrent times to mammary tumors for 59 rats is used to illustrate the application of the new models. We compare several models including constant or piecewise constant subject-specific frailty and a fixed number or a random number for the change points in the baseline using the pseudo-marginal likelihood criterion. We show that models with a random number of change points in the baseline improve upon that of a fixed number.