Models for Recurrent Events Data with Dependent Termination: A Bayesian Perspective
In this article, we present theoretical properties, identifiability results and practical consequences of key modeling assumptions of several fully specified stochastic models for recurrent events data with risk of termination dependent on the history of the recurrent events. We focus mostly on a class of fully specified models which allows both negative and positive association between the risk of termination and the rate of recurrent events via a {\it frailty} variable. We also explore the relationship as well as the major differences between these models in terms of motivation and interpretation in practice. We discuss associated Bayesian methods based on Markov chain Monte Carlo tools, and novel model diagnostic tools to aid our fully specified model based inference. We demonstrate the usefulness of our methodology through an analysis of a data set from a clinical trial. In conclusion, we explore possible extensions and limitations of the methodology.
