A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting

Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples. This revised version was published online in July 2006 with corrections to the Cover Date.