Abstract
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.
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Sargent, D.J. A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting. Lifetime Data Anal 3, 13–25 (1997). https://doi.org/10.1023/A:1009612117342
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DOI: https://doi.org/10.1023/A:1009612117342