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A flexible approach to time-varying coefficients in the Cox regression setting. (English) Zbl 0896.62126
Summary: 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 [D. R. Cox, J. R. Stat. Soc. Ser. B 34, 187-220 (1972; Zbl 0243.62041)]. Typically, it is assumed that a covariate’s effect on the hazard function is constant throughout the course of the study.
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.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62F15 Bayesian inference
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