Bayesian Analysis of the Proportional Hazards Model with Time‐Varying Coefficients |
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Authors: | Gwangsu Kim Yongdai Kim Taeryon Choi |
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Institution: | 1. Department of StatisticsSeoul National University;2. Data Science for Knowledge Creation Research CenterSeoul National University;3. Department of StatisticsKorea University |
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Abstract: | We study a Bayesian analysis of the proportional hazards model with time‐varying coefficients. We consider two priors for time‐varying coefficients – one based on B‐spline basis functions and the other based on Gamma processes – and we use a beta process prior for the baseline hazard functions. We show that the two priors provide optimal posterior convergence rates (up to the term) and that the Bayes factor is consistent for testing the assumption of the proportional hazards when the two priors are used for an alternative hypothesis. In addition, adaptive priors are considered for theoretical investigation, in which the smoothness of the true function is assumed to be unknown, and prior distributions are assigned based on B‐splines. |
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Keywords: | Bayes factor consistency beta process posterior convergence rate proportional hazards model time‐varying coefficients |
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