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Abstract:
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We present a general framework for fitting Bayesian semiparametric proportional hazards (PH), proportional odds (PO), and accelerated failure time (AFT) models. The formulation consists of a parametric part of the relative risk factors, relative odds or acceleration factors, and a nonparametric part of the baseline survival function. The baseline is modeled via a mixture of Polya trees prior, which provides an intermediate choice between a strictly parametric analysis and allowing the baseline to be completely arbitrary. MCMC is carried out through an empirical Bayes approach coupled with adaptive block updating, where a fit from a standard parametric survival model serves to provide starting proposals. The algorithm is easy to implement and fast, for interval-censored data, as well as standard right-censored, uncensored, and mixtures of these. An important aspect of this work is that, by assuming the same, flexible model for the baseline survival, the PH, PO, and AFT models are placed on a common ground, providing a principle basis for model selection. As an extension, variable selection and spatial frailty models will also be discussed.
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