Bayesian random threshold estimation in a Cox proportional hazards cure model |
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Authors: | Lili Zhao Dai Feng Emily L. Bellile Jeremy M. G. Taylor |
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Affiliation: | 1. Department of Biostatistics, University of Michigan, , Ann Arbor, MI, U.S.A.;2. Biometrics Research, Merck Research Lab, , Rahway, NJ, U.S.A.;3. University of Michigan Comprehensive Cancer Center, , Ann Arbor, MI, U.S.A. |
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Abstract: | In this paper, we develop a Bayesian approach to estimate a Cox proportional hazards model that allows a threshold in the regression coefficient, when some fraction of subjects are not susceptible to the event of interest. A data augmentation scheme with latent binary cure indicators is adopted to simplify the Markov chain Monte Carlo implementation. Given the binary cure indicators, the Cox cure model reduces to a standard Cox model and a logistic regression model. Furthermore, the threshold detection problem reverts to a threshold problem in a regular Cox model. The baseline cumulative hazard for the Cox model is formulated non‐parametrically using counting processes with a gamma process prior. Simulation studies demonstrate that the method provides accurate point and interval estimates. Application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease‐specific survival changes after the threshold. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | threshold Cox model cure model mixture model Markov chain Monte Carlo |
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