Posterior propriety and computation for the Cox regression model with applications to missing covariates
成果类型：
Article
署名作者：
Chen, Ming-Hui; Ibrahim, Joseph G.; Shao, Qi-Man
署名单位：
University of Connecticut; University of North Carolina; University of North Carolina Chapel Hill; Hong Kong University of Science & Technology
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/93.4.791
发表日期：
2006
页码：
791807
关键词：
摘要：
In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the regression coefficient, beta, in Cox's partial likelihood, which can be obtained as the limiting marginal posterior distribution of beta through the specification of a gamma process prior for the cumulative baseline hazard and a uniform improper prior for beta. We also examine necessary and sufficient conditions for posterior propriety of the regression coefficients, beta, using full likelihood Bayesian approaches in which a gamma process prior is specified for the cumulative baseline hazard. We examine characterisation of posterior propriety under completely observed data settings as well as for settings involving missing covariates. Latent variables are introduced to facilitate a straightforward Gibbs sampling scheme in the Bayesian computation. A real dataset is presented to illustrate the proposed methodology.
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