Posterior propriety and computation for the Cox regression model with applications to missing covariates
Posterior propriety and computation for the Cox regression model with applications to missing covariates
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DOI：
10.1093/biomet/93.4.791
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发表时间：
2006-12-01
期刊：
影响因子：
2.7
通讯作者：
Shao, Qi-Man
中科院分区：
文献类型：
--
作者：
Chen, Ming-Hui;Ibrahim, Joseph G.;Shao, Qi-Man
在本文中，我们对考克斯回归模型的贝叶斯推断进行了深入的理论研究。我们为考克斯偏似然中的回归系数β的后验合理性建立了充分必要条件，该条件可通过对累积基线风险指定伽马过程先验以及对β指定均匀的不恰当先验，作为β的极限边缘后验分布而得到。我们还使用全似然贝叶斯方法研究了回归系数β的后验合理性的充分必要条件，其中对累积基线风险指定了伽马过程先验。我们研究了在完全观测数据设置以及涉及缺失协变量的设置下后验合理性的特征。在贝叶斯计算中引入潜在变量以促进一种简单的吉布斯抽样方案。给出了一个真实数据集以说明所提出的方法。
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.