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Posterior propriety and computation for the Cox regression model with applications to missing covariates

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  • Ming-Hui Chen
  • Joseph G. Ibrahim
  • Qi-Man Shao

Abstract

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, β, in Cox's partial likelihood, which can be obtained as the limiting marginal posterior distribution of β through the specification of a gamma process prior for the cumulative baseline hazard and a uniform improper prior for β. We also examine necessary and sufficient conditions for posterior propriety of the regression coefficients, β, 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. Copyright 2006, Oxford University Press.

Suggested Citation

  • Ming-Hui Chen & Joseph G. Ibrahim & Qi-Man Shao, 2006. "Posterior propriety and computation for the Cox regression model with applications to missing covariates," Biometrika, Biometrika Trust, vol. 93(4), pages 791-807, December.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:4:p:791-807
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    File URL: http://hdl.handle.net/10.1093/biomet/93.4.791
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    Cited by:

    1. Joseph Ibrahim & Geert Molenberghs, 2009. "Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 1-43, May.
    2. Joseph Ibrahim & Geert Molenberghs, 2009. "Rejoinder on: Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 68-75, May.
    3. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    4. Chen, Ming-Hui & Ibrahim, Joseph G. & Shao, Qi-Man, 2009. "Maximum likelihood inference for the Cox regression model with applications to missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2018-2030, October.
    5. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Multiple Imputation for Regression Models with Missing Mixed Continuous-Discrete Covariates," Discussion Paper Series DP2018-15, Research Institute for Economics & Business Administration, Kobe University.
    6. Lubomír Štěpánek & Filip Habarta & Ivana Malá & Ladislav Štěpánek & Marie Nakládalová & Alena Boriková & Luboš Marek, 2023. "Machine Learning at the Service of Survival Analysis: Predictions Using Time-to-Event Decomposition and Classification Applied to a Decrease of Blood Antibodies against COVID-19," Mathematics, MDPI, vol. 11(4), pages 1-27, February.

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