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A Bayesian justification of Cox's partial likelihood

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  • Debajyoti Sinha

Abstract

In this paper, we establish both naive and formal Bayesian justifications of Cox's (1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time-dependent covariates and time-varying regression parameters. We establish results for continuous time as well as grouped survival data. In addition, we present a Bayesian justification of a modified partial likelihood for handling ties. We also present tools for simplification of the Gibbs sampling algorithm for implementing partial likelihood based Bayesian inference in various practical applications. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Debajyoti Sinha, 2003. "A Bayesian justification of Cox's partial likelihood," Biometrika, Biometrika Trust, vol. 90(3), pages 629-641, September.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:3:p:629-641
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    Cited by:

    1. Steffen Ventz & Rahul Mazumder & Lorenzo Trippa, 2022. "Integration of survival data from multiple studies," Biometrics, The International Biometric Society, vol. 78(4), pages 1365-1376, December.
    2. Hyunsoon Cho & Joseph G. Ibrahim & Debajyoti Sinha & Hongtu Zhu, 2009. "Bayesian Case Influence Diagnostics for Survival Models," Biometrics, The International Biometric Society, vol. 65(1), pages 116-124, March.
    3. Gwangsu Kim & Yongdai Kim & Taeryon Choi, 2017. "Bayesian Analysis of the Proportional Hazards Model with Time-Varying Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 524-544, June.

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