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Biometrika 2003 90(3):629-641; doi:10.1093/biomet/90.3.629
© 2003 by Biometrika Trust
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A Bayesian justification of Cox's partial likelihood

Debajyoti Sinha1, Joseph G.Ibrahim2 and Ming-Hui Chen3

1 Department of Biometry and Epidemiology, Medical University of South Carolina, 135 Cannon Street, Suite 305 E, Charleston, South Carolina 29425, U.S.Asinhad{at}musc.edu 2 Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, CB#7420, Chapel Hill, North Carolina 27599, U.S.A.ibrahim{at}bios.unc.edu 3 Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, Connecticut 06269, U.S.A. mhchen{at}stat.uconn.edu

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.

Key Words: Continuous survival data; Frailty model; Gamma process; Gibbs sampling; Grouped survival data; Proportional hazards model; Time-dependent covariate; Time-dependent parameter

Received January 2002. Revised January 2003


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