Journal
BIOMETRIKA
Volume 90, Issue 3, Pages 629-641Publisher
BIOMETRIKA TRUST
DOI: 10.1093/biomet/90.3.629
Keywords
continuous survival data; frailty model; gamma process; Gibbs sampling; grouped survival data; proportional hazards model; time-dependent covariate; time-dependent parameter
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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 Bayeslan inference in various practical applications.
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