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Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysis

In: Nonparametric Bayesian Inference

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  • Jean-Marie Rolin

    (Université Catholique de Louvain, Institut de Statistique)

Abstract

In this chapter, a very general model of survival data with (exclusive or inclusive) right censoring, explanatory processes, and a baseline predictable hazard function is considered in the context of nonparametric Bayesian analysis. Particular cases are semi-parametric proportional hazards and multiplicative intensity models. If the baseline predictable hazard function is a Levy process, then its distribution conditionally on the censoring times and the explanatory processes is still a Levy process and is completely described. In a semi-parametric case, the posterior distribution of the parameter is also obtained. These posterior distributions are computed for Beta processes and Gamma processes in the proportional hazards and multiplicative intensity models. The noninformative case provides a new likelihood for the parameters even in case of ties, contrary to the Cox likelihood.

Suggested Citation

  • Jean-Marie Rolin, 2024. "Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysis," Springer Books, in: Jean-Pierre Florens & Michel Mouchart (ed.), Nonparametric Bayesian Inference, chapter 0, pages 247-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61329-6_11
    DOI: 10.1007/978-3-031-61329-6_11
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