Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysis

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.