Bayesian Survival Analysis Using Gamma Processes with Adaptive Time Partition

TL;DR

This paper introduces a Bayesian survival analysis method using gamma process priors for the baseline hazard, with an adaptive approach to determine the optimal time partition based on posterior estimates.

Contribution

It develops a novel Bayesian framework that models the cumulative baseline hazard with a gamma process and estimates the time partition adaptively from data.

Findings

Posterior-based estimation of interval cutpoints.

Flexible modeling of baseline hazard functions.

Improved inference in survival analysis.

Abstract

In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modeled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions.