Bayesian survival analysis using gamma processes with adaptive time partition

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 modelled 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.

Keywords:

• Bayesian survival analysis
• gamma process
• proportional hazards model
• reversible jump Markov chain Monte Carlo

2010 Mathematics Subject Classification:

• 62G05 Non-parametric estimation

Disclosure statement

No potential conflict of interest was reported by the authors.