  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.
