  Survival models are used to analyze time-to-event data in a variety of
disciplines. Proportional hazard models provide interpretable parameter
estimates, but proportional hazards assumptions are not always appropriate.
Non-parametric models are more flexible but often lack a clear inferential
framework. We propose a Bayesian tree partition model which is both flexible
and inferential. Inference is obtained through the posterior tree structure and
flexibility is preserved by modeling the the hazard function in each partition
using a latent exponentiated Gaussian process. An efficient reversible jump
Markov chain Monte Carlo algorithm is accomplished by marginalizing the
parameters in each partition element via a Laplace approximation. Consistency
properties for the estimator are established. The method can be used to help
determine subgroups as well as prognostic and/or predictive biomarkers in
time-to-event data. The method is applied to a liver survival dataset and is
compared with some existing methods on simulated data.
