A Bayesian Survival Tree Partition Model Using Latent Gaussian Processes

TL;DR

This paper introduces a Bayesian survival tree model that combines flexibility and interpretability by partitioning data and modeling hazards with latent Gaussian processes, useful for subgroup analysis and biomarker discovery.

Contribution

It proposes a novel Bayesian tree partition model with Gaussian process hazard modeling and an efficient MCMC algorithm, enhancing inference and flexibility in survival analysis.

Findings

Model applied successfully to liver survival data

Outperforms existing methods on simulated data

Provides interpretable subgroup and biomarker insights

Abstract

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.