Survival Regression Models With Dependent Bayesian Nonparametric Priors

Abstract

We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum and on the Cox proportional hazards model of Kim and Lee. The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently model the hazard as a function of covariates while allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data. Supplementary materials for this article are available online.

Keywords:

• Bayesian nonparametrics
• Dependent completely random measures
• Survival analysis

Supplementary Materials

Further asymptotic results for the GANTR model, details for CoRMs with LogNormal scores and Gamma directing Lévy measure, proofs of main results, details for simulation algorithm and likelihood gradient, additional simulation studies and additional fits for the kidney transplant study.

Additional information

Funding

Fabrizio Leisen was supported by the European Community’s Seventh Framework Programme [FP7/2007–2013] under grant agreement no. 630677.