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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.

Survival Regression Models With Dependent Bayesian Nonparametric Priors