Bayesian nonparametric mean residual life regression

Abstract: The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the survival distribution. However, it has received limited attention in terms of inference methods under a probabilistic modeling framework. We seek to provide general inference methodology for mean residual life regression. We employ Dirichlet process mixture modeling for the joint stochastic mechanism of the covariates and the survival response. This density regression approach implies a flexible model structure for the mean residual life of the conditional response distribution, allowing general shapes for mean residual life as a function of covariates given a specific time point, as well as a function of time given particular values of the covariates. We further extend the mixture model to incorporate dependence across experimental groups. This extension is built from a dependent Dirichlet process prior for the group-specific mixing distributions, with common atoms and weights that vary across groups through latent bivariate Beta distributed random variables. We discuss properties of the regression models, and develop methods for posterior inference. The different components of the methodology are illustrated with simulated data examples, and the model is also applied to a data set comprising right censored survival times.