  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. Survival data often include a set of predictor variables for
the survival response distribution, and in many cases it is natural to include
the covariates as random variables into the modeling. We thus employ Dirichlet
process mixture modeling for the joint stochastic mechanism of the covariates
and survival responses. This 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 covariate vector. To expand the scope of the modeling framework, we extend
the mixture model to incorporate dependence across experimental groups, such as
treatment and control groups. This extension is built from a dependent
Dirichlet process prior for the group-specific mixing distributions, with
common locations and weights that vary across groups through latent bivariate
Beta distributed random variables. We develop properties of the regression
models, and discuss methods for prior specification and 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.
