With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas and Gelfand (2001) we formulate a semiparametric median residual life regression model induced by a semiparametric accelerated failure time regression model. We employ the median since for the rich nonparametric class of distributions over which we model, the mean need not always exist. We utilize a Bayesian approach which allows full and exact inference. Classical work essentially ignores covariates and is either based upon parametric assumptions or is limited to asymptotic inference in nonparametric settings. No regression modeling of median residual life appears to exist. The Bayesian modeling is developed through Dirichlet process mixing. The models are fitted using Gibbs sampling. Residual life inference is implemented extending the approach of Gelfand and Kottas (to appear). Finally, we present a fairly detailed analysis of a set of survival times with moderate censoring for patients with small cell lung cancer.

Key Words: Censoring; Dirichlet process mixing; residual survival curve; skewness; split densities.

The manuscript is available in postscript and pdf formats.