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.

翻译：平均残存寿命函数是生存分布的一个关键泛函。它具有实用的解释意义，即给定生存到某一特定时间点后的预期剩余寿命，同时也能刻画生存分布的特征。然而，在概率建模框架下，其推断方法受到的关注有限。本文旨在为平均残存寿命回归提供通用的推断方法论。我们采用狄利克雷过程混合模型来刻画协变量与生存响应的联合随机机制。这种密度回归方法为条件响应分布的平均残存寿命提供了灵活的结构，允许平均残存寿命既可作为给定特定时间点下协变量的函数呈现一般形态，也可作为给定协变量值下时间的函数。我们进一步扩展该混合模型以纳入实验组间的依赖性。这一扩展基于组特异性混合分布的相依狄利克雷过程先验，其公共原子与跨组变化的权重通过潜二元贝塔分布随机变量实现。我们讨论了回归模型的性质，并发展了后验推断方法。通过模拟数据示例展示了方法论的不同组成部分，并将该模型应用于包含右删失生存时间的数据集。