The mean residual life function is a key functional for a survival distribution. It has 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. In this paper, 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 propose a Dirichlet process mixture modeling approach 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 proposed regression models, and discuss methods for prior specification and posterior inference. The different components of the methodology are illustrated with simulated data sets. Moreover, the modeling approach is applied to a data set comprising right censored survival times of patients with small cell lung cancer.

翻译：平均剩余寿命函数是生存分布的关键泛函。它作为给定生存至特定时间点后的预期剩余寿命具有实际应用价值，同时也能刻画生存分布特征。然而，在概率建模框架下，针对该函数的推断方法研究相对有限。本文旨在为平均剩余寿命回归提供通用的推断方法论。生存数据通常包含影响生存响应分布的预测变量集合，且在许多情况下将协变量作为随机变量纳入建模是自然的选择。为此，我们提出基于狄利克雷过程混合模型的方法，对协变量与生存响应的联合随机机制进行建模。该方法为条件响应分布的平均剩余寿命提供了灵活的模型结构，使得平均剩余寿命既能作为给定时间点上的协变量函数呈现多样形态，也能作为给定协变量向量值的时间函数呈现多样形态。为扩展建模框架的适用范围，我们将混合模型扩展至包含实验组间依赖关系（如处理组与对照组）。该扩展基于组特定混合分布的相依狄利克雷过程先验，各组共享公共位置参数，但权重通过潜在二元贝塔分布随机变量实现组间差异。我们建立了所提回归模型的理论性质，并讨论了先验设定与后验推断方法。通过模拟数据集验证了方法论各组成部分的有效性。此外，该建模方法被应用于包含小细胞肺癌患者右删失生存时间的数据集。