Mean residual life (MRL) is the remaining life expectancy of a subject who has survived to a certain time point and can be used as an alternative to hazard function for characterizing the distribution of a time-to-event variable. Inference and application of MRL models have primarily focused on full-cohort studies. In practice, case-cohort and nested case-control designs have been commonly used within large cohorts that have long follow-up and study rare diseases, particularly when studying costly molecular biomarkers. They enable prospective inference as the full-cohort design with significant cost-saving benefits. In this paper, we study the modeling and inference of a family of generalized MRL models under case-cohort and nested case-control designs. Built upon the idea of inverse selection probability, the weighted estimating equations are constructed to estimate regression parameters and baseline MRL function. Asymptotic properties of the proposed estimators are established and finite-sample performance is evaluated by extensive numerical simulations. An application to the New York University Women’s Health Study is presented to illustrate the proposed models and demonstrate a model diagnostic method to guide practical implementation.

中文翻译：

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病例队列和嵌套病例对照研究的广义平均剩余寿命模型。

平均剩余寿命 (MRL) 是存活到某个时间点的受试者的剩余预期寿命，可用作风险函数的替代方法，用于表征时间到事件变量的分布。MRL 模型的推理和应用主要集中在全队列研究上。在实践中，病例队列和嵌套病例对照设计通常用于长期随访和研究罕见疾病的大型队列，特别是在研究昂贵的分子生物标志物时。它们使前瞻性推理成为具有显着成本节约优势的全队列设计。在本文中，我们研究了在病例队列和嵌套病例对照设计下的一系列广义 MRL 模型的建模和推理。基于逆选择概率的思想，构建加权估计方程来估计回归参数和基线 MRL 函数。建立了所提出的估计器的渐近特性，并通过广泛的数值模拟来评估有限样本的性能。提出了对纽约大学妇女健康研究的应用程序，以说明所提出的模型并展示指导实际实施的模型诊断方法。