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.
