Partially linear single-index generalized mean residual life models

Mean residual life (MRL) function defines the remaining life expectancy of a subject who has survived to a time point and is an important alternative to the hazard function for characterizing the distribution of a time-to-event variable. Existing MRL models primarily focus on studying the association between risk factors and disease risks using linear model specifications in multiplicative or additive scale. When risk factors have complex correlation structures, nonlinear effects, or interactions, the prefixed linearity assumption may be insufficient to capture the relationship. Single-index modeling framework offers flexibility in reducing dimensionality and modeling nonlinear effects. In this article, we propose a class of partially linear single-index generalized MRL models, the regression component of which consists of both a semiparametric single-index part and a linear regression part. Regression spline technique is employed to approximate the nonparametric single-index function, and parameters are estimated using an iterative algorithm. Double-robust estimators are also proposed to protect against the misspecification of censoring distribution or MRL models. A further contribution of this article is a nonparametric test proposed to formally evaluate the linearity of the single-index function. Asymptotic properties of the estimators are established, and the finite-sample performance is evaluated through extensive numerical simulations. The proposed models and inference approaches are demonstrated by a New York University Langone Health (NYULH) COVID-19 dataset.