Semiparametric regression of mean residual life with censoring and covariate dimension reduction

TL;DR

This paper introduces a flexible semiparametric regression model for censored survival data that estimates mean residual life, incorporates covariate dimension reduction, and provides efficient inference methods validated through simulations and real data analysis.

Contribution

It develops a novel semiparametric mean residual life model with covariate dimension reduction and efficient estimation techniques for censored data.

Findings

Estimators are root-n consistent and asymptotically normal.

The method effectively predicts residual life in survival data.

Application to kidney transplantation data demonstrates practical utility.

Abstract

We propose a new class of semiparametric regression models of mean residual life for censored outcome data. The models, which enable us to estimate the expected remaining survival time and generalize commonly used mean residual life models, also conduct covariate dimension reduction. Using the geometric approaches in semiparametrics literature and the martingale properties with survival data, we propose a flexible inference procedure that relaxes the parametric assumptions on the dependence of mean residual life on covariates and how long a patient has lived. We show that the estimators for the covariate effects are root-$n$ consistent, asymptotically normal, and semiparametrically efficient. With the unspecified mean residual life function, we provide a nonparametric estimator for predicting the residual life of a given subject, and establish the root-$n$ consistency and asymptotic normality for this estimator. Numerical experiments are conducted to illustrate the feasibility of the proposed estimators. We apply the method to analyze a national kidney transplantation dataset to further demonstrate the utility of the work.