Double-robust semiparametric estimator for differences in restricted mean lifetimes in observational studies

Restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times. Differences in this quantity can be used as a basis for comparing several groups. For example, transplant surgeons, nephrologists, and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making. As the factor of interest is not randomized, covariate adjustment is needed to account for imbalances in confounding factors. In this report, we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors. The proposed method involves building working models for the time-to-event and coarsening mechanism (i.e., group assignment and censoring). We show that the proposed estimator possesses the double robust property; i.e., when either the time-to-event or coarsening process is modeled correctly, the estimator is consistent and asymptotically normal. Simulation studies are conducted to assess its finite-sample performance and the method is applied to national kidney transplant data.