Semiparametric estimation of restricted mean survival time as a function of restriction time

The restricted mean survival time (RMST) is an appealing measurement in clinical or epidemiological studies with censored survival outcome and receives a lot of attention in the past decades. It provides a useful alternative to the Cox model for evaluating the covariate effect on survival time. The covariate effect on RMST usually varies with the restriction time. However, existing methods cannot address this problem properly. In this article, we propose a semiparametric framework that directly models RMST as a function of the restriction time. Our proposed model adopts a widely-used proportional form, enabling the estimation of RMST predictions across an interval using a unified model. Furthermore, the covariate effect for multiple restriction time points can be derived simultaneously. We develop estimators based on estimating equations theories and establish the asymptotic properties of the proposed estimators. The finite sample properties of the estimators are evaluated through extensive simulation studies. We further illustrate the application of our proposed method through the analysis of two real data examples. Supplementary Material are available online.