Semiparametric Additive Modeling of the Restricted Mean Survival Time

Abstract

Analysis of the restricted mean survival time (RMST) has become increasingly common in biomedical studies during the last decade as a means of estimating treatment or covariate effects on survival. Advantages of RMST over the hazard ratio (HR) include increased interpretability and lack of reliance on the often tenuous proportional hazards assumption. Some authors have argued that RMST regression should generally be the frontline analysis as opposed to methods based on counting process increments. However, in order for the use of the RMST to be more mainstream, it is necessary to broaden the range of data structures to which pertinent methods can be applied. In this report, we address this issue from two angles. First, most of existing methodological development for directly modeling RMST has focused on multiplicative models. An additive model may be preferred due to goodness of fit and/or parameter interpretation. Second, many settings encountered nowadays feature high-dimensional categorical (nuisance) covariates, for which parameter estimation is best avoided. Motivated by these considerations, we propose stratified additive models for direct RMST analysis. The proposed methods feature additive covariate effects. Moreover, nuisance factors can be factored out of the estimation, akin to stratification in Cox regression, such that focus can be appropriately awarded to the parameters of chief interest. Large-sample properties of the proposed estimators are derived, and a simulation study is performed to assess finite-sample performance. In addition, we provide techniques for evaluating a fitted model with respect to risk discrimination and predictive accuracy. The proposed methods are then applied to liver transplant data to estimate the effects of donor characteristics on posttransplant survival time.