Estimation of combined treatment effects by restricted mean survival time

Restricted mean survival time (RMST) endpoints are becoming commonly used as trialists look to analyse time-to-event outcomes without the restrictions of the proportional hazards assumption. An additional benefit of RMST endpoints which has so far remained unexplored is their capability to combine treatment main effects and treatment-by-covariate interaction terms into single one-dimensional estimators under both proportional and non-proportional hazards. By utilising RMST estimators, trialists may assess treatment effects associated with multiple covariates, including interaction terms - an inherent limitation of proportional hazards models when this assumption is violated.

We present a simulation study using a case study of a randomised controlled trial of Gamma interferon for the treatment of chronic granulomatous disease. We evaluate the power and type I error rate of parametric and non-parametric RMST estimators of combined treatment effects under both proportional and non-proportional hazards. Performance is evaluated when the model or the knot point is specified correctly or misspecified. We also explore the effect of truncation time.

Simulations show that parametric RMST estimators offer greater power when covariate effects and knot-point locations are correctly specified or only mildly misspecified. However, their performance deteriorates as omitted covariate effects increase or knot locations become more misspecified. Under substantial misspecification, the non-parametric estimator is more robust, maintaining stable type I error rates and improved power. For the non-parametric approach, power increases with later truncation times.

This paper demonstrates the role of RMST estimators for survival analysis in the presence of main treatment effects and treatment-by-covariate interactions - highlighting the utility of RMST estimators in the analysis of trials with combined treatment effects. This paper offers further practical guidance on the strengths and limitations of parametric and non-parametric RMST estimators in the presence of model misspecification. It also serves as a case study for trialists wishing to explore RMST estimators by simulations tailored to their own research context.