Restricted mean survival time for interval‐censored data

Restricted mean survival time (RMST) evaluates the mean event‐free survival time up to a prespecified time point. It has been used as an alternative measure of treatment effect owing to its model‐free structure and clinically meaningful interpretation of treatment benefit for right‐censored data. In clinical trials, another type of censoring called interval censoring may occur if subjects are examined at several discrete time points and the survival time falls into an interval rather than being exactly observed. The missingness of exact observations under interval‐censored cases makes the nonparametric measure of treatment effect more challenging. Employing the linear smoothing technique to overcome the ambiguity, we propose a new model‐free measure for the interval‐censored RMST. As an alternative to the commonly used log‐rank test, we further construct a hypothesis testing procedure to assess the survival difference between two groups. Simulation studies show that the bias of our proposed interval‐censored RMST estimator is negligible and the testing procedure delivers promising performance in detecting between‐group difference with regard to size and power under various configurations of survival curves. The proposed method is illustrated by reanalyzing two real datasets containing interval‐censored observations.