On permutation tests for comparing restricted mean survival time with small sample from randomized trials

Between-group comparison based on the restricted mean survival time (RMST) is getting attention as an alternative to the conventional logrank/hazard ratio approach for time-to-event outcomes in randomized controlled trials (RCTs). The validity of the commonly used nonparametric inference procedure for RMST has been well supported by large sample theories. However, we sometimes encounter cases with a small sample size in practice, where we cannot rely on the large sample properties. Generally, the permutation approach can be useful to handle these situations in RCTs. However, a numerical issue arises when implementing permutation tests for difference or ratio of RMST from two groups. In this article, we discuss the numerical issue and consider six permutation methods for comparing survival time distributions between two groups using RMST in RCTs setting. We conducted extensive numerical studies and assessed type I error rates of these methods. Our numerical studies demonstrated that the inflation of the type I error rate of the asymptotic methods is not negligible when sample size is small, and that all of the six permutation methods are workable solutions. Although some permutation methods became a little conservative, no remarkable inflation of the type I error rates were observed. We recommend using permutation tests instead of the asymptotic tests, especially when the sample size is less than 50 per arm.