A note on confidence intervals for the restricted mean survival time based on transformations in small sample size

Restricted mean survival time (RMST) is one measure now used to summarize time-to-event type data, but it has been pointed out that the distribution of differences in RMST deviates markedly from a normal distribution for controlled clinical trials with small sample sizes. Therefore, we conducted a numerical simulation of the RMST in which the one-sample survival time follows a Weibull distribution, comparing eight different confidence intervals combining two types of variance with four types of variable transformations, including no transformation. The evaluation items were the coverage probability and the above and below error probabilities for the true value. The variance types were based on Greenwood's formula and its Kaplan-Meier correction. The arcsine square root transformation, logit transformation, and complementary log-log transformation were used as the variable transformations. When the sample size was small and the event rate was low, the confidence interval of the untransformed RMST tended to have a small coverage probability and to be overestimated. Variance by Kaplan-Meier correction improved the coverage. The problems of coverage and overestimation were also improved by variable transformations, and in particular, applying the logit transformation and the complementary log-log transformation both resulted in substantial improvements. Our study suggested that it is preferable to construct the confidence intervals of RMST using the logit transformation for variances based on Greenwood's formula in small sample size trials. The SAS code to replicate the analyses is available at https://github.com/HiroyaHashimoto/SAS-Programs.