Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

翻译：生存分析中的若干方法依赖于比例风险假设。然而，该假设约束性极强，在实践中往往缺乏合理性。因此，在应用中迫切需要不依赖比例风险假设的效应估计量。受限平均生存时间（RMST）是其中典型代表：其定义为生存曲线在预设时间点前的曲线下面积，从而将生存曲线概括为有意义的估计量。针对基于RMST的两样本比较，既往研究发现小样本情况下渐近检验的第一类错误膨胀，因此已开发出两样本置换检验。本文的首要目标是将置换检验进一步推广至一般因子设计与一般对比假设，通过考虑Wald型检验统计量及其渐近性质实现，同时引入分组Bootstrap方法。此外，当全局检验通过比较超过两组的RMST检测出显著差异时，亟需明确哪些具体的RMST差异导致了该结果，但全局检验无法提供此类信息。为此，我们在第二步中开发了RMST的多重检验，以同时推断多个原假设。在此过程中，通过纳入局部检验统计量之间渐近精确的依赖结构以提升统计功效。最后，通过模拟实验分析所提出的全局检验与多重检验方法在小样本条件下的性能，并利用真实数据示例进行展示。