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基于比例风险假设。然而，该假设具有严格限制性，在实践中往往难以成立。因此，在实际应用中，不依赖比例风险假设的效应估计量极具价值。受限平均生存时间（RMST）便是其中典型示例，其定义为生存曲线至预设时间点所围面积，从而将生存曲线归纳为有意义的估计量。针对基于RMST的两样本比较，既往研究发现渐近检验在小样本情况下会导致第一类错误膨胀，故而已开发出两样本置换检验。本文的首要目标是通过考虑沃尔德型检验统计量及其渐近性质，将置换检验进一步推广至一般因子设计和一般对比假设。此外，还考虑了分组自助法。当全局检验通过比较两组以上RMST检测到显著差异时，通常需明确哪些具体RMST差异导致了该结果——然而全局检验无法提供此类信息。为此，本研究的第二步将开发RMST多重检验方法，以同时推断多个零假设。在此过程中，通过纳入局部检验统计量间的渐近精确依赖结构来提升检验效能。最后，通过模拟实验分析所提出的全局检验和多重检验程序在小样本中的表现，并利用真实数据示例加以说明。