Abstract：
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.
摘要：
生存分析中的几种方法都是基于比例风险假设。然而,这种假设限制性很强，在实践中往往不合理。因此,在实际应用中，不依赖于比例风险假设的效应估计是非常可取的。一个流行的例子是受限平均生存时间(RMST)。它被定义为存活曲线下的面积，直到一个预先指定的时间点，因此，将存活曲线总结成一个有意义的估计。对于基于RMST的双样本比较，先前的研究发现了小样本渐近检验的I型误差的膨胀，因此,已经开发了双样本置换测试。本文的第一个目标是通过考虑Wald型检验统计量及其渐近行为，进一步扩展一般阶乘设计和一般对比假设的置换检验。此外,考虑了分组引导方法。此外，当全局测试通过比较两组以上的RMST来检测到显着差异时，感兴趣的是具体的RMST差异导致结果。然而,全局测试不提供此信息。因此,在第二步中开发了RMST的多个测试，以同时推断几个空假设。特此,结合了局部检验统计量之间的渐近精确依赖结构，以获得更多的功率。最后,在仿真中分析了所提出的全局和多个测试程序的小样本性能，并在一个真实的数据示例中进行了说明。
