For equivalence trials with survival outcomes, a popular testing approach is the elegant test for equivalence of two survival functions suggested by Wellek (Biometrics 49: 877–881, 1993). This test evaluates whether or not the difference between the true survival curves is practically irrelevant by specifying an equivalence margin on the hazard ratio under the proportional hazards assumption. However, this approach is based on extrapolating the behavior of the survival curves to the whole time axis, whereas in practice survival times are only observed until the end of follow-up. We propose a modification of Welleks test that only addresses equivalence until end of follow-up and derive the large sample properties of this test. Another issue is the proportional hazards assumption which may not be realistic. If this assumption is violated, one may severely misjudge the actual treatment effect with a hazard ratio quantification and wrongly declare equivalence. We suggest a non-parametric test for assessing survival equivalence within the follow-up period. We derive the large sample properties of this test and provide an approximation to the limiting distribution under some mild assumptions on the functional form of the difference between the two survival curves. Both suggestions are investigated by simulation and applied to a clinical trial on survival of gastric cancer patients.

对于具有生存结果的等效性试验，一种流行的测试方法是 Wellek 建议的两个生存函数等效性的优雅测试（Biometrics 49: 877–881, 1993）。该检验通过在风险比例假设下指定风险比的等效边际来评估真实生存曲线之间的差异是否实际上无关。然而，这种方法基于将生存曲线的行为外推到整个时间轴，而实际上生存时间仅观察到随访结束。我们建议对 Welleks 测试进行修改，该修改仅解决随访结束前的等效性问题，并推导出该测试的大样本属性。另一个问题是可能不现实的比例风险假设。如果违反这个假设，人们可能会以风险比量化严重错误地判断实际治疗效果并错误地宣布等效性。我们建议使用非参数检验来评估随访期内的生存等效性。我们推导出该测试的大样本特性，并在对两条生存曲线之间差异的函数形式的一些温和假设下提供了极限分布的近似值。这两项建议均通过模拟研究并应用于胃癌患者生存的临床试验。我们推导出该测试的大样本特性，并在对两条生存曲线之间差异的函数形式的一些温和假设下提供了极限分布的近似值。这两项建议均通过模拟研究并应用于胃癌患者生存的临床试验。我们推导出该测试的大样本特性，并在对两条生存曲线之间差异的函数形式的一些温和假设下提供了极限分布的近似值。这两项建议均通过模拟研究并应用于胃癌患者生存的临床试验。