BACKGROUND Standard futility analyses designed for a proportional hazards setting may have serious drawbacks when non-proportional hazards are present. One important type of non-proportional hazards occurs when the treatment effect is delayed. That is, there is little or no early treatment effect but a substantial later effect. METHODS We define optimality criteria for futility analyses in this setting and propose simple search procedures for deriving such rules in practice. RESULTS We demonstrate the advantages of the optimal rules over commonly used rules in reducing the average number of events, the average sample size, or the average study duration under the null hypothesis with minimal power loss under the alternative hypothesis. CONCLUSION Optimal futility rules can be derived for a non-proportional hazards setting that control the loss of power under the alternative hypothesis while maximizing the gain in early stopping under the null hypothesis.

中文翻译：

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具有不成比例风险的随机临床试验的无效性监测：最佳条件功效方法。

背景技术当存在不成比例的危险时，为成比例的危险设置而设计的标准无效性分析可能具有严重的缺陷。当治疗效果延迟时，就会出现一种重要的非比例风险。也就是说，早期治疗效果很小或没有，但后期效果显着。方法 我们定义了这种情况下无效性分析的最优标准，并提出了在实践中推导此类规则的简单搜索程序。结果我们证明了最优规则相对于常用规则的优势在于，在减少零假设下的平均事件数、平均样本量或平均研究持续时间方面，在备择假设下具有最小的功率损失。结论 对于非比例风险设置，可以导出最佳无效规则，该规则控制备择假设下的功率损失，同时最大化原假设下早期停止的增益。