Three-arm non-inferiority (NI) trial including the experimental treatment, an active reference treatment, and a placebo where the outcome of interest is binary are considered. While the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), however, recent FDA guideline suggested measures such as relative risk (RR), odds ratio (OR), number needed to treat (NNT) among others, on the basis of which NI can be claimed for binary outcome. Albeit, developing test based on these different functions of binary outcome are challenging. This is because the construction and interpretation of NI margin for such functions are non-trivial extensions of RD based approach. A Frequentist test based on traditional fraction margin approach for RR, OR and NNT are proposed first. Furthermore a conditional testing approach is developed by incorporating assay sensitivity (AS) condition directly into NI testing. A detailed discussion of sample size/power calculation are also put forward which could be readily used while designing such trials in practice. A clinical trial data is reanalyzed to demonstrate the presented approach.

中文翻译：

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三组试验中风险比、优势比和治疗次数的非劣效性检验

三组非劣效性 (NI) 试验包括实验治疗、活性参考治疗和安慰剂，其中考虑了感兴趣的结果是二元的。虽然风险差异 (RD) 是用于测试功效（或有效性）的最常见和经过充分探索的功能形式，但是，最近的 FDA 指南建议了诸如相对风险（RR）、优势比（OR）、需要治疗的人数等措施。 NNT) 等，在此基础上 NI 可以声明为二元结果。尽管如此，基于二元结果的这些不同功能开发测试是具有挑战性的。这是因为此类函数的 NI 裕度的构建和解释是基于 RD 方法的重要扩展。首先提出了一种基于传统分数边际方法的频率测试，用于 RR、OR 和 NNT。此外，通过将测定灵敏度 (AS) 条件直接纳入 NI 测试，开发了一种条件测试方法。还提出了样本量/功效计算的详细讨论，在实践中设计此类试验时可以很容易地使用这些讨论。重新分析临床试验数据以证明所提出的方法。