Tang derived the exact power formulas for t tests and analysis of covariance (ANCOVA) in superiority, noninferiority (NI), and equivalence trials. The power calculation in equivalence trials can be simplified by using Owen’s Q function, which is available in standard statistical software. We extend the exact power determination method for ANCOVA to unstratified and stratified multi-arm randomized trials. The method is applied to the design of multi-arm trials and gold standard NI trials. Supplementary materials for this article are available online.

中文翻译：

---

关于t检验和协方差分析的精确功效计算的注意事项

Tang得出了在优劣，非劣效性（NI）和等效性试验中进行t检验和协方差分析（ANCOVA）的精确功效公式。可使用标准统计软件中提供的Owen Q函数简化等效试验中的功效计算。我们将ANCOVA的精确功率确定方法扩展到未分层和分层的多组随机试验。该方法适用于多臂试验和金标准NI试验的设计。可在线获得本文的补充材料。