例：A parallel two-group design will be used to test whether the Group 1 (treatment) proportion (P1) is greater than the Group 2 (control) proportion (P2) (H0: P1 - P2 ≤ 0 versus H1: P1 - P2 > 0).
The comparison will be made using a one-sided, two-sample Z-Test with unpooled variance, with a Type I error rate (α) of 0.025. The control group proportion (P2) is assumed to be 0.2. To detect a proportion difference (P1 - P2) of 0.2 (or P1 of 0.4) with 90% power, the number of subjects needed will be 106 in Group 1 (treatment) and 106 in Group 2 (control).
One non-binding futility analysis at 50% information fraction.
East tool：
1. 录入look=1。
2.录入 look=2,futility的boundary family选择conditonal power，点击Design的两组率来compute CP，然后点击Non-binding，Interim=0.5。
Food and Drug Administration, 2019, 适应性设计指南，通常采用Non-binding的无效性界值，其与有效性界值无关，不会增加假阳性率，但power会产生损失。
针对例子的Power损失计算如下：
Power 损失=0.901（第二张截图，只有look=1的power）-0.889（look=2，总样本量不变，但是50%的数据时候，做non-binding的无效分析）=0.012。
Scheme properties除了包含Power的损失，还有一个指标是Stop under H0（参考最后一图片boundary crossing probablity under H0）。
但大家需要考虑的问题是：
1.非劣效和优效是否不同。
2.两组的差异是否一直是常数。
欢迎后台留言讨论。
参考文献：
Gallo P, Mao L, Shih VH (2014). Alternative views on setting clinical trial futility criteria. J Biopharm Stat 24:976-93.
Food and Drug Administration, 2019. Adaptive designs for Clinical trials of drugs and biologics guidance for industry. FDA.
