ABSTRACT In addition to point estimate for the probability of response in a two-stage design (e.g. Simon's two-stage design for binary endpoints), confidence limits should be computed and reported. The current method of inverting the p-value function to compute the confidence interval does not guarantee coverage probability in a two-stage setting. The existing exact approach to calculate one-sided limits is based on the overall number of responses to order the sample space. This approach could be conservative because many sample points have the same limits. We propose a new exact one-sided interval based on p-value for the sample space ordering. Exact intervals are computed by using binomial distributions directly, instead of a normal approximation. Both exact intervals preserve the nominal confidence level. The proposed exact interval based on the p-value generally performs better than the other exact interval with regard to expected length and simple average length of confidence intervals.

中文翻译：

---

两阶段设计中响应概率的精确置信限

摘要 除了对两阶段设计中的响应概率进行点估计（例如，Simon 的二元终点两阶段设计）外，还应计算并报告置信限。当前通过反转 p 值函数来计算置信区间的方法不能保证两阶段设置中的覆盖概率。计算单边限制的现有精确方法是基于对样本空间进行排序的响应总数。这种方法可能比较保守，因为许多样本点具有相同的限制。我们提出了一种基于 p 值的新的精确单边区间用于样本空间排序。精确间隔是通过直接使用二项式分布而不是正态近似来计算的。两个精确区间均保留名义置信水平。就置信区间的预期长度和简单平均长度而言，基于 p 值提出的精确区间通常比其他精确区间表现更好。