Group sequential single arm designs are common in phase II trials as well as attribute testing and acceptance sampling. After the trial is completed, especially if the recommendation is to proceed to further testing, there is interest in full inference on treatment efficacy. For a binary response, there is the potential to construct exact upper and lower confidence limits, the first published method for which is Jennison and Turnbull (1983). We place their method within the modern theory of exact confidence limits and provide a new general result that ensures that the exact limits are consistent with the test result, an issue that has been largely ignored in the literature. Amongst methods based on the minimal sufficient statistic, we propose two exact methods that out‐perform Jennison and Turnbull's method across 10 selected designs. One of these we prefer and recommend for practical and theoretical reasons. We also investigate a method based on inverting Fisher's combination test, as well as a pure tie‐breaking variant of it. For the range of designs considered, neither of these methods result in large enough improvements in efficiency to justify violation of the sufficiency principle. For any nonadaptive sequential design, an R‐package is provided to select a method and compute the inference from a given realization.

中文翻译：

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一组连续单臂二元试验后的确切置信限

小组顺序单臂设计在II期试验以及属性测试和验收抽样中很常见。在试验完成之后，尤其是如果建议继续进行测试，则有可能对治疗效果进行全面推断。对于二元响应，有可能构建确切的置信上限和下限，最早发表的方法是Jennison和Turnbull（1983）。我们将其方法置于精确置信度极限的现代理论之内，并提供了一个新的通用结果，可确保精确极限与测试结果相符，这一问题在文献中已被很大程度上忽略。在基于最小充分统计量的方法中，我们提出了两种精确的方法，它们在10个选定设计中的表现优于Jennison和Turnbull的方法。由于实际和理论上的原因，我们更喜欢并推荐其中之一。我们还研究了一种基于费舍尔组合检验倒置的方法，以及该方法的纯平局决胜方案。对于所考虑的设计范围，这两种方法均未在效率上取得足够大的改进，足以证明违反了充分性原则。对于任何非自适应顺序设计，都提供了R包以选择一种方法并根据给定的实现计算推论。