Efficient confidence limits for adaptive one-arm two-stage clinical trials with binary endpoints

Abstract Background Recently, several adaptive one-arm two-stage designs have been developed by fully using the information from previous stages to reduce the expected sample size in clinical trials with binary endpoints as primary outcome. It is important to compute exact confidence limits for these studies. Methods In this article, we propose three new one-sided limits by ordering the sample space based on p-value, average response rate at each stage, and asymptotic lower limit, as compared to another three existing sample size ordering approaches based on average response rate. Among the three proposed approaches, the one based on the average response rate at each stage is not exact, and the remaining two approaches are exact with the coverage probability guaranteed. Results We compare these exact intervals by using the two commonly used criteria: simple average length and expected length. The existing three approaches based on average response rate have similar performance, and they have shorter expected lengths than the two proposed exact approaches although the gain is small, while this trend is reversed under the simple average criterion. Conclusions We would recommend the two exact proposed approaches based on p-value and asymptotic lower limit under the simple average length criterion, and the approach based on average response rate under the expected length criterion.