Decoupling power and type I error rate considerations when incorporating historical control data using a test-then-pool approach

To accelerate a randomized controlled trial, historical control data may be used after ensuring little heterogeneity between the historical and current trials. The test-then-pool approach is a simple frequentist borrowing method that assesses the similarity between historical and current control data using a two-sided test. A limitation of the conventional test-then-pool method is the inability to control the type I error rate and power for the primary hypothesis separately and flexibly for heterogeneity between trials. This is because the two-sided test focuses on the absolute value of the mean difference between the historical and current controls. In this paper, we propose a new test-then-pool method that splits the two-sided hypothesis of the conventional method into two one-sided hypotheses. Testing each one-sided hypothesis with different significance levels allows for the separate control of the type I error rate and power for heterogeneity between trials. We also propose a significance-level selection approach based on the maximum type I error rate and the minimum power. The proposed method prevented a decrease in power even when there was heterogeneity between trials while controlling type I error at a maximum tolerable type I error rate larger than the targeted type I error rate. The application of depression trial data and hypothetical trial data further supported the usefulness of the proposed method.