Power priors and type I error control: constrained borrowing of external control data

Recently, hybrid designs have garnered significant attention in the healthcare industry due to their potential to improve statistical power and trial efficiency by augmenting randomized controlled trial data with external controls. The power prior methodology provides a versatile framework for constructing and analyzing data from hybrid designs. However, the use of external control data poses a risk of introducing bias, particularly in the presence of prior-data conflict, which can distort treatment effect estimates. Such biases may lead to erroneous conclusions, including the approval of ineffective treatments or the rejection of beneficial ones. To address these concerns, it is essential to borrow an appropriate amount of external data to maintain the type I error rate at an acceptable level, typically determined during trial planning in discussion with regulatory authorities. In this article, we present a novel power prior method to incorporate historical control data while safeguarding against inflation of the type I error rate beyond the maximally allowable nominal level. Through comprehensive simulation studies and an illustrative example, we demonstrate the practical advantages of our approach. The results illustrate that our method provides trial sponsors with a scientifically rigorous strategy for leveraging external control data in constructing efficient and reliable hybrid designs.