Analytical Evaluation of the 2‐in‐1 Adaptive Design for Binary Endpoints

To reduce drug development costs and time in therapeutic areas with high unmet medical needs, sponsors are often motivated to accelerate the drug development process, specifically by skipping the Phase 2 trial and starting the Phase 3 trial directly after the Phase 1 trial. To address this need, a novel design called 2‐in‐1 adaptive design has been proposed recently. This design allows a trial to maintain a small trial or to expand to a large trial adaptively based on decisions made based on the interim analysis. Although several statistical methods have been proposed for the 2‐in‐1 adaptive design, they specifically emphasize clinical trials with continuous or time‐to‐event endpoints assuming the normal approximation of the test statistic. Methods for the 2‐in‐1 adaptive design with binary endpoints are notably lacking. For binary endpoints, some statistical tests do not rely on the normal approximation. Therefore, it is not clear whether the operating characteristics obtained by existing 2‐in‐1 adaptive design methods in the context of continuous or time‐to‐event endpoints can be generalized to cases with binary endpoints. For this study, we propose formulas to evaluate the type I error rate and power for the 2‐in‐1 adaptive design for binary endpoints. Our proposed formulas can evaluate the exact type I error rate and power without using Monte Carlo simulations. Moreover, the proposed formulas are useful for any statistical test of binary endpoints. Numerical investigations under different scenarios demonstrated that the operating characteristics for the 2‐in‐1 adaptive design with binary endpoints are similar to those with continuous or time‐to‐event endpoints. We present the application of our proposed formulas to a clinical trial in patients with pyruvate kinase deficiency.