Designing Efficient Hybrid and Single-Arm Trials: External Control Borrowing and Sample Size Calculation

Abstract

External controls (ECs) from historical trials or real-world data have gained increasing attention as a way to augment hybrid and single-arm trials, especially when balanced randomization is infeasible. While most existing work has focused on post-trial inference using ECs, their role in prospective trial design remains less explored. We address this gap by focusing on the sample size determination and power analysis for an experimental design problem that encompasses standard randomized controlled trials (RCTs), hybrid trials, and single-arm trials. Building on estimators derived from the efficient influence function, we develop hybrid and single-arm design strategies that leverage comparable EC data to reduce the required sample size of the current study. We derive asymptotic variance expressions for these estimators in terms of interpretable, population-level quantities and introduce a pre-experimental variance estimation procedure to guide sample size calculation, ensuring prespecified type I error and power for the relevant hypothesis test. Simulation studies demonstrate that the proposed hybrid and single-arm designs maintain valid type I error and achieve target power across diverse scenarios while requiring substantially fewer subjects in the current study than RCT designs. A real data application further illustrates the practical utility and advantages of the proposed hybrid and single-arm designs.