Enhancing Statistical Validity and Power in Hybrid Controlled Trials: A Randomization Inference Approach with Conformal Selective Borrowing

Randomized controlled trials (RCTs) are the gold standard for causal inference but may lack power because of small populations in rare diseases and limited participation in common diseases due to equipoise concerns. Hybrid controlled trials, which integrate external controls (ECs) from historical studies or large observational data, improve statistical efficiency and are appealing for drug evaluations. However, non-randomized ECs can introduce biases and inflate the type I error rate, especially when the RCT sample size is small. To address this, we propose a Fisher randomization test (FRT) that employs a semiparametric efficient test statistic combining RCT and EC data, with assignments resampled using the actual randomization procedure. The proposed FRT controls the type I error rate even with unmeasured confounding among ECs. However, borrowing biased ECs can reduce FRT power, so we introduce conformal selective borrowing (CSB) to individually borrow comparable ECs. We propose an adaptive procedure to determine the selection threshold, minimizing the mean squared error of a class of CSB estimators and enhancing FRT power. The advantages of our method are demonstrated through simulations and an application to a lung cancer RCT with ECs from the National Cancer Database. Our method is available in the R package intFRT.