Robust Estimation and Inference in Hybrid Controlled Trials

Hybrid controlled trials (HCTs) combine randomized controlled trials (RCTs) with external control data to enhance efficiency, but bias may arise when external controls differ systematically from trial participants. We propose conformal selective borrowing, a novel framework with automatic tuning that adaptively incorporates external data while preserving valid post-selection inference through randomization tests. This method unites modern conformal prediction techniques from machine learning with classical randomization principles pioneered by Fisher, improving statistical power while maintaining exact finite-sample type I error control. The framework offers a rigorous and flexible approach for generating credible evidence in settings where RCTs are small or patient accrual is slow. We illustrate its utility across continuous, binary, and time-to-event outcomes, present new theoretical results, and demonstrate its application in a non-small cell lung cancer case study.

causal inference

conformal prediction

data integration

external control

randomization inference