Improving Precision of RCT-Based CATE Estimation using Data Borrowing with Double Calibration

Understanding how treatment effects vary across patient characteristics is essential for personalized medicine, yet randomized controlled trials (RCTs) are often underpowered to detect heterogeneous treatment effects (HTEs). We propose a framework that improves the efficiency of conditional average treatment effect (CATE) estimation in RCTs by leveraging large observational studies (OS) while preserving RCT unbiasedness. Framing CATE estimation as a supervised learning problem, we show that estimation variance is minimized using the counterfactual mean outcome (CMO) as an augmentation function. We derive finite-sample error bounds and give conditions under which OS data improves CMO estimation, and thus CATE efficiency, even under confounding in the OS or outcome distribution shift between populations. We introduce R-OSCAR (Robust Observational Studies for CMO-Augmented RCT), a two-stage estimator that calibrates OS outcome predictions to the RCT population and corrects residual bias through regularized regression. For any OS-derived nuisance, R-OSCAR is consistent for the RCT-population CATE, and is efficient relative to RCT-only estimators when the RCT-OS outcome mean discrepancy is estimable from the RCT at lower complexity than the full RCT outcome model. A cross-fitted RCT diagnostic determines, from observable data alone, whether borrowing from a given OS is supported. Simulations show R-OSCAR can reduce the RCT sample size needed for HTE detection by up to 75%, while remaining robust to misspecification. We validate on two case studies: a semi-synthetic analysis of the Tennessee STAR study with constructed observational confounding, and the Greenlight Plus pediatric-obesity trial linked with external electronic-health-record controls, where borrowing improves control-arm estimation for small trials and the diagnostic certifies it only where the records cover the trial population.