Randomized Clinical Trials (RCTs) measure an intervention's efficacy, but they may not be generalizable to a desired target population if the RCT is not equitable. Thus, representativeness of RCTs has become a national priority. Synthetic Controls (SCs) that incorporate observational data into RCTs have shown great potential to produce more efficient studies, but their equity is rarely considered. Here, we examine how to improve treatment effect estimation and equity of a trial by augmenting "on-trial" concurrent controls with SCs to form a Hybrid Control Arm (HCA). We introduce FRESCA - a framework to evaluate HCA construction methods using RCT simulations. FRESCA shows that doing propensity and equity adjustment when constructing the HCA leads to accurate population treatment effect estimates while meeting equity goals with potentially less "on-trial" patients. This work represents the first investigation of equity in HCA design that provides definitions, metrics, compelling questions, and resources for future work.
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