Improving Sensitivity Analysis By Synthesizing Randomized Clinical Trials With Limited Overlap

While randomized clinical trials (RCTs) are widely regarded as the gold standard for estimating average treatment effects, their external validity is often constrained by limited sample sizes and restrictive inclusion/exclusion criteria, which may compromise the generalizability of findings to broader real-world populations. Conversely, observational studies typically consist of representative real-world samples but are susceptible to bias due to unmeasured confounders, undermining their internal validity. To address the limitation, sensitivity analysis is often used to estimate bounds for the average treatment effect (ATE) without relying on stringent assumptions of other existing methods. This article introduces a novel synthesis sensitivity analysis estimator that enhances sensitivity analysis in observational studies by incorporating RCT data, even when limited covariate overlap exists between datasets due to differential inclusion/exclusion criteria. We show that the proposed estimator will give a tighter bound when a "separability" condition holds for the sensitivity parameter. Theoretical proofs and simulations show that this method provides a tighter bound than the sensitivity analysis using only observational study data. We apply this method to combine observational study data on drug effectiveness comparison with a partially overlapping RCT data, yielding tighter average treatment effect bounds.