Transporting Trial Evidence Under Posterior Drift and Possible Hidden Confounding

Abstract

Randomized trials provide internally valid treatment-effect evidence, but trial participants may not represent the target population. In contrast, observational studies are often closer to the target population, but their treatment assignment may be affected by possible hidden confounding. We develop a robust posterior-drift framework for estimating the average treatment effect in an observational target population when exact conditional-effect transportability may fail. The framework represents observational conditional potential-outcome regressions as their randomized-trial counterparts plus source-specific drifts. The randomized trial serves as an internally valid anchor, while the observational study supplies the target covariate distribution and partial information about the target causal contrast. To account for possible hidden confounding, we consider a Rosenbaum-type uncertainty set induced by a sensitivity parameter on the generalized propensity score and estimate the drift through a minimax worst-case risk criterion. We derive efficiency results in auxiliary regimes, establish uniform concentration and near-optimality guarantees for the minimax estimator, and handle general parametric and smooth nonparametric drift classes. Simulations and an ACTG 175--WIHS application show that the proposed analysis yields more cautious and interpretable target-population effect estimates than exact-transportability analyses.