Proximal Difference-in-Differences for Long-Term Causal Learning under Confounding and Outcome Drift

Estimating long-term treatment effects is essential for scientific and industrial evaluation, yet the limited follow-up duration of randomized controlled trials (RCTs) poses a significant challenge. Even the growing use of open-label extensions fails to resolve this issue, as such designs systematically censor long-term control trajectories. While supplementing RCTs with real-world evidence is a common strategy, existing methods often rely on restrictive exchangeability assumptions that fail under latent confounding. We propose a novel proximal framework to integrate long-term real-world evidence into RCTs with open-label extensions. Our approach successfully identifies long-term effects even in the presence of time-varying latent confounding effects and inter-study outcome drift. We provide a doubly robust locally efficient estimator that provides further resilience to model misspecification. Empirical results demonstrate that our framework maintains validity in complex data-generating processes that compromise standard approaches.