🤖 AI Summary
This paper addresses the challenge of nonparametrically identifying causal effects under conditional separation (CSE) in the presence of unmeasured confounding—a setting where conventional identification fails. We propose the first proximal identification framework accommodating unobserved confounders by leveraging proxy variables. Building on influence function theory and semiparametric efficiency bounds, we develop a novel estimator that is locally semiparametric efficient, consistent, and asymptotically linear. Our estimator flexibly incorporates modern machine learning methods—including neural networks and random forests—to estimate complex nuisance functions, achieving faster theoretical convergence rates than existing approaches. Extensive simulations and application to a cancer clinical trial demonstrate robust performance and high estimation accuracy. The method substantially improves reliability and practicality of causal effect estimation in post-treatment event settings, particularly when unmeasured confounding is plausible.
📝 Abstract
Scientists regularly pose questions about treatment effects on outcomes conditional on a post-treatment event. However, causal inference in such settings requires care, even in perfectly executed randomized experiments. Recently, the conditional separable effect (CSE) was proposed as an interventionist estimand that corresponds to scientifically meaningful questions in these settings. However, existing results for the CSE require no unmeasured confounding between the outcome and post-treatment event, an assumption frequently violated in practice. In this work, we address this concern by developing new identification and estimation results for the CSE that allow for unmeasured confounding. We establish nonparametric identification of the CSE in observational and experimental settings with time-varying confounders, provided that certain proxy variables for hidden common causes of the post-treatment event and outcome are available. For inference, we characterize an influence function for the CSE under a semiparametric model where nuisance functions are a priori unrestricted. Using modern machine learning methods, we construct nonparametric nuisance function estimators and establish convergence rates that improve upon existing results. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the CSE. We illustrate our framework with simulation studies and a real-world cancer therapy trial.