Proximal Mediation Analysis with Hidden Recanting Witnesses

2026-06-16

AI Summary

This study addresses the challenge in mediation analysis posed by treatment-induced mediator–outcome confounding—often termed “defiers”—which is typically unobserved and violates standard identification assumptions, thereby complicating estimation of path-specific effects. The paper introduces proximal causal inference into this setting for the first time, proposing three novel identification strategies and developing a semiparametric inference framework based on product-of-robust estimators and minimax debiased learning. The resulting estimator is consistent if at least one of the auxiliary models is correctly specified and achieves the semiparametric efficiency bound when all models are correctly specified and satisfy appropriate convergence rate conditions. Both simulation studies and empirical applications demonstrate the method’s validity and robustness.

Abstract

Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.

Problem

• mediation analysis
• recanting witnesses
• causal inference
• unobserved confounding
• path-specific effects

Innovation

• proximal causal inference
• mediation analysis
• recanting witnesses
• multiply robust estimator
• semiparametric efficiency