Proximal Path-Specific Inference

2026-05-10

AI Summary

This study addresses the challenge of reliably estimating path-specific effects in causal mediation analysis when unmeasured confounding is present, particularly treatment-induced mediator–outcome confounding. The authors propose a novel approach that integrates proxy variables with proximal causal inference, constructing proximal confounding bridge functions based on observed covariates. They develop four nonparametric identification strategies and introduce a quadruply robust, locally efficient debiased machine learning estimator. Under relatively weak assumptions, the proposed method achieves √n-consistency and asymptotic normality, maintaining robustness even when nuisance functions converge at slow rates. Simulations and an application to CDC birth data demonstrate its empirical validity, successfully identifying the independent pathway through which prenatal care affects preterm birth via preeclampsia.

Abstract

Causal mediation analysis has been extended to estimate path-specific effects with multiple intermediate variables, isolating treatment effects through a mediator of interest while excluding pathways through its ancestors. Such analyses address bias from recanting witnesses, i.e., treatment-induced mediator-outcome confounders. However, existing methods typically rely on stringent assumptions precluding general unmeasured confounding, which are often violated in practice. In this paper, we relax these restrictions by leveraging observed covariates as proxy variables to accommodate unmeasured confounding among the treatment, recanting witness, mediator, and outcome. Using proximal confounding bridge functions, we develop four nonparametric identification strategies for the path-specific effect. We further derive the efficient influence function and propose a quadruply robust, locally efficient estimator. To handle high-dimensional nuisance parameters, we propose a proximal debiased machine learning approach. We theoretically guarantee that our estimator achieves $\sqrt{n}$-consistency and asymptotic normality even when machine learning estimators for nuisance functions converge at slower rates. Our approaches are validated via semiparametric and nonparametric simulations and an application to the CDC WONDER Natality study, estimating the path-specific effect of prenatal care on preterm birth through preeclampsia, independent of maternal smoking during pregnancy.

Problem

• causal mediation analysis
• path-specific effects
• unmeasured confounding
• recanting witness
• proximal inference

Innovation

• proximal inference
• path-specific effect
• recanting witness
• quadruply robust estimator
• debiased machine learning