Proximal Path-Specific Inference

TL;DR

This paper introduces new methods for causal mediation analysis that handle unmeasured confounding using proxy variables, providing robust estimators validated through simulations and real data.

Contribution

It develops four nonparametric identification strategies and a quadruply robust estimator leveraging proximal confounding bridge functions.

Findings

Achieves $\\sqrt{n}$-consistency and asymptotic normality with machine learning.

Validates methods via simulations and real data on prenatal care and preterm birth.

Provides a novel approach to handle unmeasured confounding in mediation analysis.

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.