Proximal Inference on Population Intervention Indirect Effect

2025-04-16

AI Summary

This paper addresses the identification and estimation of population intervention indirect effects (PIIEs) under triple unmeasured confounding—confounding along the exposure–outcome, exposure–mediator, and mediator–outcome pathways—particularly in observational studies where exposure is nonmanipulable or ethically constrained. We first extend PIIE identification to this complex confounding setting. Second, we propose three proximal identification frameworks leveraging proxy variables. Third, we derive the semiparametric efficiency bound and develop a multiply robust, locally efficient debiased machine learning (DML) estimator. Theoretically, the estimator is shown to be √n-consistent and asymptotically normal. Simulation studies demonstrate substantially improved confidence interval coverage compared to conventional methods. Empirical analysis quantifies the indirect effect of alcohol consumption on depression risk mediated by depersonalization symptoms.

Technology Category

• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The population intervention indirect effect (PIIE) is a novel mediation effect representing the indirect component of the population intervention effect. Unlike traditional mediation measures, such as the natural indirect effect, the PIIE holds particular relevance in observational studies involving unethical exposures, when hypothetical interventions that impose harmful exposures are inappropriate. Although prior research has identified PIIE under unmeasured confounders between exposure and outcome, it has not fully addressed the confounding that affects the mediator. This study extends the PIIE identification to settings where unmeasured confounders influence exposure-outcome, exposure-mediator, and mediator-outcome relationships. Specifically, we leverage observed covariates as proxy variables for unmeasured confounders, constructing three proximal identification frameworks. Additionally, we characterize the semiparametric efficiency bound and develop multiply robust and locally efficient estimators. To handle high-dimensional nuisance parameters, we propose a debiased machine learning approach that achieves $sqrt{n}$-consistency and asymptotic normality to estimate the true PIIE values, even when the machine learning estimators for the nuisance functions do not converge at $sqrt{n}$-rate. In simulations, our estimators demonstrate higher confidence interval coverage rates than conventional methods across various model misspecifications. In a real data application, our approaches reveal an indirect effect of alcohol consumption on depression risk mediated by depersonalization symptoms.

Problem

• Identifies PIIE with unmeasured confounders in mediator relationships
• Uses proxy variables for unmeasured confounders in mediation analysis
• Develops robust estimators for PIIE in high-dimensional settings

Innovation

• Proximal identification with proxy variables
• Debiased machine learning for nuisance parameters
• Multiply robust and efficient estimators