Optimal Adjustment Sets for Nonparametric Estimation of Weighted Controlled Direct Effect

2025-06-11

AI Summary

This paper addresses the nonparametric identification and estimation of the weighted controlled direct effect (WCDE) in observational studies, aiming to robustly isolate the direct causal effect of exposure on outcome—critical for fairness assessment and mediation analysis. We establish the necessary and sufficient conditions for unique nonparametric identifiability of the WCDE. Building upon this, we derive its efficient influence function and construct an asymptotically linear estimator. Furthermore, we characterize the optimal covariate adjustment set that minimizes the asymptotic variance, revealing a novel adjustment requirement arising from mediator–confounder interactions. The proposed framework substantially reduces estimation variance, thereby enhancing accuracy, robustness, and practicality in direct effect identification. It provides a rigorous theoretical foundation and computationally efficient estimation tools for causal mediation analysis and algorithmic fairness evaluation.

Technology Category

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

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: Fairness-aware retrieval and ranking

Abstract

The weighted controlled direct effect (WCDE) generalizes the standard controlled direct effect (CDE) by averaging over the mediator distribution, providing a robust estimate when treatment effects vary across mediator levels. This makes the WCDE especially relevant in fairness analysis, where it isolates the direct effect of an exposure on an outcome, independent of mediating pathways. This work establishes three fundamental advances for WCDE in observational studies: First, we establish necessary and sufficient conditions for the unique identifiability of the WCDE, clarifying when it diverges from the CDE. Next, we consider nonparametric estimation of the WCDE and derive its influence function, focusing on the class of regular and asymptotically linear estimators. Lastly, we characterize the optimal covariate adjustment set that minimizes the asymptotic variance, demonstrating how mediator-confounder interactions introduce distinct requirements compared to average treatment effect estimation. Our results offer a principled framework for efficient estimation of direct effects in complex causal systems, with practical applications in fairness and mediation analysis.

Problem

• Identifies conditions for unique WCDE identifiability in observational studies
• Develops nonparametric WCDE estimation with influence function analysis
• Determines optimal covariate adjustment to minimize asymptotic variance

Innovation

• Nonparametric estimation of weighted controlled direct effect
• Influence function derivation for asymptotically linear estimators
• Optimal covariate adjustment minimizes asymptotic variance