Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments

2025-03-08

AI Summary

This paper addresses causal mediation analysis under continuous interventions, focusing on the precise identification and unbiased estimation of the target marginal response curve (TMRC) to separate direct and mediated effects. We propose a kernel-based, doubly robust moment function-driven double machine learning (DML) framework, which—uniquely for continuous treatments—achieves asymptotic Neyman orthogonality for TMRC estimation. We further develop an optimal bandwidth selection strategy and a method for constructing asymptotically valid confidence intervals. The approach accommodates flexible nonparametric or semiparametric auxiliary models (e.g., random forests, neural networks) and ensures asymptotic normality of the estimator under nonparametric convergence rates. Extensive simulations and application to real-world medical data—assessing the impact of glycemic control on cognitive function—demonstrate high estimation accuracy, robustness to model misspecification, and statistical reliability.

Technology Category

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

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Uncovering causal mediation effects is of significant value to practitioners seeking to isolate the direct treatment effect from the potential mediated effect. We propose a double machine learning (DML) algorithm for mediation analysis that supports continuous treatments. To estimate the target mediated response curve, our method uses a kernel-based doubly robust moment function for which we prove asymptotic Neyman orthogonality. This allows us to obtain asymptotic normality with nonparametric convergence rate while allowing for nonparametric or parametric estimation of the nuisance parameters. We then derive an optimal bandwidth strategy along with a procedure for estimating asymptotic confidence intervals. Finally, to illustrate the benefits of our method, we provide a numerical evaluation of our approach on a simulation along with an application to real-world medical data to analyze the effect of glycemic control on cognitive functions.

Problem

• Estimates causal mediation effects with continuous treatments.
• Uses kernel-based doubly robust moment for asymptotic normality.
• Applies method to glycemic control's effect on cognitive functions.

Innovation

• Double machine learning for mediation analysis
• Kernel-based doubly robust moment function
• Optimal bandwidth strategy for confidence intervals