Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments
Houssam Zenati, Judith Abécassis, Julie Josse, Bertrand Thirion
TL;DR
This paper tackles causal mediation analysis with continuous treatments by introducing a kernel-based double debiased learning (DML) estimator that achieves asymptotic normality under nonparametric nuisance learning. The core methodological advances are a Neyman-orthogonal kernel moment function and a Bayes-transformed cross-conditional mean that avoids mediator-density estimation, enabling scalable inference for high-dimensional mediators. The authors establish a thorough asymptotic theory, derive a data-driven AMSE-optimal bandwidth, and provide consistent confidence intervals even when nuisance components are misspecified. Empirically, the method outperforms traditional estimators across simulations and a UKBB cognitive-function application, offering improved stability at boundary regions and robust uncertainty quantification, with practical guidance on bandwidth choice and nuisance-learning strategies.
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.