Double machine learning for partially linear mediation models with high-dimensional confounders

To estimate and statistically infer the direct and indirect effects of exposure and mediator variables while accounting for high-dimensional confounding variables, we propose a partially linear mediation model to incorporate a flexible mechanism of confounders. To obtain asymptotically efficient estimators for the effects of interest under the influence of the nuisance functions with high-dimensional confounders, we construct two Neyman-orthogonal score functions to remove regularization bias. Flexible machine learning methods and data splitting with cross-fitting are employed to address the overfitting issue and estimate unknown nuisance functions efficiently. We rigorously investigate the asymptotic expressions of the proposed estimators for the direct, indirect and total effects and then derive their asymptotic normality properties. In addition, two Wald statistics are constructed to test the direct and indirect effects, respectively, and their limiting distributions are obtained. The satisfactory performance of our proposed estimators is demonstrated by simulation results and a genome-wide analysis of blood DNA methylation dataset.