Debiased Causal Mediation Analysis in Ultra-High-Dimensional Settings in the Presence of Interaction Effects

Abstract

Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects an outcome, providing deeper causal insights and guiding effective interventions. Despite substantial advances in mediation analysis with fixed- or low-dimensional mediators and covariates, estimation and inference for mediation functionals remain limited when both mediators and covariates are ultra-high-dimensional. In this paper, we propose an estimator for the mediation functional in a high-dimensional setting that accommodates the treatment--covariate interactions in the mediator model, as well as treatment--covariate and treatment--mediator interactions in the outcome model. As the parameter of interest involves high-dimensional components from different treatment arms and regression equations, existing debiasing approaches are not directly applicable, motivating our multi-step debiasing technique for handling such structurally complex functionals. We establish that the proposed estimator is $\sqrt{n}$-consistent and asymptotically normal, enabling valid inference for natural direct and indirect effects. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients.