Deconfounded‐Debiased Estimation and Inference for High‐Dimensional Mediation Analysis With Pervasive Hidden Confounders

Mediation analysis is a powerful tool for elucidating the causal mechanisms by which exposures influence outcomes through mediators. However, conventional approaches often yield biased estimates of mediation effects in scenarios involving high-dimensional exposures and high-dimensional mediators, alongside a small number of pervasive hidden confounders that simultaneously affect the exposures, mediators, and outcome or the exposures and outcome. To address these challenges, we propose a deconfounded-debiased method for estimation and inference in high-dimensional mediation analysis based on the difference-in-coefficients strategy. This approach effectively corrects biases arising from both pervasive hidden confounders and high-dimensionality without requiring prior knowledge of hidden confounders or a sparse precision matrix assumption. We establish the asymptotic normality of the proposed estimators for both direct and indirect effects, and develop hypothesis testing procedures that asymptotically achieve validity and power lower bounds. Simulation experiments demonstrate our method's superior finite-sample performance in both estimation and inference, especially in the presence of pervasive hidden confounding. We also apply the proposed method to real data from the Alzheimer's Disease Neuroimaging Initiative to identify serum metabolites that influence Alzheimer's disease progression through DNA methylation pathways.