High-dimensional Many-to-many-to-many Mediation Analysis

2026-04-03

AI Summary

This study addresses the challenge of identifying complex mediation effects among high-dimensional multivariate exposures, mediators, and outcomes by formally introducing the first “many-to-many-to-many” (MMM) mediation analysis framework. The proposed method simultaneously performs high-dimensional variable selection, estimates the indirect effect matrix, and predicts multivariate outcomes, while establishing asymptotic normality theory to enable interpretable cross-layer pathway inference. Applied to Alzheimer’s disease data, the approach successfully uncovers biologically meaningful genetic–neural–cognitive pathways, substantially improving out-of-sample classification and prediction accuracy. The work thus offers both methodological innovation and practical utility in high-dimensional mediation analysis.

Abstract

We study high-dimensional mediation analysis in which exposures, mediators, and outcomes are all multivariate, and both exposures and mediators may be high-dimensional. We formalize this as a many (exposures)-to-many (mediators)-to-many (outcomes) (MMM) mediation analysis problem. Methodologically, MMM mediation analysis simultaneously performs variable selection for high-dimensional exposures and mediators, estimates the indirect effect matrix (i.e., the coefficient matrices linking exposure-to-mediator and mediator-to-outcome pathways), and enables prediction of multivariate outcomes. Theoretically, we show that the estimated indirect effect matrices are consistent and element-wise asymptotically normal, and we derive error bounds for the estimators. To evaluate the efficacy of the MMM mediation framework, we first investigate its finite-sample performance, including convergence properties, the behavior of the asymptotic approximations, and robustness to noise, via simulation studies. We then apply MMM mediation analysis to data from the Alzheimer's Disease Neuroimaging Initiative to study how cortical thickness of 202 brain regions may mediate the effects of 688 genome-wide significant single nucleotide polymorphisms (SNPs) (selected from approximately 1.5 million SNPs) on eleven cognitive-behavioral and diagnostic outcomes. The MMM mediation framework identifies biologically interpretable, many-to-many-to-many genetic-neural-cognitive pathways and improves downstream out-of-sample classification and prediction performance. Taken together, our results demonstrate the potential of MMM mediation analysis and highlight the value of statistical methodology for investigating complex, high-dimensional multi-layer pathways in science. The MMM package is available at https://github.com/THELabTop/MMM-Mediation.

Problem

• high-dimensional mediation
• many-to-many-to-many
• multivariate exposures
• multivariate mediators
• multivariate outcomes

Innovation

• high-dimensional mediation
• many-to-many-to-many
• indirect effect matrix
• variable selection
• multivariate outcomes