Mediation Analysis with Graph Mediator

TL;DR

This paper develops a novel mediation analysis framework where the mediator is a graph, using Gaussian covariance graph models, likelihood estimators, and applies it to fMRI data to uncover brain network mediators.

Contribution

It introduces a new mediation analysis method with graph mediators, including estimation algorithms and theoretical properties, applied to neuroimaging data.

Findings

Identified a brain network mediating sex differences in motor task performance.

Proposed efficient algorithms with good asymptotic properties.

Validated approach through simulation studies.

Abstract

This study introduces a mediation analysis framework when the mediator is a graph. A Gaussian covariance graph model is assumed for graph representation. Causal estimands and assumptions are discussed under this representation. With a covariance matrix as the mediator, parametric mediation models are imposed based on matrix decomposition. Assuming Gaussian random errors, likelihood-based estimators are introduced to simultaneously identify the decomposition and causal parameters. An efficient computational algorithm is proposed and asymptotic properties of the estimators are investigated. Via simulation studies, the performance of the proposed approach is evaluated. Applying to a resting-state fMRI study, a brain network is identified within which functional connectivity mediates the sex difference in the performance of a motor task.