Mediation Analysis with Multiple Exposures and Multiple Mediators.

A mediation analysis approach is proposed for multiple exposures, multiple mediators, and a continuous scalar outcome under the linear structural equation modeling framework. It assumes that there exist orthogonal components that demonstrate parallel mediation mechanisms on the outcome, and thus is named principal component mediation analysis (PCMA). Likelihood-based estimators are introduced for simultaneous estimation of the component projections and effect parameters. The asymptotic distribution of the estimators is derived for low-dimensional data. A bootstrap procedure is introduced for inference. Simulation studies illustrate the superior performance of the proposed approach. Applied to a proteomics-imaging dataset from the Alzheimer's disease neuroimaging initiative (ADNI), the proposed framework identifies protein deposition - brain atrophy - memory deficit mechanisms consistent with existing knowledge and suggests potential AD pathology by integrating data collected from different modalities.