  Motivated by an imaging proteomics study for Alzheimer's disease (AD), in
this article, we propose a mediation analysis approach with high-dimensional
exposures and high-dimensional mediators to integrate data collected from
multiple platforms. The proposed method combines principal component analysis
with penalized least squares estimation for a set of linear structural equation
models. The former reduces the dimensionality and produces uncorrelated linear
combinations of the exposure variables, whereas the latter achieves
simultaneous path selection and effect estimation while allowing the mediators
to be correlated. Applying the method to the AD data identifies numerous
interesting protein peptides, brain regions, and protein-structure-memory
paths, which are in accordance with and also supplement existing findings of AD
research. Additional simulations further demonstrate the effective empirical
performance of the method.
