  With fast advancements in technologies, the collection of multiple types of
measurements on a common set of subjects is becoming routine in science. Some
notable examples include multimodal neuroimaging studies for the simultaneous
investigation of brain structure and function, and multi-omics studies for
combining genetic and genomic information. Integrative analysis of multimodal
data allows scientists to interrogate new mechanistic questions. However, the
data collection and generation of integrative hypotheses is outpacing available
methodology for joint analysis of multimodal measurements. In this article, we
study high-dimensional multimodal data integration in the context of mediation
analysis. We aim to understand the roles different data modalities play as
possible mediators in the pathway between an exposure variable and an outcome.
We propose a mediation model framework with two data types serving as separate
sets of mediators, and develop a penalized optimization approach for parameter
estimation. We study both the theoretical properties of the estimator through
an asymptotic analysis, and its finite-sample performance through simulations.
We illustrate our method with a multimodal brain pathway analysis having both
structural and functional connectivities as mediators in the association
between sex and language processing.
