  Technological advancements in noninvasive imaging facilitate the construction
of whole brain interconnected networks, known as brain connectivity. Existing
approaches to analyze brain connectivity frequently disaggregate the entire
network into a vector of unique edges or summary measures, leading to a
substantial loss of information. Motivated by the need to explore the effect
mechanism among genetic exposure, brain connectivity and time to disease onset,
we propose an integrative Bayesian framework to model the effect pathway
between each of these components while quantifying the mediating role of brain
networks. To accommodate the biological architectures of brain connectivity
constructed along white matter fiber tracts, we develop a structural modeling
framework that includes a symmetric matrix-variate accelerated failure time
model and a symmetric matrix response regression to characterize the effect
paths. We further impose within-graph sparsity and between-graph shrinkage to
identify informative network configurations and eliminate the interference of
noisy components. Extensive simulations confirm the superiority of our method
compared with existing alternatives. By applying the proposed method to the
landmark Alzheimer's Disease Neuroimaging Initiative study, we obtain
neurobiologically plausible insights that may inform future intervention
strategies.
