  Genetic association studies for brain connectivity phenotypes have gained
prominence due to advances in non-invasive imaging techniques and quantitative
genetics. Brain connectivity traits, characterized by network configurations
and unique biological structures, present distinct challenges compared to other
quantitative phenotypes. Furthermore, the presence of sample relatedness in
most imaging genetics studies limits the feasibility of adopting existing
network-response modeling. In this paper, we fill this gap by proposing a
Bayesian network-response mixed-effect model that considers a network-variate
phenotype and incorporates population structures including pedigrees and
unknown sample relatedness. To accommodate the inherent topological
architecture associated with the genetic contributions to the phenotype, we
model the effect components via a set of effect subnetworks and impose an
inter-network sparsity and intra-network shrinkage to dissect the phenotypic
network configurations affected by the risk genetic variant. To facilitate
uncertainty quantification of signaling components from both genotype and
phenotype sides, we develop a Markov chain Monte Carlo (MCMC) algorithm for
posterior inference. We evaluate the performance and robustness of our model
through extensive simulations. By further applying the method to study the
genetic bases for brain structural connectivity using data from the Human
Connectome Project with excessive family structures, we obtain plausible and
interpretable results. Beyond brain connectivity genetic studies, our proposed
model also provides a general linear mixed-effect regression framework for
network-variate outcomes.
