  We develop a Bayesian bivariate spatial model for multivariate regression
analysis applicable to studies examining the influence of genetic variation on
brain structure. Our model is motivated by an imaging genetics study of the
Alzheimer's Disease Neuroimaging Initiative (ADNI), where the objective is to
examine the association between images of volumetric and cortical thickness
values summarizing the structure of the brain as measured by magnetic resonance
imaging (MRI) and a set of 486 SNPs from 33 Alzheimer's Disease (AD) candidate
genes obtained from 632 subjects. A bivariate spatial process model is
developed to accommodate the correlation structures typically seen in
structural brain imaging data. First, we allow for spatial correlation on a
graph structure in the imaging phenotypes obtained from a neighbourhood matrix
for measures on the same hemisphere of the brain. Second, we allow for
correlation in the same measures obtained from different hemispheres
(left/right) of the brain. We develop a mean-field variational Bayes algorithm
and a Gibbs sampling algorithm to fit the model. We also incorporate Bayesian
false discovery rate (FDR) procedures to select SNPs. We implement the
methodology in a new release of the R package bgsmtr. We show that the new
spatial model demonstrates superior performance over a standard model in our
application. Data used in the preparation of this article were obtained from
the Alzheimer's Disease Neuroimaging Initiative (ADNI) database
(adni.loni.usc.edu).
