S-GMAS: Genome-Wide Mediation Analysis With Brain Subcortical Shape Mediators.

Mediation analysis is widely utilized in neuroscience to investigate the role of brain image phenotypes in the neurological pathways from genetic exposures to clinical outcomes. However, it is still difficult to conduct mediation analyses with whole genome-wide exposures and brain subcortical shape mediators due to several challenges including (i) large-scale genetic exposures, that is, millions of single-nucleotide polymorphisms (SNPs); (ii) nonlinear Hilbert space for shape mediators; and (iii) statistical inference on the direct and indirect effects. To tackle these challenges, this paper proposes a genome-wide mediation analysis framework with brain subcortical shape mediators. First, to address the issue caused by the high dimensionality in genetic exposures, a fast genome-wide association analysis is conducted to discover potential genetic variants with significant genetic effects on the clinical outcome. Second, the square-root velocity function representations are extracted from the brain subcortical shapes, which fall in an unconstrained linear Hilbert subspace. Third, to identify the underlying causal pathways from the detected SNPs to the clinical outcome implicitly through the shape mediators, we utilize a shape mediation analysis framework consisting of a shape-on-scalar model and a scalar-on-shape model. Furthermore, the bootstrap resampling approach is adopted to investigate both global and spatial significant mediation effects. Finally, our framework is applied to the corpus callosum shape data from the Alzheimer's Disease Neuroimaging Initiative.