  We propose a statistical framework to integrate radiological magnetic
resonance imaging (MRI) and genomic data to identify the underlying
radiogenomic associations in lower grade gliomas (LGG). We devise a novel
imaging phenotype by dividing the tumor region into concentric spherical layers
that mimics the tumor evolution process. MRI data within each layer is
represented by voxel--intensity-based probability density functions which
capture the complete information about tumor heterogeneity. Under a
Riemannian-geometric framework these densities are mapped to a vector of
principal component scores which act as imaging phenotypes. Subsequently, we
build Bayesian variable selection models for each layer with the imaging
phenotypes as the response and the genomic markers as predictors. Our novel
hierarchical prior formulation incorporates the interior-to-exterior structure
of the layers, and the correlation between the genomic markers. We employ a
computationally-efficient Expectation--Maximization-based strategy for
estimation. Simulation studies demonstrate the superior performance of our
approach compared to other approaches. With a focus on the cancer driver genes
in LGG, we discuss some biologically relevant findings. Genes implicated with
survival and oncogenesis are identified as being associated with the spherical
layers, which could potentially serve as early-stage diagnostic markers for
disease monitoring, prior to routine invasive approaches.
