  In this study, we tested the interaction effect of multimodal datasets using
a novel method called the kernel method for detecting higher order interactions
among biologically relevant mulit-view data. Using a semiparametric method on a
reproducing kernel Hilbert space (RKHS), we used a standard mixed-effects
linear model and derived a score-based variance component statistic that tests
for higher order interactions between multi-view data. The proposed method
offers an intangible framework for the identification of higher order
interaction effects (e.g., three way interaction) between genetics, brain
imaging, and epigenetic data. Extensive numerical simulation studies were first
conducted to evaluate the performance of this method. Finally, this method was
evaluated using data from the Mind Clinical Imaging Consortium (MCIC) including
single nucleotide polymorphism (SNP) data, functional magnetic resonance
imaging (fMRI) scans, and deoxyribonucleic acid (DNA) methylation data,
respectfully, in schizophrenia patients and healthy controls. We treated each
gene-derived SNPs, region of interest (ROI) and gene-derived DNA methylation as
a single testing unit, which are combined into triplets for evaluation. In
addition, cardiovascular disease risk factors such as age, gender, and body
mass index were assessed as covariates on hippocampal volume and compared
between triplets. Our method identified $13$-triplets ($p$-values $\leq 0.001$)
that included $6$ gene-derived SNPs, $10$ ROIs, and $6$ gene-derived DNA
methylations that correlated with changes in hippocampal volume, suggesting
that these triplets may be important in explaining schizophrenia-related
neurodegeneration. With strong evidence ($p$-values $\leq 0.000001$), the
triplet ({\bf MAGI2, CRBLCrus1.L, FBXO28}) has the potential to distinguish
schizophrenia patients from the healthy control variations.

Machine Learning