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In this study, we tested the interaction effect of multimodal datasets usinga novel method called the kernel method for detecting higher order interactionsamong biologically relevant mulit-view data. Using a semiparametric method on areproducing kernel Hilbert space (RKHS), we used a standard mixed-effectslinear model and derived a score-based variance component statistic that testsfor higher order interactions between multi-view data. The proposed methodoffers an intangible framework for the identification of higher orderinteraction effects (e.g., three way interaction) between genetics, brainimaging, and epigenetic data. Extensive numerical simulation studies were firstconducted to evaluate the performance of this method. Finally, this method wasevaluated using data from the Mind Clinical Imaging Consortium (MCIC) includingsingle nucleotide polymorphism (SNP) data, functional magnetic resonanceimaging (fMRI) scans, and deoxyribonucleic acid (DNA) methylation data,respectfully, in schizophrenia patients and healthy controls. We treated eachgene-derived SNPs, region of interest (ROI) and gene-derived DNA methylation asa single testing unit, which are combined into triplets for evaluation. Inaddition, cardiovascular disease risk factors such as age, gender, and bodymass index were assessed as covariates on hippocampal volume and comparedbetween triplets. Our method identified $13$-triplets ($p$-values $\leq 0.001$)that included $6$ gene-derived SNPs, $10$ ROIs, and $6$ gene-derived DNAmethylations that correlated with changes in hippocampal volume, suggestingthat these triplets may be important in explaining schizophrenia-relatedneurodegeneration. With strong evidence ($p$-values $\leq 0.1$), thetriplet ({\bf MAGI2, CRBLCrus1.L, FBXO28}) has the potential to distinguishschizophrenia patients from the healthy control variations.

Kernel Method for Detecting Higher Order Interactions in multi-view Data: An Application to Imaging, Genetics, and Epigenetics