A general kernel machine regression framework using principal component analysis for jointly testing main and interaction effects: Applications to human microbiome studies

Abstract

The effect of a treatment on a health or disease response can be modified by genetic or microbial variants. It is the matter of interaction effects between genetic or microbial variants and a treatment. To powerfully discover genetic or microbial biomarkers, it is crucial to incorporate such interaction effects in addition to the main effects. However, in the context of kernel machine regression analysis of its kind, existing methods cannot be utilized in a situation, where a kernel is available but its underlying real variants are unknown. To address such limitations, I introduce a general kernel machine regression framework using principal component analysis for jointly testing main and interaction effects. It begins with extracting principal components from an input kernel through the singular value decomposition. Then, it employs the principal components as surrogate variants to construct three endogenous kernels for the main effects, interaction effects, and both of them, respectively. Hence, it works with a kernel as an input without knowing its underlying real variants, and also detects either the main effects, interaction effects, or both of them robustly. I also introduce its omnibus testing extension to multiple input kernels, named OmniK. I demonstrate its use for human microbiome studies.