Equivalence of Kernel Machine Regression and Kernel Distance Covariance for Multidimensional Trait Association Studies
This work provides a theoretical link between two popular methods for genetic association studies, potentially improving analysis in fields like genomics and neuroimaging, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of associating genetic markers with multidimensional phenotypes by establishing the equivalence between kernel-machine regression (KMR) and kernel distance covariance (KDC), leading to a novel generalization of KDC that incorporates covariates. It demonstrates this through simulation studies and an application to Alzheimer's disease data, showing that SNPs of FLJ16124 exhibit strong pairwise interaction effects correlated with brain volume changes.
Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression frameworks that models the covariate effects parametrically, while the genetic markers are considered non-parametrically. KDC represents a class of methods that includes distance covariance (DC) and Hilbert-Schmidt Independence Criterion (HSIC), which are nonparametric tests of independence. We show the equivalence between the score test of KMR and the KDC statistic under certain conditions. This result leads to a novel generalization of the KDC test that incorporates the covariates. Our contributions are three-fold: (1) establishing the equivalence between KMR and KDC; (2) showing that the principles of kernel machine regression can be applied to the interpretation of KDC; (3) the development of a broader class of KDC statistics, that the members are the quantities of different kernels. We demonstrate the proposals using simulation studies. Data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) is used to explore the association between the genetic variants on gene \emph{FLJ16124} and phenotypes represented in 3D structural brain MR images adjusting for age and gender. The results suggest that SNPs of \emph{FLJ16124} exhibit strong pairwise interaction effects that are correlated to the changes of brain region volumes.