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Associating genetic markers with a multidimensional phenotype is an importantyet challenging problem. In this work, we establish the equivalence between twopopular methods: kernel-machine regression (KMR), and kernel distancecovariance (KDC). KMR is a semiparametric regression frameworks that models thecovariate effects parametrically, while the genetic markers are considerednon-parametrically. KDC represents a class of methods that includes distancecovariance (DC) and Hilbert-Schmidt Independence Criterion (HSIC), which arenonparametric tests of independence. We show the equivalence between the scoretest of KMR and the KDC statistic under certain conditions. This result leadsto a novel generalization of the KDC test that incorporates the covariates. Ourcontributions are three-fold: (1) establishing the equivalence between KMR andKDC; (2) showing that the principles of kernel machine regression can beapplied to the interpretation of KDC; (3) the development of a broader class ofKDC statistics, that the members are the quantities of different kernels. Wedemonstrate the proposals using simulation studies. Data from the Alzheimer'sDisease Neuroimaging Initiative (ADNI) is used to explore the associationbetween the genetic variants on gene \emph{FLJ16124} and phenotypes representedin 3D structural brain MR images adjusting for age and gender. The resultssuggest that SNPs of \emph{FLJ16124} exhibit strong pairwise interactioneffects that are correlated to the changes of brain region volumes.

Equivalence of Kernel Machine Regression and Kernel Distance Covariance for Multidimensional Trait Association Studies