  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.
