  In genome wide association studies (GWAS), researchers are often dealing with
non-normally distributed traits or a mixture of discrete-continuous traits.
However, most of the current region-based methods rely on multivariate linear
mixed models (mvLMMs) and assume a multivariate normal distribution for the
phenotypes of interest. Hence, these methods are not applicable to disease or
non-normally distributed traits. Therefore, there is a need to develop unified
and flexible methods to study association between a set of (possibly rare)
genetic variants and non-normal multivariate phenotypes. Copulas are
multivariate distribution functions with uniform margins on the $[0, 1]$
interval and they provide suitable models to deal with non-normality of errors
in multivariate association studies. We propose a novel unified and flexible
Copula-Based Multivariate Association Test (CBMAT) for discovering association
between a genetic region and a bivariate continuous or mixed phenotype. We also
derive a data-driven analytic p-value procedure of the proposed region-based
score-type test. Through simulation studies, we demonstrate that CBMAT has well
controlled type I error rates and higher power to detect associations compared
with other existing methods, for discrete and non-normally distributed traits.
At last, we apply CBMAT to detect the association between two genes located on
chromosome 11 and several lipid levels measured on 1,477 subjects from the
ASLPAC study.
