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

A copula-based set-variant association test for bivariate continuous or mixed phenotypes