ABSTRACT
Although the primary objective of case-control studies is to assess the effects of genetic variants between cases and controls, secondary phenotypes are often collected in such studies without much extra cost. Copulas are commonly used in statistical literature to formulate multivariate distribution. The basic idea is that one first specifies the marginal distribution for each variable. After certain transformation on each marginal variable, the transformed variable follows a uniform distribution. In a related work, Zhang et al. proposed a copula model for testing the interaction effect between two risk factors on the disease rate under the case-control design. The two risk factors are allowed to be continuous or discrete. Although there is a rich literature on the analysis of the univariate secondary phenotype data under the case-control designs, methods for the multivariate secondary phenotype data are limited.
