Copula-Based Tests For Assessing The Association Between Genetic Variants And Mixed Phenotypes

High-dimensional omics studies increasingly involve heterogeneous data types and phenotypes, which traditional association methods struggle to model jointly due to incompatible marginal distributions and complex dependence structures. This thesis develops a unified copula-based framework for assessing associations between genetic variants and mixed phenotypes by decoupling flexible marginal models from their joint dependence structure. While previous copula-based approaches in this setting have focused largely on continuous and binary traits, we extend these methods to a broader class of phenotype pairs. Specifically, we introduce new association tests for bivariate outcomes involving ordinal–continuous, nominal–continuous, and survival–continuous combinations. The proposed methodology derives joint density functions for each phenotype pair, employs likelihood-based and score-type testing procedures, and implements both analytic and data-adaptive p-value calculations. Simulation studies show valid type I error control, robustness to non-normality, and increased statistical power when dependence between mixed traits is strong. These methodological advances provide a flexible and comprehensive framework for multivariate genetic association analysis in multi-omics applications, enabling more accurate and interpretable inference across diverse biological data types.