Modeling Multiple Responses via Bootstrapping Margins with an Application to Genetic Association Testing

Area of Science:

• Statistics
• Genetics
• Biostatistics

Background:

• Analyzing multiple correlated responses is crucial in fields like behavioral science (e.g., comorbidity) and genetic studies.
• Existing nonparametric methods (e.g., generalized Kendall's Tau) assess association significance but lack magnitude estimation.
• Modeling multivariate responses presents significant challenges, necessitating advanced statistical approaches.

Purpose of the Study:

• To propose a novel Gaussian copula model for analyzing multivariate binary responses.
• To develop a method that separates marginal effects from between-trait correlations.
• To enhance association testing by providing both significance and magnitude for genetic studies of complex traits.

Main Methods:

• A Gaussian copula model with discrete margins was employed for multivariate binary data.
• A bootstrapping margins approach was utilized to construct Wald's statistic for association testing.
• The method was validated through simulations and real data analysis.

Main Results:

• The proposed method effectively models marginal effects and between-trait correlations.
• The bootstrapping margins approach allows for weakened underlying assumptions, requiring only correct margin specification.
• The new method demonstrated increased power compared to existing association tests.

Conclusions:

• The proposed Gaussian copula model offers a powerful tool for analyzing multivariate binary responses in genetic association studies.
• This approach provides valuable insights into the magnitude and significance of associations between risk factors and multiple traits.
• The method enhances the ability to study complex traits by offering a more comprehensive analysis than traditional methods.