Copula-based regression models for a bivariate mixed discrete and continuous outcome.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Correlated mixed discrete and continuous outcomes present analytical challenges in regression modeling.
• Existing methods may lack interpretability or flexibility in handling outcome associations.

Purpose of the Study:

• To develop a robust regression framework for joint modeling of mixed discrete and continuous outcomes.
• To enhance the interpretability of regression parameters and association measures.
• To provide a flexible approach for analyzing correlated outcomes in various fields.

Main Methods:

• Utilizing copula functions, specifically the Gaussian copula, to model the dependence structure between outcomes.
• Specifying marginal regression models (e.g., generalized linear models) for individual outcome types.
• Employing a latent variable framework for discrete outcomes to ensure unique joint distribution determination.

Main Results:

• The proposed copula-based regression model provides marginally meaningful regression parameters.
• The association between outcomes is characterized independently by the copula, offering a 'margin-free' interpretation.
• Simulation studies demonstrated the bias and efficiency of likelihood-based estimation methods.

Conclusions:

• The copula approach offers a powerful and interpretable method for analyzing correlated mixed discrete and continuous outcomes.
• The model is applicable to real-world data, as shown by the burn injury case study.
• This framework advances statistical modeling for complex data structures.