Copula based flexible modeling of associations between clustered event times

Area of Science:

• Biostatistics
• Statistical Modeling
• Survival Analysis

Background:

• Multivariate survival data exhibit correlations within clusters.
• Accurate modeling is crucial for understanding complex event times.

Purpose of the Study:

• To develop and apply advanced copula models for multivariate survival data.
• To address challenges in modeling clustered and right-censored survival data.
• To establish criteria for robust model selection in survival analysis.

Main Methods:

• Construction of multi-dimensional copulas with flexible dependence structures.
• Modeling clustered right-censored survival data using mixtures of max-infinitely divisible bivariate copulas.
• Likelihood-based fitting with finite difference approximation for copula derivatives.
• Formulation of conditions for consistent information criteria for model selection.

Main Results:

• Developed a novel approach for modeling correlated survival data.
• Successfully fitted complex clustered right-censored survival data.
• Demonstrated the utility of the methodology with a four-dimensional time-to-mastitis dataset.
• Provided theoretical underpinnings for model selection consistency.

Conclusions:

• The proposed copula methodology offers a flexible and robust framework for multivariate survival data analysis.
• The finite difference approximation effectively handles complex likelihood calculations.
• The established conditions ensure reliable model selection for clustered survival data.