A diagnostic for association in bivariate survival models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Bivariate failure time data analysis requires appropriate copula models.
• Censoring in failure times complicates model selection.
• Existing diagnostic methods may lack interpretability.

Purpose of the Study:

• To propose easily implemented diagnostic methods for copula models in bivariate failure time data.
• To assess the ability of these methods to distinguish between gamma and positive stable copula models.
• To demonstrate the utility of the proposed diagnostics using real-world data.

Main Methods:

• Development of exploratory diagnostic techniques for copula appropriateness.
• Application of methods to bivariate failure time data with potential censoring.
• Comparative analysis of gamma and positive stable copula models.

Main Results:

• The proposed methods effectively distinguish gamma from positive stable copula models under specific conditions (moderate sample size or strong association).
• Analysis of Women's Health and Aging Study (WHAS) data demonstrated the methodology.
• The positive stable model showed a better overall fit than the gamma frailty model for WHAS data, though it underestimated later associations.

Conclusions:

• The developed methods provide an interpretable quantity for copula model diagnosis.
• These diagnostics can inform practitioners about the suitability of their chosen copula models.
• Findings align with theories distinguishing catastrophic versus progressive disability onset.