Flexible parametric copula modeling approaches for clustered survival data.

Area of Science:

• Biostatistics
• Statistical Modeling
• Survival Analysis

Background:

• Copula-based survival regression models are standard for clustered multivariate survival data.
• Archimedean copulas effectively model dependence structures.
• Existing one-stage methods often rely on restrictive parametric assumptions for marginal distributions.

Purpose of the Study:

• To propose a flexible parametric Archimedean copula modeling approach using a one-stage likelihood procedure.
• To overcome the limitations of existing methods regarding parametric assumptions for marginal distributions.
• To provide a more efficient and consistent estimation method for clustered multivariate survival data.

Main Methods:

• Developed a flexible parametric Archimedean copula model.
• Employed a one-stage likelihood procedure for estimation.
• Modeled unknown marginal baseline hazards using cubic M-spline basis functions to avoid specific parametric forms.

Main Results:

• The proposed one-stage estimation method yields a consistent estimator.
• The new method demonstrates superior efficiency compared to existing one- and two-stage methods.
• The approach was validated through simulations and applied to three clinical datasets.

Conclusions:

• The proposed flexible parametric Archimedean copula model with a one-stage procedure offers an efficient and consistent approach for analyzing clustered multivariate survival data.
• Utilizing cubic M-splines for marginal baseline hazards enhances model flexibility without compromising estimation efficiency.
• The method provides a valuable tool for researchers in biostatistics and related fields, with an accessible R function provided.