Pair copula construction for longitudinal data with zero-inflated power series marginal distributions

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Temporal dependency assessment is vital across disciplines.
• Discrete longitudinal data often exhibit excess zeros, complicating modeling.
• Existing methods may not adequately handle over-dispersion and excess zeros in count data.

Purpose of the Study:

• To propose a novel statistical framework for modeling count repeated measurements with excess zeros.
• To accommodate longitudinal count outcomes using power series distributions and D-vine copula structures.
• To provide a flexible and robust method for analyzing complex longitudinal count data.

Main Methods:

• Utilized power series family of distributions for count outcomes.
• Employed pair copula constructions with a D-vine structure to model longitudinal response variables.
• Obtained parameter estimates via a two-stage maximum likelihood approach.
• Conducted simulation studies to evaluate performance and robustness.

Main Results:

• The proposed D-vine copula framework effectively models count data with excess zeros.
• Simulation studies demonstrated the method's performance compared to generalized linear mixed effects (GLME) models.
• Assessed the robustness of D-vine and GLME models concerning random effects distribution.

Conclusions:

• The developed framework provides a powerful tool for analyzing longitudinal count data with excess zeros.
• The D-vine copula approach offers advantages in flexibility and robustness over standard GLME models.
• Applied the method to a real-world kidney allograft rejection dataset, demonstrating its practical utility.