Marginalized zero-altered models for longitudinal count data.

Area of Science:

• Biostatistics
• Epidemiology
• Toxicology

Background:

• Count data frequently display more zeros than predicted by standard distributions (e.g., Poisson, negative binomial).
• Analyzing zero-inflated count data in longitudinal or correlated settings is of significant interest.
• Existing zero-inflated models with random effects can suffer from poor coefficient interpretability and numerical instability.

Purpose of the Study:

• To propose a novel marginal model for zero-inflated count data with correlated observations.
• To ensure interpretable parameterization of covariate associations using log relative rates.
• To facilitate direct comparison between methods that ignore versus explicitly model zero inflation.

Main Methods:

• Developed a marginal model incorporating random effects for correlation.
• Parameterized associations via log relative rates for enhanced interpretability.
• Conducted simulation studies to evaluate bias and variance of different model formulations.
• Applied the proposed model to toxicological data on emissions and cardiac arrhythmias.

Main Results:

• The proposed marginal model provides interpretable log relative rates.
• Simulations demonstrated the performance characteristics (bias, variance) of the new model compared to standard approaches.
• The model successfully analyzed toxicological data, assessing the impact of emissions on cardiac arrhythmias.

Conclusions:

• The proposed marginal model offers an interpretable and numerically stable approach for analyzing zero-inflated correlated count data.
• This framework enables robust comparison of methods for handling excess zeros.
• The approach is applicable to real-world toxicological studies, such as evaluating environmental exposures and health outcomes.