Zero-modified Poisson model: Bayesian approach, influence diagnostics, and an application to a Brazilian...

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Count data often exhibit excess zeros, posing challenges for standard regression models.
• Zero-modified Poisson (ZMP) regression offers flexibility in handling zero-inflated or zero-deflated data.
• Bayesian inference provides a powerful framework for complex statistical modeling.

Purpose of the Study:

• To develop and evaluate a Bayesian inference method for the zero-modified Poisson (ZMP) regression model.
• To assess the model's performance and sensitivity to influential data points.
• To apply the ZMP model to real-world epidemiological data.

Main Methods:

• Development of a Bayesian framework for ZMP regression.
• Utilizing a class of prior densities based on an information matrix.
• Employing Kullback-Leibler divergence for sensitivity analysis.
• Conducting simulation studies to assess methodology performance.

Main Results:

• The developed Bayesian ZMP method provides a flexible approach for count data analysis.
• Sensitivity analysis identified influential cases, ensuring robust results.
• Simulation studies demonstrated the effectiveness of the proposed methodology.
• The ZMP model was successfully applied to leptospirosis notification data.

Conclusions:

• The proposed Bayesian ZMP regression method is a valuable tool for analyzing count data with excess zeros.
• The methodology offers flexibility and robustness, suitable for epidemiological studies.
• The application to leptospirosis data highlights its practical utility in public health surveillance.