Bivariate negative binomial regression model with excess zeros and right censoring: an application to Indonesian data

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Count data with excess zeros and extreme values present challenges for standard statistical models.
• Existing bivariate models may not adequately capture the complexities of correlated health count data.

Purpose of the Study:

• To introduce and evaluate a novel bivariate hurdle negative binomial (BHNB) regression model.
• To address correlated bivariate count data characterized by excess zeros and few extreme observations.
• To improve the modeling of health-related count data, such as illness days.

Main Methods:

• Development of a bivariate hurdle negative binomial (BHNB) regression model incorporating right censoring.
• Parameter estimation using maximum likelihood with conjugate gradient optimization.
• Application to survey data on illness-related days missed and days spent in bed.
• Comparison with a right-censored bivariate negative binomial (BNB) model.
• Conducting a simulation study to assess model properties.

Main Results:

• The proposed BHNB model demonstrated superior goodness-of-fit for estimated frequencies compared to the BNB model.
• Simulation results support the utility and properties of the BHNB model for handling complex count data.
• The model effectively captures excess zeros and potential extreme values in bivariate count data.

Conclusions:

• The bivariate hurdle negative binomial (BHNB) regression model offers a robust approach for analyzing correlated bivariate count data with excess zeros.
• The BHNB model provides a better fit for health-related survey data than traditional bivariate negative binomial models.
• This methodology enhances the accuracy of statistical analyses in biostatistics and epidemiology.