Bayesian Approach in Estimating Parameters of Zero-Inflated Negative Binomial Regression Model Using Cauchy Prior: Simulation Study on Pneumonia

Abstract

The Bayesian approach is one of the parameter estimation methods that can be applied to Zero-Inflated Negative Binomial (ZINB) regression analysis. The ZINB regression model is used to analyze over-dispersion data with excess zeros. This study aims to evaluate the performance of ZINB regression parameter estimation using a Bayesian approach with Cauchy prior in pneumonia studies. The analysis is applied to secondary data as well as to simulated data with various scenarios based on different sample sizes and proportions of zero values such that the optimal model can be determined. The results show that ZINB regression models using the Bayesian approach provide stable parameter estimates as sample sizes and proportions of zeros increase. In cases of under-five deaths due to pneumonia, the data often contains many zeros because not all regions report cases. The ZINB model effectively addresses over-dispersion and excess zeros through a combination of negative binomial and zero-inflation models. This provides more accurate modeling results to support policymaking. The Bayesian approach also provides flexibility in integrating prior information and handling small samples, making the ZINB model well suited for health data with rare events and many zeros.