Modeling HIV and AIDS data in Trenggalek and Ponorogo with a bivariate zero-inflated Poisson approach

Abstract

The presence of excess zeros and overdispersion in count data often leads to biased parameter estimates when analyzed using the standard Poisson regression model. This study aims to model the number of HIV and AIDS cases in Trenggalek and Ponorogo Regencies using the Bivariate Zero-Inflated Poisson (BZIP) regression approach. The BZIP model accommodates correlated count responses as well as excess zeros, commonly found in epidemiological data. Two response variables, the number of HIV cases (Y₁) and the number of AIDS cases (Y₂), were analyzed against five explanatory variables: the percentage of the population aged 25–29 years (X₁), low education level (X₂), condom use among couples of reproductive ages (X₃), participation in health education programs (X₄), and community health insurance coverage (X₅). Parameter estimation was performed using the Expectation-Maximization (EM) algorithm. The results show that health education significantly increases the likelihood that an area has no HIV cases, while health insurance significantly reduces the number of AIDS cases. Moreover, individuals aged 25–29 years were identified as the group most at risk for AIDS. The model also confirmed strong overdispersion and zero inflation, supporting the use of BZIP as a more appropriate model than the standard bivariate Poisson regression. Additionally, the BZIP model achieved the best performance, indicated by the lowest AIC value compared to previous models.