Modeling Pulmonary Tuberculosis Case Based on HIV and AIDS Cases in Indonesia Using Negative Binomial Regression Least Square Spline

The incidence of active pulmonary tuberculosis (TB) is on the rise, particularly among individuals co-infected with HIV and AIDS. This heightened susceptibility stems from the compromised immune systems in these populations, which increases the likelihood of TB bacteria activation. In Indonesia, TB remains a significant opportunistic infection among HIV/AIDS patients, complicating treatment efforts and frequently resulting in severe health outcomes, including mortality. Statistical analyses of TB incidence often reveal overdispersion, a phenomenon that can introduce bias into estimation results. To address this, a nonparametric negative binomial regression model utilizing the least square spline (NNBR-LSS) estimator was employed to model pulmonary tuberculosis incidence, considering the influence of HIV and AIDS case numbers. Data for this study were sourced from the 2023 Indonesian Health Profile, published by the Ministry of Health (Kemenkes). Model estimation results indicate a positive correlation: an increase in HIV and AIDS cases is associated with a corresponding increase in pulmonary tuberculosis cases. This relationship is characterized by a pseudo R-square value of 64.8%, suggesting a strong epidemiological link between the two diseases. The deviance test statistic for the NNBR-LSS model was calculated to be 19.525, which is lower than the deviance statistic obtained using a standard parametric regression approach (40.92087). This suggests that the NNBR-LSS model offers improved predictive accuracy compared to traditional parametric methods. These findings are valuable for informing targeted epidemiological interventions, strategic planning, and aligning public health initiatives.