Comparison of geographically weighted and mixed geographically weighted negative binomial regression models for tuberculosis incidence

Abstract

Tuberculosis (TB) remains a major public health concern characterized by spatial variation and overdispersion in case counts. In small-area analyses, differences in local characteristics may generate spatial heterogeneity in the relationships between risk factors and TB cases. Conventional Poisson regression is often inadequate because the equidispersion assumption is frequently violated and the model does not account for spatially varying effects. This study aims to model the number of TB cases in Makassar City in 2024 across 15 districts by comparing Geographically Weighted Negative Binomial Regression (GWNBR) and Mixed Geographically Weighted Negative Binomial Regression (MGWNBR). Seven predictor variables were examined: population density, health workforce, health facility, Immunodeficiency Virus (HIV)/Acquired Immune Deficiency Syndrome (AIDS), access to safe water, clean and healthy behavior practices (CHB), and malnutrition prevalence. Diagnostic tests indicated the presence of overdispersion and spatial heterogeneity, thereby justifying the application of spatial count regression models. Model comparison based on deviance and the Akaike Information Criterion (AIC) demonstrated that MGWNBR provided a superior fit. The CHB variable exhibited a global effect, whereas the remaining predictors showed spatially varying effects. These findings suggest that determinants of TB cases are not spatially homogeneous, and that a mixed modeling framework more effectively captures local dynamics while maintaining model parsimony. The results support the development of geographically targeted TB control strategies in small-area settings.