Spatial Heterogeneity of Tuberculosis Incidence Using Geographically Weighted Negative Binomial Regression (GWNBR) in Indonesia - Riry Sriningsih; Mohammad Soleh; Muhammad Subhan; Reni Prima Gusty (ZERO: Jurnal Sains, Matematika dan Terapan, 2026)
Poisson regression is widely used for count data but relies on the equidispersion assumption, which is often violated in epidemiological data due to overdispersion. Negative Binomial Regression (NBR) addresses this issue by introducing a dispersion parameter. However, both models assume spatial homogeneity of parameters. This study applies Geographically Weighted Negative Binomial Regression (GWNBR) to analyze tuberculosis (TB) cases across 38 provinces in Indonesia in 2024. The response variable is the number of TB cases, with predictors including population density, smoking prevalence (age   15), poverty rate, and number of hospitals. Overdispersion was confirmed (deviance/df = 12,020), justifying the use of NBR. Model comparison shows that GWNBR provides improved fit relative to global models, with lower AIC than the NBR model (716.45 vs 732.29). Spatial heterogeneity was confirmed by the Breusch–Pagan test (BP = 21.011; p  0.01). Provinces exhibit distinct patterns of significant determinants; for example, in West Sumatra, poverty and smoking show strong positive local effects, while in several eastern provinces smoking is not significant. These findings highlight the importance of spatially adaptive TB control policies rather than uniform national strategies.