Geographically Weighted Negative Binomial Regression (GWNBR) Modeling of Tuberculosis (TB) in North Sumatra

Ayunda, Afrila (Universitas Islam Negeri Sumatera Utara)
Husein, Ismail (Universitas Islam Negeri Sumatera Utara)
Faigle, Ulrich (Mathematisches Institut, Universität zu Köln, Köln, Germany)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 1 (2025): Zero: Jurnal Sains Matematika dan Terapan

Tuberculosis (TB) remains a serious public health challenge in North Sumatra, Indonesia, necessitating precise statistical modeling to understand its spatial patterns and associated risk factors. This study applies three statistical approaches — Poisson Regression, Negative Binomial Regression (NBR), and Geographically Weighted Negative Binomial Regression (GWNBR) — to investigate the distribution of TB cases across 33 districts and cities in North Sumatra in 2022. An overdispersion test revealed significant variance, indicating the inappropriateness of the Poisson model. The NBR model identified the number of medical personnel as the sole significant covariate, yielding an AIC of 478.31. A Breusch–Pagan test confirmed significant spatial heterogeneity across areas, justifying the use of GWNBR. The GWNBR approach captured spatially varying relationships between TB incidence and covariates, providing more localized insights and yielding an AIC of 512.34. The findings highlight the importance of adopting spatially adaptive methods when modeling disease patterns, allowing for targeted, area-specific public health interventions.