A spatiotemporal negative binomial model with dynamic dispersion: An application to Tuberculosis infections

2026-09-09

AI Summary

该研究通过引入具有动态分散参数的负二项空间整数值广义自回归条件异方差模型，解决了巴西圣保罗州结核病感染的空间异质性和时间波动性问题。

Abstract

Tuberculosis (TB) remains a critical public health concern in Brazil, characterized by pronounced spatial heterogeneity and fluctuating temporal volatility. In this paper, we study monthly TB notifications across 61 microregions of Sao Paulo state from 2001 to 2024. To do this, we introduce a negative binomial spatial integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) model featuring jointly dynamic conditional means and time-varying dispersion. To capture inter-regional spillovers, we incorporate both discrete adjacency structures and a novel continuous distance-based formulation leveraging the Matern correlation function. Parameter estimation via conditional maximum likelihood employs a two-step profile-likelihood iterative scheme, demonstrating solid finite-sample performance in simulation studies. Applied to the Sao Paulo TB surveillance data, the framework substantially outperforms standard Poisson and fixed-dispersion spatiotemporal baselines in empirical fit and uncertainty quantification, maintaining nominal 95% predictive coverage across both dense metropolitan centers and rural microregions. Our results reveal marked spatial heterogeneity in baseline incidence, dynamic overdispersion driven by localized outbreaks, and short-range spatial interaction decay. By accurately modeling spatiotemporal volatility, the proposed methodology provides a robust statistical tool to support public health surveillance, policy-making, and resource allocation.

Problem

• Tuberculosis
• spatiotemporal heterogeneity
• dynamic dispersion
• public health surveillance

Innovation

• spatiotemporal negative binomial model
• dynamic dispersion
• INGARCH
• Matern correlation function
• spillover effect