具有动态离散参数的时空负二项模型：应用于结核病感染
A spatiotemporal negative binomial model with dynamic dispersion: An application to Tuberculosis infections
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中文总结 AI 辅助
本文提出一种具有动态离散参数的负二项空间INGARCH模型，用于分析圣保罗州结核病数据，通过两步估计和Matern相关函数捕捉时空波动，优于基线模型，支持公共卫生决策。
中文摘要 AI 辅助
结核病（TB）仍然是巴西一个重要的公共卫生问题，其特征是显著的空间异质性和波动的时序波动性。本文研究了2001年至2024年圣保罗州61个微区域每月的结核病通报数据。为此，我们引入了一个负二项空间整数值广义自回归条件异方差（INGARCH）模型，该模型具有联合动态条件均值和时变离散参数。为了捕捉区域间的溢出效应，我们结合了离散邻接结构和一种基于Matern相关函数的新型连续距离公式。通过条件最大似然估计，采用两步剖面似然迭代方案，模拟研究显示了良好的有限样本性能。应用于圣保罗结核病监测数据时，该框架在经验拟合和不确定性量化方面显著优于标准泊松和固定离散参数的时空基线模型，在密集大都市中心和农村微区域均保持了95%的名义预测覆盖率。我们的结果揭示了基线发病率的显著空间异质性、由局部暴发驱动的动态过度离散以及短程空间相互作用的衰减。通过准确建模时空波动性，所提出的方法为支持公共卫生监测、政策制定和资源分配提供了稳健的统计工具。
英文摘要
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.
发表机构
- Universidade Federal da Paraíba（帕拉伊巴联邦大学）
- University College Dublin（都柏林大学学院）
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