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arXiv 2302.04582stat.MEstat.AP
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疾病分布的可靠事件率

Reliable event rates for disease mapping

Harrison Quick, Guangzi Song

摘要:

在分析空间参照事件数据时,宣布速率为“可靠”的标准仍然是一个有争议的问题。然而,这些不同的标准有一个共同点,即在小面积分析环境中,它们很少满足粗略估计,这促使人们使用空间模型来提高可靠性。虽然合理,但最近的工作量化了空间统计学文献中流行的模型在多大程度上可以压倒数据中包含的信息,导致过度平滑。在这里,我们首先提供了一个定义的“可靠”的估计事件发生率,可用于原油和基于模型的估计,并允许离散和连续的可靠性声明。然后,我们构建了一个空间贝叶斯框架,允许用户将先验信息注入到他们的模型中,以提高可靠性,同时也防止过度平滑。我们将我们的方法应用于宾夕法尼亚州的县级出生数据,突出了空间模型中过度平滑的影响,以及我们的方法如何使用户能够更好地将注意力集中在存在足够数据以推动推理决策的领域。最后,我们简要讨论了如何在小面积研究的设计中使用可靠性的定义。

英文摘要:

When analyzing spatially referenced event data, the criteria for declaring rates as "reliable" is still a matter of dispute. What these varying criteria have in common, however, is that they are rarely satisfied for crude estimates in small area analysis settings, prompting the use of spatial models to improve reliability. While reasonable, recent work has quantified the extent to which popular models from the spatial statistics literature can overwhelm the information contained in the data, leading to oversmoothing. Here, we begin by providing a definition for a "reliable" estimate for event rates that can be used for crude and model-based estimates and allows for discrete and continuous statements of reliability. We then construct a spatial Bayesian framework that allows users to infuse prior information into their models to improve reliability while also guarding against oversmoothing. We apply our approach to county-level birth data from Pennsylvania, highlighting the effect of oversmoothing in spatial models and how our approach can allow users to better focus their attention to areas where sufficient data exists to drive inferential decisions. We then conclude with a brief discussion of how this definition of reliability can be used in the design of small area studies.

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