Structure Induced by a Multiple Membership Transformation on the Conditional Autoregressive Model

IF 4.9 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Bayesian Analysis Pub Date : 2022-08-13 DOI:10.1214/23-ba1370

Marco Gramatica, S. Liverani, Peter Congdon

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引用次数: 0

Abstract

The objective of disease mapping is to model data aggregated at the areal level. In some contexts, however, (e.g. residential histories, general practitioner catchment areas) when data is arising from a variety of sources, not necessarily at the same spatial scale, it is possible to specify spatial random effects, or covariate effects, at the areal level, by using a multiple membership principle (MM) (Petrof et al. 2020, Gramatica et al. 2021). A weighted average of conditional autoregressive (CAR) spatial random effects embeds spatial information for a spatially-misaligned outcome and estimate relative risk for both frameworks (areas and memberships). In this paper we investigate the theoretical underpinnings of these application of the multiple membership principle to the CAR prior, in particular with regard to parameterisation, properness and identifiability. We carry out simulations involving different numbers of memberships as compared to number of areas and assess impact of this on estimating parameters of interest. Both analytical and simulation study results show under which conditions parameters of interest are identifiable, so that we can offer actionable recommendations to practitioners. Finally, we present the results of an application of the multiple membership model to diabetes prevalence data in South London, together with strategic implications for public health considerations

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条件自回归模型的多重隶属变换诱导的结构

疾病绘图的目的是对区域层面上汇总的数据进行建模。然而，在某些情况下（例如，居住史、全科医生集水区），当数据来自各种来源，而不一定在同一空间尺度上时，可以通过使用多成员原理（MM）在区域水平上指定空间随机效应或协变量效应（Petrof等人2020，Gramatica等人2021）。条件自回归（CAR）空间随机效应的加权平均嵌入了空间错位结果的空间信息，并估计了两个框架（区域和成员）的相对风险。在本文中，我们研究了将多重隶属度原理应用于CAR先验的理论基础，特别是在参数化、适当性和可识别性方面。与区域数量相比，我们进行了涉及不同成员数量的模拟，并评估了这对估计感兴趣的参数的影响。分析和模拟研究结果都表明，在何种条件下，感兴趣的参数是可识别的，因此我们可以向从业者提供可操作的建议。最后，我们介绍了将多成员模型应用于伦敦南部糖尿病患病率数据的结果，以及对公共卫生考虑的战略意义

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bayesian Analysis 数学-数学跨学科应用

CiteScore

6.50

自引率

13.60%

发文量

审稿时长

>12 weeks

期刊介绍： Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.