Neyens Thomas, Lawson Andrew B, Kirby Russell S, Faes Christel
I-Biostat, Hasselt University, Hasselt, Belgium.
Division of Biostatistics and Epidemiology, College of Medicine, Medical University of South Carolina, Charleston, SC, U.S.A.
Stat Med. 2016 Aug 15;35(18):3189-202. doi: 10.1002/sim.6914. Epub 2016 Feb 29.
To describe the spatial distribution of diseases, a number of methods have been proposed to model relative risks within areas. Most models use Bayesian hierarchical methods, in which one models both spatially structured and unstructured extra-Poisson variance present in the data. For modelling a single disease, the conditional autoregressive (CAR) convolution model has been very popular. More recently, a combined model was proposed that 'combines' ideas from the CAR convolution model and the well-known Poisson-gamma model. The combined model was shown to be a good alternative to the CAR convolution model when there was a large amount of uncorrelated extra-variance in the data. Less solutions exist for modelling two diseases simultaneously or modelling a disease in two sub-populations simultaneously. Furthermore, existing models are typically based on the CAR convolution model. In this paper, a bivariate version of the combined model is proposed in which the unstructured heterogeneity term is split up into terms that are shared and terms that are specific to the disease or subpopulation, while spatial dependency is introduced via a univariate or multivariate Markov random field. The proposed method is illustrated by analysis of disease data in Georgia (USA) and Limburg (Belgium) and in a simulation study. We conclude that the bivariate combined model constitutes an interesting model when two diseases are possibly correlated. As the choice of the preferred model differs between data sets, we suggest to use the new and existing modelling approaches together and to choose the best model via goodness-of-fit statistics. Copyright © 2016 John Wiley & Sons, Ltd.
为了描述疾病的空间分布，已经提出了许多方法来对区域内的相对风险进行建模。大多数模型使用贝叶斯分层方法，在该方法中，对数据中存在的空间结构化和非结构化超泊松方差进行建模。对于单一疾病的建模，条件自回归（CAR）卷积模型非常流行。最近，有人提出了一种组合模型，该模型融合了CAR卷积模型和著名的泊松-伽马模型的思想。当数据中存在大量不相关的额外方差时，组合模型被证明是CAR卷积模型的一个很好的替代方案。对于同时对两种疾病进行建模或同时对两个亚人群中的一种疾病进行建模，可用的解决方案较少。此外，现有模型通常基于CAR卷积模型。在本文中，我们提出了一种双变量版本的组合模型，其中非结构化异质性项被分解为共享项和特定于疾病或亚人群的项，同时通过单变量或多变量马尔可夫随机场引入空间依赖性。通过对美国佐治亚州和比利时林堡的疾病数据进行分析以及在一项模拟研究中，对所提出的方法进行了说明。我们得出结论，当两种疾病可能相关时，双变量组合模型是一个有趣的模型。由于不同数据集对首选模型的选择不同，我们建议同时使用新的和现有的建模方法，并通过拟合优度统计来选择最佳模型。版权所有© 2016约翰威立父子有限公司。
