Quick Harrison, Song Guangzi, Tabb Loni Philip
Department of Epidemiology and Biostatistics, Drexel University, 3215 Market Street,Philadelphia, PA 19104, USA.
Department of Epidemiology and Biostatistics, Drexel University, 3215 Market Street,Philadelphia, PA 19104, USA.
Spat Spatiotemporal Epidemiol. 2021 Jun;37:100420. doi: 10.1016/j.sste.2021.100420. Epub 2021 Mar 27.
The use of the conditional autoregressive framework proposed by Besag, York, and Mollié (1991; BYM) is ubiquitous in Bayesian disease mapping and spatial epidemiology. While it is understood that Bayesian inference is based on a combination of the information contained in the data and the information contributed by the model, quantifying the contribution of the model relative to the information in the data is often non-trivial. Here, we provide a measure of the contribution of the BYM framework by first considering the simple Poisson-gamma setting in which quantifying the prior's contribution is quite clear. We then propose a relationship between gamma and lognormal priors that we then extend to cover the framework proposed by BYM. Following a brief simulation study in which we illustrate the accuracy of our lognormal approximation of the gamma prior, we analyze a dataset comprised of county-level heart disease-related death data across the United States. In addition to demonstrating the potential for the BYM framework to correspond to a highly informative prior specification, we also illustrate the sensitivity of death rate estimates to changes in the informativeness of the BYM framework.
贝萨格（Besag）、约克（York）和莫利耶（Mollié）于1991年提出的条件自回归框架（BYM）在贝叶斯疾病地图绘制和空间流行病学中应用广泛。虽然人们知道贝叶斯推断是基于数据中包含的信息与模型所提供信息的结合，但量化模型相对于数据中信息的贡献往往并非易事。在此，我们首先通过考虑简单的泊松 - 伽马设定来衡量BYM框架的贡献，在该设定中量化先验的贡献相当明确。然后，我们提出伽马先验和对数正态先验之间的一种关系，并将其扩展以涵盖BYM提出的框架。在进行了一项简短的模拟研究以说明我们对伽马先验的对数正态近似的准确性之后，我们分析了一个由美国各县心脏病相关死亡数据组成的数据集。除了展示BYM框架对应高度信息丰富的先验规范的潜力外，我们还说明了死亡率估计对BYM框架信息丰富度变化的敏感性。
