Epidemiological investigations of regionally aggregated spatial data often involve detecting spatial health disparities among neighboring regions on a map of disease mortality or incidence rates. Analyzing such data introduces spatial dependence among health outcomes and seeks to report statistically significant spatial disparities by delineating boundaries that separate neighboring regions with disparate health outcomes. However, there are statistical challenges to appropriately define what constitutes a spatial disparity and to construct robust probabilistic inferences for spatial disparities. We enrich the familiar Bayesian linear regression framework to introduce spatial autoregression and offer model-based detection of spatial disparities. We derive exploitable analytical tractability that considerably accelerates computation. Simulation experiments conducted on a county map of the entire United States demonstrate the effectiveness of our method, and we apply our method to a data set from the Institute of Health Metrics and Evaluation (IHME) on age-standardized US county-level estimates of lung cancer mortality rates.

翻译：对区域汇总空间数据的流行病学调查通常涉及在地图上的疾病死亡率或发病率中检测相邻区域之间的空间健康差异。分析此类数据会引入健康结果之间的空间依赖性，并试图通过划定分隔具有不同健康结果的相邻区域的边界来报告具有统计学意义的空间差异。然而，在如何正确定义何为空间差异以及如何为空间差异构建稳健的概率推断方面存在统计挑战。我们丰富了常见的贝叶斯线性回归框架，引入了空间自回归，并提供了基于模型的空间差异检测方法。我们推导出了可利用的解析易处理性，从而显著加速了计算。在美国全国县级地图上进行的模拟实验证明了我们方法的有效性，并且我们将该方法应用于健康指标与评估研究所（IHME）关于美国县级年龄标准化肺癌死亡率估计值的数据集。