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：针对区域聚合空间数据的流行病学调查通常涉及在地图疾病死亡率或发病率上检测相邻区域间的空间健康差异。分析此类数据会引入健康结果间的空间依赖性，并通过划定边界来分离具有不同健康结果的相邻区域，以报告统计上显著的空间差异。然而，在准确定义何为空间差异以及构建稳健的空间差异概率推断方面存在统计挑战。我们扩展了常见的贝叶斯线性回归框架，引入空间自回归，并提供基于模型的空间差异检测方法。我们推导出可解析处理的数学形式，显著加速了计算过程。在全美县级地图上进行的模拟实验验证了该方法的有效性，并将其应用于健康指标与评估研究所（IHME）提供的美国县级年龄标准化肺癌死亡率估计数据集。