Spatial Variable Selection and An Application to Virginia Lyme Disease Emergence

Lyme disease is an infectious disease, that is, caused by a bacterium called <i>Borrelia burgdorferi</i> sensu stricto. In the United States, Lyme disease is one of the most common infectious diseases. The major endemic areas of the disease are New England, Mid-Atlantic, East-North Central, South Atlantic, and West North-Central. Virginia is on the front-line of the disease’s diffusion from the northeast to the south. One of the research objectives for the infectious disease community is to identify environmental and economic variables that are associated with the emergence of Lyme disease. In this article, we use a spatial Poisson regression model to link the spatial disease counts and environmental and economic variables, and develop a spatial variable selection procedure to effectively identify important factors by using an adaptive elastic net penalty. The proposed methods can automatically select important covariates, while adjusting for possible spatial correlations of disease counts. The performance of the proposed method is studied and compared with existing methods via a comprehensive simulation study. We apply the developed variable selection methods to the Virginia Lyme disease data and identify important variables that are new to the literature. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

莱姆病（Lyme disease）是一种细菌性传染病，由狭义伯氏疏螺旋体（*Borrelia burgdorferi* sensu stricto）引发。在美国，莱姆病是最为常见的传染病之一。该病的主要流行区域涵盖新英格兰、中大西洋、东中北部、南大西洋及中西北部地区。弗吉尼亚州正处于该疾病从东北向南部扩散的前沿区域。传染病学界的核心研究目标之一，便是甄别与莱姆病暴发相关的环境与经济变量。本文采用空间泊松回归模型，构建空间疾病计数与环境、经济变量间的关联关系，并结合自适应弹性网惩罚项，开发出一套空间变量选择流程，以高效识别关键影响因子。所提方法可在校正疾病计数潜在空间相关性的同时，自动筛选重要协变量。本文通过全面的模拟仿真实验，对所提方法的性能展开了研究，并与现有主流方法进行了对比分析。我们将所开发的变量选择方法应用于弗吉尼亚州莱姆病数据集，识别出了一系列此前未见文献报道的关键变量。本文的补充材料（包含可用于复现研究工作的标准化材料说明）可作为在线补充资料获取。