Spatial Variable Selection and An Application to Virginia Lyme Disease Emergence

ABSTRACT

Lyme disease is an infectious disease, that is, caused by a bacterium called Borrelia burgdorferi 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.

KEYWORDS:

• Gaussian process
• GLMM
• Multicollinearity
• Poisson regression
• Spatial count data
• Spatial correlation

Acknowledgments

The authors would like to thank the editor, an associate editor, three referees, and an associate editor for reproducibility, for their valuable comments that helped in improving this article significantly. The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources.

Additional information

Funding

The research by Xie, Li, Kolivras, and Gaines was supported by National Science Foundation Grant BCS-1122876 to Virginia Tech. The research by Hong and Xu was partially supported by National Science Foundation Grants BCS-1122876, CNS-1565314, and CNS-1838271 to Virginia Tech.