New insight of spatial scan statistics via high-dimensional regression model

Abstract

The spatial scan statistic is widely used to detect disease clusters in epidemiological surveillance. Since the seminal work by Kulldorff (1997), numerous extensions have emerged, including methods for defining scan regions, detecting multiple clusters, and expanding statistical models. Notably, Jung (2009) and Zhang and Lin (2009) introduced a regression-based approach accounting for covariates, encompassing classical methods. In this talk, we extend the regression-based approach by incorporating the well-known sparse L0 penalty and show that the derivation of spatial scan statistics can be expressed as an equivalent optimization problem. Our extended framework accommodates extensions such as space-time scan statistics and detecting multiple clusters while naturally connecting with existing spatial regression-based cluster detection. In addition, considering the relation to mean-shifted regression models (She and Owen 2011, Lee et al. 2012), clusters identified by spatial scan statistics can be viewed as outliers in terms of robust statistics. 

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