Scan statistics have been extensively studied since Naus ﬁrst stated the problem of clustering points on a line and in two dimensions in 1965 (Naus 1965a, 1965b). Various topics on scan statistics are thoroughly covered in the books by Glaz and Balakrishnan (1999) and Glaz et al. (2001, 2009). In spatial epidemiology, we are often concerned with the location, size, and intensity of clusters when studying local area clustering (Pfeiﬀer et al. 2008). The spatial scan statistic proposed by Kulldorﬀ (1997) is one of the most popular methods for
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T&F Cat #K23899 — K23899 C009 — page 180 — 2/17/2016 — 20:26
identifying local clusters. This method imposes a large number of scanning windows with variable sizes on a study region and compares the areas inside versus those outside the scanning windows. The procedure of ﬁnding the most likely cluster is formulated using a hypothesis testing framework with a test statistic based on the likelihood ratio test.