A Note on the Poisson Likelihood Ratio Test Statistic for Kulldorff's Scan Methods

Methods based on scan statistics are widely used in health-related applications to detect clusters of disease. The most common methods are based on the Bernoulli and Poisson models. Kulldorff (1997 Kulldorff , M. ( 1997 ). A spatial scan statistic . Communications in Statistics—Theory and Methods 26 : 1481 – 1496 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) derived the likelihood ratio test statistic for his scan method for both of these models. His scan statistic is widely used with freely available software, SaTScan^? (see Kulldorff, 2005 Kulldorff , M. ( 2005 ). SaTScan: software for the spatial, temporal, and space-time scan statistics , version 5.1 [computer program]. Information Management Services 2005; Available: http://www.satscan.org/. Accessed July 2007 . [Google Scholar]). We provide an alternative derivation of the likelihood ratio test statistic in the Poisson case. Our derivation is simpler and more general in the sense that it applies when the incidences are not aggregated into subregional counts.