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

Abstract

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) 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). 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.

Keywords:

• Cluster detection
• Poisson process
• SaTScan^™ software
• Scan statistic

Mathematics Subject Classification:

• 62H11
• 62M30