A spatial scan statistic for compound poisson data, using the negative binomial distribution and accounting for population stratification

Since the interest in studying spatial relations in plant populations was raised in the 1950s, much effort has been devoted to the development of methods for spatial data analysis. One such development focused on techniques for detecting spatial clusters of cases and events in the biological sciences and epidemiology during the late 1980s and the following decade. More recently, research has examined detecting clusters of correlated count data associated with health conditions of individuals. Such a method allows researchers to examine spatial relationships of disease-related events rather than just incidents or prevalent cases. We introduce a spatial scan test that identifies clusters of events in a study region. Because an individual case may have multiple (repeated) events, we base the test on a special compound Poisson model. Based on this special class (a compound Poisson representation of the negative binomial distribution), advantages in computation over the general compound Poisson model that relies on a recursive formula are realized. We illustrate our method for cluster detection on emergency department visits, where individuals may make multiple asthma-related visits. We also demonstrate the spatial scan test adjusted by key population characteristics such as sex or age.