A Double-Scan Statistic for Clusters of Two Types of Events

Abstract
We develop a scan-type statistic to measure the unusualness of the clustering of two types of events over time. The statistic allows for a lagged effect between the two types of events. We derive the expected number of nonoverlapping clumps of clusters under retrospective and prospective chance models of no association. Results are derived and approaches are given to handle both uniform and more general distributions of events over time. We investigate the power of the statistic against an alternative where the observed data is a mixture of linked and unassociated clusters. The statistic is applied to data on homicide/suicide clusters over a 7-year period for several counties and several sex/race combinations.