The spatial scan statistic proposed by Kulldorff has been applied to a wide variety of epidemiological studies for cluster detection. This scan statistic, however, uses a circular window to define the potential cluster areas and thus has difficulty in correctly detecting actual noncircular clusters. A recent proposal by Duczmal and Assunção for detecting noncircular clusters is shown to detect a cluster of very irregular shape that is much larger than the true cluster in our experiences.
We propose a flexibly shaped spatial scan statistic that can detect irregular shaped clusters within relatively small neighborhoods of each region. The performance of the proposed spatial scan statistic is compared to that of Kulldorff's circular spatial scan statistic with Monte Carlo simulation by considering several circular and noncircular hot-spot cluster models. For comparison, we also propose a new bivariate power distribution classified by the number of regions detected as the most likely cluster and the number of hot-spot regions included in the most likely cluster.