A Spatial Scan Statistic with a Restricted Likelihood Ratio

Kulldorff (1997) developed a circular spatial scan statistic for identifying the most likely cluster of disease that maximizes the likelihood ratio and his software SaTScan has been widely used for geographical disease cluster detection and disease surveillance. To detect non-circular clusters which cannot be detected by Kulldorff's circular spatial scan statistic, several non-circular spatial scan statistics have been proposed. However, it does not seem to be well recognized that these spatial scan statistics tend to detect the most likely cluster much larger than the true cluster by swallowing neighbouring regions with non-elevated risk. This paper proposes a new spatial scan statistic free from such an undesirable property by modifying the likelihood ratio so that it scans only the regions with elevated risk. Monte Carlo Simulation study shows that the proposed circular spatial scan statistic is shown to have better ability to identify the true cluster compared with Kulldorff's one in all the cluster models considered. The proposed circular spatial scan statisitc is illustrated with mortality data from cerebrovascular disease in Tokyo Metropolitan area, Japan.