Spatial scan statistics can be dangerous

Spatial scan statistics are widely used tools for the detection of disease clusters. Especially, the circular spatial scan statistic proposed by Kulldorff along with SaTScan software has been used in a wide variety of epidemiological studies and disease surveillance. However, as it cannot detect non-circular, irregularly shaped clusters, many authors have proposed non-circular spatial scan statistics. Above all, the flexible spatial scan statistic proposed by Tango and Takahashi along with FleXScan software has also been used. However, it does not seem to be well recognized that these spatial scan statistics, especially SaTScan, tend to detect the most likely cluster, much larger than the true cluster by absorbing neighboring regions with nonelevated risk of disease occurrence. Therefore, if researchers reported the detected most likely cluster as they are, it might lead to a criticism to them due to the fact that some regions with nonelevated risk are included in the detected most likely cluster. In this paper, to avoid detecting such undesirable and misleading clusters which might cause a social concern, we shall propose the use of the restricted likelihood ratio proposed by Tango and illustrate the procedure with two kinds of mortality data in Japan.