An extended power of cluster detection tests.

Several tests have been proposed to detect spatial disease clustering without prior information on their locations. In order to compare the performance of these tests, most authors employ the usual power, i.e. the rejection probability of the null hypothesis of no clustering due to various reasons. However, the usual power is not always appropriate for evaluating the cluster detection tests since their purpose is to both reject the null hypothesis and identify the cluster areas accurately. In this paper, we propose an extended power of the cluster detection tests, which includes the usual power as a special case. Further, we define the profile of the extended power, which can be expected to play an important role in the evaluation and comparison of several cluster detection tests. The proposed extended power and its profile are demonstrated by two tests--Kulldorff's circular spatial scan statistic and a flexible spatial scan statistic proposed by Tango and Takahashi.