Power of the scan statistic for detection of clustering

The scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame. Previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed, and under the unconditional model which let the total number of events be a random variable. This paper derives approximations for the power of the scan test for a pulse alternative. Under this alternative, the relative risk of disease on a subinterval (tau, tau + w), tau unknown, is theta-fold as high as it is for other subintervals of length w. Two sets of approximations are given for each model. The first approximation gives highly accurate results, but requires use of a personal computer. The second procedure can be performed on a hand-held calculator and appears very accurate for the cases examined.