A standardized scan statistic for detecting spatial clusters with estimated parameters

The scan statistic based on likelihood ratios (LRs) have been widely discussed for detecting spatial clusters. When developing the scan statistic, it uses the maximum likelihood estimates of the incidence rates inside and outside candidate clusters to substitute the true values in the LR statistic. However, the parameter estimation has a significant impact on the sensitivity of the scan statistic, which favors the detection of clusters in areas with large population sizes. By presenting the effects of parameter estimation on Kulldorff's scan statistic, we suggest a standardized scan statistic for spatial cluster detection. Compared to the traditional scan statistic, the standardized scan statistic can account for the varying mean and variance of the LR statistic due to inhomogeneous background population sizes. Extensive simulations have been performed to compare the power of the two cluster detection methods with known or/and estimated parameters. The simulation results show that the standardization can help alleviate the effects of parameter estimation and improve the detection of localized clusters. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012 Copyright © 2012 Wiley Periodicals, Inc.