Abstract
Numerous methods have been proposed for detecting spatial clustering of disease. Two methods for likelihood-based inference using parametric models for clustering are the spatial scan statistic and the weighted average likelihood ratio (WALR) test. The spatial scan statistic provides a measure of evidence for clustering at a specific, data-identified location; it can be biased towards finding clusters in areas with greater spatial resolution. The WALR test provides a more global assessment of the evidence for clustering and identifies cluster locations in a relatively unbiased fashion using a posterior distribution over potential clusters. We consider two new statistics which attempt to combine the specificity of the scan statistic with the lack of bias of the WALR test: a scan statistic based on a penalized likelihood ratio and a localized version of the WALR test. We evaluate the power of these tests and bias of the associated estimates through simulations and demonstrate their application using the well-known New York leukemia data.