Risk Adjusted Bernoulli Spatial Scan Statistics

Kulldorff’s scan statistics identify likely spatial, temporal, and spatial-temporal clusters via likelihood hypotheses tests of whether the observed rate of cases within a geographic or longitudinal region is statistically larger than that outside the region. The conventional versions of this test are based on the assumption that all opportunities (e.g., people) inside the region have the same probability of being a case (e.g., having disease), and similarly outside the region. In reality this assumption rarely holds, for example with the probability of having cancer being a function of numerous risk factors (age, race, family history, etc). We develop and investigate the performance of a risk-adjusted scan statistic for such situations, with the likelihood function now based on a heterogeneous probability model.