Data-driven inference for the spatial scan statistic

A modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found under null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference.A practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.Spatial cluster analysis is considered an important technique for the elucidation of disease causes and epidemiological surveillance [1]. Kulldorff's spatial scan statistic, defined as a likelihood ratio, is the usual measure of the strength of geographic clusters [2,3]. The circular scan [4], a particular case of the spatial scan statistic, is currently the most used tool for the detection and inference of spatial clusters of disease.The spatial scan statistic considers a study region A divided into m areas, with total population N and C total cases. A zone is any collection of areas. The null hypothesis assumes that there are no clusters and the cases are uniformly distributed, such that the expected number of cases in each area is proportional to its population. A commonly used model assumes that the number of cases in each area is Poisson distributed proportionally to its population. Let cz be the number of observed cases and nz be the population of the zone z. The expected number of cases under null hypothesis is given by μz = C(nz/N ). The relative risk of z is I(z) = cz/μz and the relative risk outside z is O(z) = (C