A study on the use of Gumbel approximation with the Bernoulli spatial scan statistic

p-value approximations for spatial scan statistics using extreme value distributions

Spatial scan statistics are widely applied to identify spatial clusters in geographic disease surveillance. To evaluate the statistical significance of detected clusters, Monte Carlo hypothesis testing is often used because the null distribution of spatial scan statistics is not known. A drawback of the method is that we have to increase the number of replications to obtain accurate p-values. Gumbel-based p-value approximations for spatial scan statistics have recently been proposed and evaluated for Poisson and Bernoulli models. In this study, we examine the use of a generalized extreme value distribution to approximate the null distribution of spatial scan statistics as well as the Gumbel distribution. Through simulation, p-value approximations using extreme value distributions for spatial scan statistics are assessed for multinomial and ordinal models in addition to Poisson and Bernoulli models.