Wald-based spatial scan statistics for cluster detection

The spatial scan test, which is often carried out by maximizing a likelihood ratio-based statistic over a collection of cluster candidates, is widely used in cluster detection and disease surveillance. As the likelihood ratio statistic may not be available if the exact distribution of the response variable is not specified, a Wald-based spatial scan approach is proposed. The idea is to construct a special explanatory variable for spatial clusters in the linear function of a statistical model. The spatial scan test is carried out by scanning the special explanatory variable over the collection of cluster candidates. An advantage is that the Wald-based spatial scan statistic can bridge spatial clusters and linear functions of statistical models. It can be easily combined with well-known statistical models beyond generalized linear models. It is expected that the proposed approach will have a great impact on cluster detection when the likelihood inference is intractable or unavailable.