ScanZID: Spatial Scan Statistics with Zero Inflation and Dispersion

The spatial scan statistic is one of the most important methods to detect and monitor spatial disease clusters. Usually it is assumed that disease cases follow a Poisson, Binomial, Bernoulli, or negative binomial distribution. In practice, however, case count datasets frequently present zero inflation and/or dispersion (underdispersion or overdispersion), resulting in the violation of those commonly used models, thus increasing type I error occurrence. This paper describes the spatial scan statistic with the zero inflation and dispersion (ScanZID) to accommodate simultaneously the excess of zeroes and dispersion. The null and alternative model parameters are estimated by the expectation-maximization (EM) algorithm, and the p-value is obtained through the fast double bootstrap test. An application is presented for Hanseniasis data in the Brazilian Amazon.