Zero-inflated Bell scan: A more flexible spatial scan statistic

Abstract

Spatial scan statistic has been widely employed in spatial disease surveillance and spatial cluster detection. However, the over-dispersion and excess of zeros are often presented in real-world data, causing not only the violation of likelihood assumption for the Poisson model, but also excessive Type I error or false alarms. In this paper, we propose the Bell scan and the zero-inflated Bell scan statistics which cover the over-dispersion and/or excess of zeros in the data. The proposed scan methods can be potentially applied to the event data in a simple way. Considering zero-inflated models, we compare the Bell, Poisson and binomial scan statistics based on relative risk bias, precision, recall of cluster detection, and power. By our simulations, we show that the Bell scan is a robust and a powerful alternative in comparison with the traditional scan models. We finally illustrate the new methodology with two real data scan analyses.