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.

空间扫描统计已广泛用于空间疾病监测和空间簇检测。但是，在现实世界的数据中经常会出现过度分散和过多的零，这不仅违反了Poisson模型的似然性假设，而且导致过多的I型错误或错误警报。在本文中，我们提出了贝尔扫描和零膨胀贝尔扫描统计信息，它们涵盖了数据中的零位的过度分散和/或过量。所提出的扫描方法可以以简单的方式潜在地应用于事件数据。考虑零膨胀模型，我们根据相对风险偏倚，准确性，聚类检测的召回率和功效比较Bell，Poisson和二项式扫描统计量。通过我们的模拟，我们证明，与传统扫描模型相比，贝尔扫描是一种强大而强大的替代方案。最后，我们通过两次实际数据扫描分析来说明新方法。