Optimizing maximum window size in spatial scan statistic for ordinal data

Abstract

Spatial scan statistics are widely used in spatial epidemiology to identify areas with high or low rates of outcome. This scan-based method needs a scanning window, which is defined by its shape and maximum size. When deciding on the upper limit of the window size, 50% of the total population is often used. However, there is no rationale and the reported clusters could be too larger than the true ones.

Recently, Han et al. (2011) proposed using the Gini coefficient as a measure to assess the degree of heterogeneity of the cluster models. They also considered another measure called the Cluster Information Criterion (CLIC) similar to Akaike’s Information Criterion (AIC). The two measures were evaluated for the Poisson model only and applicability to other models has not been proved.

In this study, we adapt the two measures applicable to the ordinal model proposed by Jung, Kulldorff, and Klassen (2007). Through a simulation study and real data examples, we show that the two measures give consistent results except when the true clusters are irregular-shaped or located slightly apart from each other. In these cases, the Gini coefficient picks a smaller window size as an optimal maximum than CLIC. In doing so, it reflects a tendency to detect the clusters that are more close to true ones by detecting a set of several small clusters.

The results of this study demonstrate the necessity of optimizing the maximum window size in spatial scan statistic for ordinal data as well as for the Poisson model. Further, we believe that the two measures can be useful to optimize the maximum scanning window size in spatial scan statistic for ordinal data.