Spatial cluster detection for ordinal outcome data.

In geographical disease surveillance, spatial scan statistics are used to identify areas having unusually high or low rates of disease outcomes and to determine the statistical significance of detected clusters. The spatial scan statistic for ordinal data such as stage of cancer has been developed to detect clusters representing areas with high rates of more serious stages compared with the surrounding areas. Such areas were expressed using likelihood ratio ordering, which is a rather strict order restriction, and hence, the method might fail to detect spatial clusters with high rates of worse categories (e.g., later stage). In this paper, we relax the order restriction using stochastic ordering and examine differences between the two approaches in detecting spatial clusters. Through simulation studies, we show that the stochastic ordering-based approach has higher power, sensitivity, and positive predictive value under several scenarios. We illustrate the two methods with the use of a real data example.