Space-Time Clusters with Flexible Shapes

Detection of space-time clusters has an important role in epidemiology and public health. Here, we focus on the retrospective clustering analysis that is performed possibly triggered by an alarm from a surveillance system. Various approaches for detecting space-time clusters have been proposed and implemented. Many of these are based on the spatial scan statistic formulation. In this paper we present the issues to consider when choosing the shape of the cluster in such analyses. One criterion is the flexibility of the shape and its ability to model the phenomenon being studied. Another subtle and related factor is that with a more flexible shape clusters can appear more by chance. This will be reflected in the p-value obtained through Monte Carlo hypothesis testing. Choosing more complex cluster shapes can impact the computational requirements and also constrain the cluster detection approaches that could be applied. Importantly, the approach and heuristics used can impact key aspects of the results and their interpretation (e.g., p-value estimate). We use the New Mexico brain cancer data set to illustrate these tradeoffs. Clusters with two different shapes (cylinder, square pyramid) are detected in this data and compared. The results show the insights that can be gained from these shapes, individually and when put together.