Space-time clusters with flexible shapes

Detection of space-time clusters plays an important role in epidemiology and public health. Different approaches for detecting space-time clusters have been proposed and implemented. Many of these approaches are based on the spatial scan statistic formulation. One key aspect of these cluster detection methods is the choice of cluster shape.

In this report, the effect of using flexible shapes for clusters is explored by discussing the issues that need to be considered and evaluated.

The first issue is the flexibility of the shape and its ability to model the disease cluster being studied. Another subtle and related factor is that with a more flexible shape, clusters can appear more often by chance, which will be reflected in the p value obtained through Monte Carlo hypothesis testing. Choosing more complex cluster shapes can affect the computational requirements and also constrain the cluster detection approaches that could be applied.

The New Mexico brain cancer data set is used to illustrate the tradeoffs. The analysis of these data should not be construed as a comprehensive investigation from the public health perspective. The data set is used to illustrate and compare clusters with two different shapes, cylinder and square pyramid. The results indicate the insights that can be gained from these shapes, individually and collectively.

The domain expert should choose the cluster shape, being aware of the disease being modeled and the analysis goals. For example, a flexible shape like the square pyramid can model either growth or shrinkage and movement of the disease and might provide insights on its origin. In addition, performing the analyses with more than one shape can lead to increased insights regarding the disease cluster.