Space-time cluster detection with cross-space-time relative risk functions

Space-time kernel density estimation (STKDE) commonly is used for space-time cluster detection. But, this technique might be limited because it does not take into account an underlying population at risk for observed events. A space-time relative risk function (STRRF) can help overcome this limitation by allowing a comparison of each kernel density of observations with that of controls. This paper proposes a cross-STRRF to identify spatio-temporal locations that experience statistically significant changes in their density of events. With events organized in a space-time voxel structure, the cross-STRRF evaluates space-time patterns by comparing event occurrences at a spatial location in a previous time period with ones in its future as well as with its spatial neighbors in its contemporaneous time period. The test statistics of the cross-STRRF values in each voxel are obtained with a permutation test in which cases and controls are shuffled within each time period to maintain the space-time envelope of events. An application to assault crime incidents in the city of Plano, Texas between 2008 and 2012 illustrates that the cross-STRRF and its significance test results emphasize spatio-temporal changes in event density rather than constantly focusing on high density regions, which STKDE does.