A k nearest neighbour test for space-time interaction

This paper describes a k nearest neighbour statistic sensitive to the pattern of cases expected of space-time clusters of health events. The Knox and Mantel tests are frequently used for space-time clustering but have two disadvantages. First, the selection of critical space-time distances for the Knox test and of a data transformation for the Mantel test is subjective. Second, the Mantel statistic is the sum of the products of space and time distances, is linear in form, and is not sensitive to non-linear associations between small space and time distances expected of contagious processes. The k nearest neighbour statistic is the number of case pairs that are k nearest neighbours in both space and time, and is evaluated under the null hypothesis of independent space and time nearest neighbour relationships. The test was applied to simulated and real data and compared to the Knox and Mantel tests using statistical power comparisons. The k nearest neighbour test proved sensitive to the space-time interaction pattern expected of disease clusters, does not require parameters (such as critical distances) to be estimated from the data, and may be used to test hypotheses about the spatial and temporal scale of the cluster process. The method addresses significant weaknesses in existing space-time cluster tests and should prove useful in the quantification and evaluation of clusters of human health events. Additional research is needed to further document the power of the test under different cluster processes.