Identifying space–time disease clusters

A cluster of cases of disease that are close both in space and in time is suggestive of an infectious aetiology. We present statistical tests for space–time clusters of disease for the two situations where the population at risk is either known or unknown as a function of space and time. The tests are derived using standard statistical methodology from a simple mathematical model of disease spread, i.e. they are derived as score tests from a likelihood function in which the infection process is modelled as a point process whose intensity becomes greater near an infector. A problem for such tests is that, when investigating whether or not a disease may be of infectious origin, the space and time distances characterising closeness to an infection are very likely to be unknown. The proposed methodology copes with this difficulty in a statistically acceptable way, without requiring multiple tests whose interpretation would be doubtful. When the underlying population size is unknown, the test reduces to a modification of the Knox test. An example of its use is given as epidemiology, risk, space–time cluster, likelihood and Knox test