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.