Testing for space-time clusters of unknown size

The Knox test is widely used in epidemiology to test for infection or contagion, which is indicated by an excess of cases that are close both in space and time. Often, however, the values of the space and time critical parameters that define 'closeness' are unknown. An exact test is proposed for this situation, its computer implementation is described and examples of its use on published data sets are given. Other possible applications of the method adopted here are discussed. This is an example of a test where nuisance parameters are absent under H-0, and where the distribution of the test statistic can be found numerically.