The Detection of Disease Clustering with Long and Variable Incubation Periods

Abstract

For diseases of unknown or uncertain aetiology, it is often of interest to test epidemiologically hypotheses concerning the possible existence of an infectious agent. Notably such studies concern Burkitt’s Lymphoma (1), childhood leukaemia (2) and multiple sclerosis (3). Since Knox (4) originally formalised the concept of space-time interaction and formulated a statistical test for its existence, a number of other tests have been proposed and applied to various diseases and conditions. When contemplating an infectious agent, it is clearly of importance to consider case-to-case contact and hence to consider the incubation, or latent, period of the disease. Although most of these statistical tests are not conceptually adequate for use with diseases other than those with very short incubation periods — they only consider one place and one time for each patient — Pike and Smith (5) consider a susceptible-infective model which does appear to be logically applicable to such situations in that it allows the natural history of the disease to be specified in terms of a period of susceptibility (during which the patient would have contracted the disease) and a period of infectivity (during which the patient would have been able to infect other potential patients). The statistical test formulated by Pike and Smith considers, for all possible pairs of patients who are infective and/or susceptible within the area under study during the study period, whether or not one patient was in the right place at the right time to infect the other patient. The test statistic is the number of such concordant pairs. Under the null hypothesis of no space-time interaction, the approximate distribution of the test statistic is available for testing this null hypothesis against the hypothesis of space-time clustering of the form specified in the hypothesised natural history of the disease.