Space‐Time Clustering Revisited

The role of space‐time clustering tests in epidemiological studies is reviewed and the principles underlying the main methods discussed. The method of Ederer et al . (1964), who studied the spatial‐temporal distribution of leukaemia, is outlined in some detail. This method relies on two indices of clustering: M 1 , the maximum number of cases in any space‐time unit, and M 2 , the maximum number of cases in any two consecutive units (by time). The conventional approach in the epidemiological literature is to report on M 1 and M 2 separately. However, this analysis ignores the fact that M 1 and M 2 are not statistically independent and consequently it has the wrong Type i error properties. Using the exact distribution, the correlation between M 1 and M 2 is computed for numerically important cases which have appeared in the literature. The problem of selecting a test statistic based on the bivariate distribution is then discussed. A test statistic, Q 2 , which is asymptotically χ 2 on two degrees of freedom is proposed and its distribution in small samples is investigated by means of a simulation study. A table of critical values for the new statistic is given.