Measuring the severity of disease clustering using Tango's index

Tango [Biometrics 40:15 (1984)] proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. This index has received considerable attention in the literature including the suggestion that it be used to detect the space-time clustering of diseases and the suggestion to use similar test statistics to detect disease clustering in space and/or time while accounting for a changing population size over the study period. This paper concerns the related question of measuring the severity of the disease clustering once it has been determined that cases are not randomly distributed over space and/or time. A family of alternatives to randomness is proposed in which space and/or time versions of Tango's index are sufficient statistics for the parameters measuring the severity of the clustering. For the special case of temporal clustering, an unbiased estimator of the clustering parameter and its sampling variance is derived, and a particularly simple interpretation of this estimator is suggested. These latter results are based on some asymptotic approximations due to Tango [Biometrics 46:351 (1990)]. An application to the trisomy data given by Wallenstein [Am. J. Epidemiol. 111:367 (1980)] is discussed.