Asymptotic distribution of an index for disease clustering

Tango (1984, Biometrics 40, 15-26) proposed an index for disease clustering in time, applicable to grouped data with the assumption that the population at risk remains fairly uniform over the study period. However, the asymptotic distribution of the index derived under the hypothesis of no clustering was rather complex for simple use. Recently, Whittemore and Keller (1986, Biometrics 42, 218) and Whittemore et al. (1987, Biometrika 74, 631-635) proved that the distribution of the index is asymptotically normal. The present paper indicates that their approximation may be poor for moderately large sample sizes and suggests a central chi-square distribution as a better approximation to the asymptotic distribution of this index.