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An approximation for the distribution of the scan statistic
Author(s) -
Wallenstein Sylvan,
Neff Norman
Publication year - 1987
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780060212
Subject(s) - scan statistic , poisson distribution , statistic , mathematics , statistics , computation , cluster (spacecraft) , distribution (mathematics) , algorithm , computer science , mathematical analysis , programming language
The scan statistic evaluates whether an apparent cluster of disease in time is due to chance. The statistic employs a ‘moving window’ of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period T . Computation of the probability of observing a certain size cluster, under the hypothesis of a uniform distribution, is infeasible when N , the total number of events, is large, and w is of moderate or small size relative to T . We give an approximation that is an asymptotic upper bound, easy to compute, and, for the purposes of hypothesis testing, more accurate than other approximations presented in the literature. The approximation applies both when N is fixed, and when N has a Poisson distribution. We illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in New York City.