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Power of the scan statistic for detection of clustering
Author(s) -
Wallenstein Sylvan,
Naus Joseph,
Glaz Joseph
Publication year - 1993
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.4780121910
Subject(s) - scan statistic , statistic , cluster analysis , statistics , mathematics , frame (networking) , null hypothesis , test statistic , interval (graph theory) , power (physics) , algorithm , computer science , statistical hypothesis testing , combinatorics , physics , telecommunications , quantum mechanics
Abstract The scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame. Previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed, and under the unconditional model which let the total number of events be a random variable. This paper derives approximations for the power of the scan test for a pulse alternative. Under this alternative, the relative risk of disease on a subinterval )τ, τ + w (, τ unknown, is θ‐fold as high as it is for other subintervals of length w . Two sets of approximations are given for each model. The first approximation gives highly accurate results, but requires use of a personal computer. The second procedure can be performed on a hand‐held calculator and appears very accurate for the cases examined.