Local Multiplicity Adjustment for the Spatial Scan Statistic Using the Gumbel Distribution
Article first published online: 15 JUL 2011
© 2011, The International Biometric Society
Volume 68, Issue 1, pages 174–182, March 2012
How to Cite
Gangnon, R. E. (2012), Local Multiplicity Adjustment for the Spatial Scan Statistic Using the Gumbel Distribution. Biometrics, 68: 174–182. doi: 10.1111/j.1541-0420.2011.01643.x
- Issue published online: 23 MAR 2012
- Article first published online: 15 JUL 2011
- Received March 2010. Revised April 2011.Accepted May 2011.
- Bonferroni adjustment;
- Gumbel distribution;
- Multiple comparisons;
- Permutation test;
- Scan statistic
Summary The spatial scan statistic is an important and widely used tool for cluster detection. It is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters. In most cluster detection problems, there is variation in the extent of local multiplicity across the study region. For example, using a fixed maximum geographic radius for clusters, urban areas typically have many overlapping potential clusters, whereas rural areas have relatively few. The spatial scan statistic does not account for local multiplicity variation. We describe a previously proposed local multiplicity adjustment based on a nested Bonferroni correction and propose a novel adjustment based on a Gumbel distribution approximation to the distribution of a local scan statistic. We compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion. These methods are then applied to the well-known New York leukemia dataset and a Wisconsin breast cancer incidence dataset.