Article first published online: 24 JAN 2013
Copyright © 2013 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 19, pages 3300–3313, 30 August 2013
How to Cite
Read, S., Bath, P.A., Willett, P. and Maheswaran, R. (2013), A study on the use of Gumbel approximation with the Bernoulli spatial scan statistic. Statist. Med., 32: 3300–3313. doi: 10.1002/sim.5746
- Issue published online: 11 JUL 2013
- Article first published online: 24 JAN 2013
- Manuscript Accepted: 3 JAN 2013
- Manuscript Received: 12 OCT 2011
- cluster detection;
- spatial scan statistic;
- Monte Carlo
The Bernoulli version of the spatial scan statistic is a well established method of detecting localised spatial clusters in binary labelled point data, a typical application being the epidemiological case–control study. A recent study suggests the inferential accuracy of several versions of the spatial scan statistic (principally the Poisson version) can be improved, at little computational cost, by using the Gumbel distribution, a method now available in SaTScanTM (www.satscan.org). We study in detail the effect of this technique when applied to the Bernoulli version and demonstrate that it is highly effective, albeit with some increase in false alarm rates at certain significance thresholds. We explain how this increase is due to the discrete nature of the Bernoulli spatial scan statistic and demonstrate that it can affect even small p-values. Despite this, we argue that the Gumbel method is actually preferable for very small p-values. Furthermore, we extend previous research by running benchmark trials on 12 000 synthetic datasets, thus demonstrating that the overall detection capability of the Bernoulli version (i.e. ratio of power to false alarm rate) is not noticeably affected by the use of the Gumbel method. We also provide an example application of the Gumbel method using data on hospital admissions for chronic obstructive pulmonary disease. Copyright © 2013 John Wiley & Sons, Ltd.