No conflict of interest was declared.
Small proportions: what to report for confidence intervals?†
Article first published online: 18 FEB 2005
Copyright © 2005 John Wiley & Sons, Ltd.
Pharmacoepidemiology and Drug Safety
Volume 14, Issue 4, pages 239–247, April 2005
How to Cite
Tobi, H., van den Berg, P. B. and de Jong-van den Berg, L. T. (2005), Small proportions: what to report for confidence intervals?. Pharmacoepidem. Drug Safe., 14: 239–247. doi: 10.1002/pds.1081
- Issue published online: 22 MAR 2005
- Article first published online: 18 FEB 2005
- Manuscript Accepted: 5 JAN 2005
- Manuscript Revised: 6 DEC 2004
- Manuscript Received: 21 AUG 2003
- confidence intervals;
- binomial proportion;
- simulation study
It is generally agreed that a confidence interval (CI) is usually more informative than a point estimate or p-value, but we rarely encounter small proportions with CI in the pharmacoepidemiological literature. When a CI is given it is sporadically reported, how it was calculated. This incorrectly suggests one single method to calculate CIs. To identify the method best suited for small proportions, seven approximate methods and the Clopper–Pearson Exact method to calculate CIs were compared.
In a simulation study for 90-, 95- and 99%CIs, with sample size 1000 and proportions ranging from 0.001 to 0.01, were evaluated systematically. Main quality criteria were coverage and interval width. The methods are illustrated using data from pharmacoepidemiology studies.
Simulations showed that standard Wald methods have insufficient coverage probability regardless of how the desired coverage is perceived. Overall, the Exact method and the Score method with continuity correction (CC) performed best. Real life examples showed the methods to yield different results too.
For CIs for small proportions (π ≤ 0.01), the use of the Exact method and the Score method with CC are advocated based on this study. Copyright © 2005 John Wiley & Sons, Ltd.