Small proportions: what to report for confidence intervals?

Authors

  • Hilde Tobi,

    Corresponding author
    1. Department of Social Pharmacy, Pharmacoepidemiology and Pharmacotherapy, Groningen University Institute for Drug Exploration, Groningen, The Netherlands
    • Department of Social Pharmacy, Pharmacoepidemiology and Pharmacotherapy, GUIDE, Ant. Deusinglaan 1, 9713 AV Groningen, The Netherlands.
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  • Paul B. van den Berg,

    1. Department of Social Pharmacy, Pharmacoepidemiology and Pharmacotherapy, Groningen University Institute for Drug Exploration, Groningen, The Netherlands
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  • Lolkje TW de Jong-van den Berg

    1. Department of Social Pharmacy, Pharmacoepidemiology and Pharmacotherapy, Groningen University Institute for Drug Exploration, Groningen, The Netherlands
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  • No conflict of interest was declared.

Abstract

Purpose

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.

Methods

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.

Results

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.

Conclusions

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.

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