Confidence intervals for a binomial proportion by S. E. Vollset, Statistics in Medicine, 12, 809-824 (1993)

Statistics in Medicine (Impact Factor: 1.83). 09/1994; 13(16):1693-8.
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    ABSTRACT: Several methods have been proposed to construct confidence intervals for the binomial parameter. Some recent papers introduced the "mean coverage" criterion to evaluate the performance of confidence intervals and suggested that exact methods, because of their conservatism, are less useful than asymptotic ones. In these studies, however, exact intervals were always represented by the Clopper-Pearson interval (C-P). Now we focus on Sterne's interval, which is also exact and known to be better than the C-P in the two-sided case. Introducing a computer intensive level-adjustment procedure which allows constructing intervals that are exact in terms of mean coverage, we demonstrate that Sterne's interval performs better than the best asymptotic intervals, even in the mean coverage context. Level adjustment improves the C-P as well, which, with an appropriate level adjustment, becomes equivalent to the mid-P interval. Finally we show that the asymptotic behaviour of the mid-P method is far poorer than is generally expected.
    Full-text · Article · Mar 2003 · Statistics in Medicine
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    ABSTRACT: 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 pharmaco-epidemiological 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 pharmaco-epidemiology 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 (pi < or = 0.01), the use of the Exact method and the Score method with CC are advocated based on this study.
    No preview · Article · Apr 2005 · Pharmacoepidemiology and Drug Safety