Confidence Interval Estimation of Proportion Near Zero or One: A Modeling Secondary Study

When computing a confidence interval for a binomial proportion p, one must choose an exact interval that has a coverage probability of at least 1-α for all values of p. In this study, we compared the confidence intervals of Clopper-Pearson, Wald, Wilson, and double ArcSin transformation in terms of maintaining a constant nominal type I error.
Simulations were used to compare four methods of estimating a confidence interval, including the Clopper-Pearson, Wald, Wilson, and double ArcSic. The data were generated from the binomial and Poison distribution with parameters p, n and µ=np, 1000 were produced . Type I error of each method was calculated per simulation. The above methods were used to estimate confidence intervals in a meta-analysis study.
The results of the simulation study showed that double ArcSin keep confidence interval at [0,1], but for some proportion has high type I error or low coverage probability. The Clopper–Pearson interval guarantees that the coverage probability is always equal to or above the nominal confidence level for any fixed p.
This study showed that confidence interval estimations the Clopper-Pearson than other methods of calculating the type I error fixed and smaller.