Improved confidence estimation for the binomial proportion with applications to clinical studies

In this paper, we establish a frequentist framework that incorporates all confidence sets with guaranteed frequentist coverage probability for the binomial proportion, where different confidence sets are completely characterized by their tail functions. Based on measures of precision in the form of interval length, probability of false coverage, and a new evaluation criterion utilizing prior information, we construct the optimal confidence set for the binomial proportion. The newly proposed methodology is applied to clinical studies. It is shown that confidence intervals obtained via the tail functions are often better than prevailing confidence intervals in view of precision.