Binomial confidence intervals for testing non-inferiority or superiority: a practitioner’s dilemma

Abstract

In testing for non-inferiority or superiority in a single arm study, the confidence interval of a single binomial proportion is frequently used. A number of such intervals are proposed in the literature and implemented in standard software packages. Unfortunately, use of different intervals leads to conflicting conclusions. Practitioners thus face a serious dilemma in deciding which one to depend on. Is there a way to resolve this dilemma? We address this question by investigating the performances of ten commonly used intervals of a single binomial proportion, in the light of two criteria, viz., coverage and expected length of the interval.