Confidence Intervals for Two Proportions—A Generalized Estimation and Information Assessment

This paper develops profile score confidence intervals (i.e., z-standard intervals) by inverting orthogonalized score estimators for comparing two independent binomial proportions in rate difference, rate ratio, or odds ratio and utilizes a generalized estimation framework of Vos and Wu (Inf. Geom. 8: 99–123, 2025) to evaluate different confidence interval methods. The orthogonalized score estimators dominate other generalized estimators in Λ-efficiency for distinguishing parameter values around the truth, so the z-standard intervals become more efficient and acquire coverage closer to the nominal level than other types of confidence intervals. In addition, the degrees of freedom and small-sample corrections (applied to the profile nuisance parameter estimates) are expected to improve the coverage of the z-standard intervals and help maintain them above the nominal level. Computational algorithms are developed to find the z-standard intervals using R’s polyroot function. Numerical studies are conducted to compare both coverage and endpoints of different types of confidence intervals.