Confidence intervals for a ratio of binomial proportions based on paired data

Abstract

Four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability. Two new methods are proposed that are based on combining two Wilson score intervals. The new methods are easy to compute and perform as well or better than the method recently proposed by Nam and Blackwelder. Two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width.