In this article, we consider confidence interval construction for proportion ratio in paired samples. Previous studies usually reported that score-based confidence intervals consistently outperformed other asymptotic confidence intervals for correlated proportion difference and ratio. However, score-based confidence intervals may not possess closed-form solutions and iterative procedures are therefore required. This article investigates the problem of confidence interval construction for ratio of two correlated proportions based on a hybrid method. Briefly, the hybrid method simply combines two separate confidence intervals for two individual proportions to produce a hybrid confidence interval for the ratio of the two individual proportions in paired studies. Most importantly, confidence intervals based on this hybrid method possess explicit solutions. Our simulation studies indicate that hybrid Wilson score confidence intervals based on Fieller's theorem performs well. The proposed confidence intervals will be illustrated with three real examples.

Matched-pair design is often adopted in equivalence or non-inferiority trials to increase the efficiency of binary-outcome treatment comparison. Briefly, subjects are required to participate in two binary-outcome treatments (e.g., old and new treatments via crossover design) under study. To establish the equivalence between the two treatments at the α significance level, a (1 − α)100% confidence interval for the correlated proportion difference is constructed and determined if it is entirely lying in the interval (−δ 0 , δ 0 ) for some clinically acceptable threshold δ 0 (e.g., 0.05). Nonetheless, some subjects may not be able to go through both treatments in practice and incomplete data thus arise. In this article, a hybrid method for confidence interval construction for correlated rate difference is proposed to establish equivalence between two treatments in matched-pair studies in the presence of incomplete data. The basic idea is to recover variance estimates from readily available confidence limits for single parameters. We compare the hybrid AgrestiCoull, Wilson score and Jeffreys confidence intervals with the asymptotic Wald and score confidence intervals with respect to their empirical coverage probabilities, expected confidence widths, ratios of left non-coverage probability, and total non-coverage probability. Our simulation studies suggest that the Agresti-Coull hybrid confidence intervals is better than the score-test-based and likelihood-ratio-based