A novel exact confidence interval for the difference of proportions in paired data using a restricted most probable statistic.

Inference on the difference between two proportions in paired data is a key issue, particularly in biomedical research and clinical trials. Numerous methods exist for constructing confidence intervals for this difference. However, approximate methods that rely on asymptotic normality can be unreliable, underscoring the need for exact confidence intervals to improve reliability. In this paper, we develop a novel interval based on the restricted most probable method, which is further optimized using the h-function method to yield an optimal exact interval, ensuring both reliability and precision. We compare the proposed interval with other exact intervals developed through methodologies such as the score method, two Tang methods, the Wang method, the adjusted Wald method, and the score method with continuity correction. Our comparative analysis, utilizing the infimum coverage probability and total interval length as evaluation metrics, demonstrates the uniformly superior performance of the proposed interval. Additionally, an example illustrates its practical application in real-world scenarios. Supplementary Materials provide another example, numerical results on coverage and non-coverage probabilities, and R code.