Improved confidence interval estimation for the relative difference in matched pair designs

There has been limited research on confidence intervals for the relative difference in matched-pair designs. Previous studies have generally reported that the logarithmic transformation method (LCI) outperforms the Fieller method (FCI). However, the LCI is based on large-sample theory, and its reliability in small-sample studies has long been questioned. To address this issue, this paper introduces several new confidence interval estimators for the relative difference in matched-pair designs. We conducted Monte Carlo simulations to compare the proposed methods with the existing LCI and FCI methods, in terms of coverage probability and expected confidence width. The results show that the SPA method (the saddlepoint approximation method) significantly outperforms all other methods across all parameter configurations, particularly in small-sample or extreme settings, where it exhibits the narrowest intervals and most stable coverage. Nevertheless, while the SPA method performs well, it is computationally intensive and fails to provide a closed-form expression for the interval, thus limiting its practical applicability. The WSM (based on the Wilson score and MOVER) achieves a good balance between interval width and coverage; its performance closely approaches that of SPA when the sample size is large. Overall, the SPA method is recommended when computational resources permit and high precision is required, while the WSM method serves as an efficient and practical alternative, especially in large-sample applications. Finally, all methods are illustrated using two real examples.