Score confidence interval with continuity correction for ratio of two independent proportions

When conducting statistical inference to compare two independent proportions in either a randomized clinical trial or an observational study, researchers commonly use relative risk to assess the relationship between two measurements. Score methods are a favored statistical technique to construct confidence intervals for relative risk as they generally exhibit superior performance in terms of coverage probability and interval width when compared to other methods such as the log transformation interval. In this paper, we propose an improvement to the asymptotic score interval by adding a continuity correction, thereby reducing the impact of the discreteness of binary outcomes and further enhancing the coverage probability. We conduct comprehensive simulation experiments to evaluate the performance of the proposed continuity-corrected score interval in various scenarios. Our results indicate that this new method has high proportions of guaranteed coverage probability. This approach may be considered as an alternative approach to the exact confidence interval. Furthermore, we provide two real-world examples to demonstrate the application of the existing intervals and the newly proposed continuity correction interval.