An optimal exact interval for risk difference in 2 $$\times$$ × 2 contingency tables with structural zeros

In studies involving infectious diseases or two-step treatment research, the 2 $$\times$$ × 2 contingency table with a structural zero serves as a common framework for data collection. In biomedical studies and related fields, inferring the risk differences through confidence intervals is of significant importance. However, the reliability of approximate intervals based on asymptotic normality is questionable, particularly in small samples. This paper aims to address this limitation by proposing exact intervals for the risk difference, enhancing both reliability and precision. Initially, a novel interval is introduced using the restricted most probable method, which is then optimized via the h-function method to create an optimal exact interval. A comparative analysis is conducted, contrasting this proposed interval with others derived from methods such as the score method, inferential model method, and modified inferential model method. Numerical studies demonstrate the superiority of the proposed interval in terms of both infimum coverage probability and total interval length. Additionally, two illustrative examples are provided to demonstrate the practical application of this interval in real-world scenarios.