An optimal exact interval for the risk ratio in the 2×2$$ 2\times 2 $$ table with structural zero

Abstract

The table with a structural zero represents a common scenario in clinical trials and epidemiology, characterized by a specific empty cell. In such cases, the risk ratio serves as a vital parameter for statistical inference. However, existing confidence intervals, such as those constructed through the score test and Bayesian methods, fail to achieve the prescribed nominal level. Our focus is on numerically constructing exact confidence intervals for the risk ratio. We achieve this by optimally combining the modified inferential model method and the ‐function method. The resulting interval is then compared with intervals generated by four existing methods: the score method, the exact score method, the Bayesian tailed‐based method and the inferential model method. This comparison is conducted based on the infimum coverage probability, average interval length and non‐coverage probability criteria. Remarkably, our proposed interval outperforms other exact intervals, being notably shorter. To illustrate the effectiveness of our approach, we discuss two examples in detail.