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

Xingyun Cao (), Weizhen Wang () and Tianfa Xie ()
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Xingyun Cao: Beijing University of Technology
Weizhen Wang: Wright State University
Tianfa Xie: Beijing University of Technology

Statistical Methods & Applications, 2025, vol. 34, issue 1, No 8, 155-170

Abstract: Abstract 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.

Keywords: Infimum coverage probability; h-function method; Restricted most probable statistic; Total interval length (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10260-024-00771-z

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