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

Author

Listed:
  • Xingyun Cao

    (Beijing University of Technology)

  • Weizhen Wang

    (Wright State University)

  • Tianfa Xie

    (Beijing University of Technology)

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.

Suggested Citation

  • Xingyun Cao & Weizhen Wang & Tianfa Xie, 2025. "An optimal exact interval for risk difference in 2 $$\times$$ × 2 contingency tables with structural zeros," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(1), pages 155-170, March.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:1:d:10.1007_s10260-024-00771-z
    DOI: 10.1007/s10260-024-00771-z
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    References listed on IDEAS

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    1. Ryan Martin & Chuanhai Liu, 2013. "Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 301-313, March.
    2. Man-Lai Tang & Nian-Sheng Tang & Vincent J. Carey, 2004. "Confidence Interval for Rate Ratio in a 2 × 2 Table with Structural Zero: An Application in Assessing False-Negative Rate Ratio When Combining Two Diagnostic Tests," Biometrics, The International Biometric Society, vol. 60(2), pages 550-555, June.
    3. Wang, Shun-Fang & Tang, Nian-Sheng & Wang, Xue-Ren, 2006. "Analysis of the risk difference of marginal and conditional probabilities in an incomplete correlated 2x2 table," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1597-1614, March.
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