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Bayesian confidence interval for difference of the proportions in a 2×2 table with structural zero

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  • Lei Shi
  • Hongyuan Sun
  • Peng Bai

Abstract

This article studies the construction of a Bayesian confidence interval for risk difference in a 2×2 table with structural zero. The exact posterior distribution of the risk difference is derived under the Dirichlet prior distribution, and a tail-based interval is used to construct the Bayesian confidence interval. The frequentist performance of the tail-based interval is investigated and compared with the score-based interval by simulation. Our results show that the tail-based interval at Jeffreys prior performs as well as or better than the score-based confidence interval.

Suggested Citation

  • Lei Shi & Hongyuan Sun & Peng Bai, 2009. "Bayesian confidence interval for difference of the proportions in a 2×2 table with structural zero," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(5), pages 483-494.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:5:p:483-494
    DOI: 10.1080/02664760802474272
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    References listed on IDEAS

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    1. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    2. Gupta, Ramesh C. & Tian, Suzhong, 2007. "Statistical inference for the risk ratio in 2x2 binomial trials with structural zero," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3070-3084, March.
    3. 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.
    4. Alan Agresti & David B. Hitchcock, 2005. "Bayesian inference for categorical data analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 297-330, December.
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    Cited by:

    1. Peng Bai & Wen Gan & Lei Shi, 2011. "Bayesian confidence interval for the risk ratio in a correlated 2 × 2 table with structural zero," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2805-2817, February.

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