IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v36y2009i5p483-494.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802474272
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802474272?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Luai Al-Labadi & Petru Ciur & Milutin Dimovic & Kyuson Lim, 2023. "Assessing Multinomial Distributions with a Bayesian Approach," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    3. Chris J. Lloyd, 2008. "A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs," Biometrics, The International Biometric Society, vol. 64(3), pages 716-723, September.
    4. Zheng Wei & Daeyoung Kim & Erin M. Conlon, 2022. "A Bayesian approach to the analysis of asymmetric association for two-way contingency tables," Computational Statistics, Springer, vol. 37(3), pages 1311-1338, July.
    5. Roy Mill, 2011. "Hiring and Learning in Online Global Labor Markets," Working Papers 11-17, NET Institute, revised Oct 2011.
    6. Frank Tuyl & Richard Gerlach & Kerrie Mengersen, 2008. "Inference for Proportions in a 2 × 2 Contingency Table: HPD or not HPD?," Biometrics, The International Biometric Society, vol. 64(4), pages 1293-1295, December.
    7. Minoda, Yuta & Yanagimoto, Takemi, 2009. "Estimation of a common slope in a gamma regression model with multiple strata: An empirical Bayes method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4178-4185, October.
    8. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    9. Maria Bekker-Nielsen Dunbar & Thomas J R Finnie & Barney Sloane & Ian M Hall, 2019. "Methods for calculating credible intervals for ratios of beta distributions with application to relative risks of death during the second plague pandemic," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-12, February.
    10. Shun-Fang Wang & Xue-Ren Wang, 2013. "Statistical inference of risk ratio in a correlated $$2 \times 2$$ table with structural zero," Computational Statistics, Springer, vol. 28(4), pages 1599-1615, August.
    11. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    12. Li, Huiqiong & Tian, Guoliang & Tang, Niansheng & Cao, Hongyuan, 2018. "Assessing non-inferiority for incomplete paired-data under non-ignorable missing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 69-81.
    13. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.
    14. Álvarez de Toledo, Pablo & Núñez, Fernando & Usabiaga, Carlos, 2020. "Matching in segmented labor markets: An analytical proposal based on high-dimensional contingency tables," Economic Modelling, Elsevier, vol. 93(C), pages 175-186.
    15. Luzia Gonçalves & M. Rosário de Oliveira & Cláudia Pascoal & Ana Pires, 2012. "Sample size for estimating a binomial proportion: comparison of different methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2453-2473, July.
    16. 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.
    17. Dickhaus Thorsten, 2015. "Simultaneous Bayesian analysis of contingency tables in genetic association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(4), pages 347-360, August.
    18. Xin Wang & Emily Berg & Zhengyuan Zhu & Dongchu Sun & Gabriel Demuth, 2018. "Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 509-528, December.
    19. Tuany Paula Castro & Carlos Daniel Paulino & Julio M. Singer, 2022. "A fair comparison of credible and confidence intervals: an example with binomial proportions," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 371-382, December.
    20. Reiczigel, Jeno & Abonyi-Tóth, Zsolt & Singer, Júlia, 2008. "An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5046-5053, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:36:y:2009:i:5:p:483-494. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.