IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0272007.html
   My bibliography  Save this article

Accurate interval estimation for the risk difference in an incomplete correlated 2 × 2 table: Calf immunity analysis

Author

Listed:
  • Hezhi Lu
  • Fengjing Cai
  • Yuan Li
  • Xionghui Ou

Abstract

Interval estimation with accurate coverage for risk difference (RD) in a correlated 2 × 2 table with structural zero is a fundamental and important problem in biostatistics. The score test-based and Bayesian tail-based confidence intervals (CIs) have good coverage performance among the existing methods. However, as approximation approaches, they have coverage probabilities lower than the nominal confidence level for finite and moderate sample sizes. In this paper, we propose three new CIs for RD based on the fiducial, inferential model (IM) and modified IM (MIM) methods. The IM interval is proven to be valid. Moreover, simulation studies show that the CIs of fiducial and MIM methods can guarantee the preset coverage rate even for small sample sizes. More importantly, in terms of coverage probability and expected length, the MIM interval outperforms other intervals. Finally, a real example illustrates the application of the proposed methods.

Suggested Citation

  • Hezhi Lu & Fengjing Cai & Yuan Li & Xionghui Ou, 2022. "Accurate interval estimation for the risk difference in an incomplete correlated 2 × 2 table: Calf immunity analysis," PLOS ONE, Public Library of Science, vol. 17(7), pages 1-23, July.
    • Handle: RePEc:plo:pone00:0272007
    DOI: 10.1371/journal.pone.0272007
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0272007
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0272007&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0272007?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
    ---><---

    References listed on IDEAS

    as
    1. Lidong, E. & Hannig, Jan & Iyer, Hari, 2008. "Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 854-865, June.
    2. 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.
    3. 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.
    4. 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.
    5. Hari K. Iyer & C.M. Jack Wang & Thomas Mathew, 2004. "Models and Confidence Intervals for True Values in Interlaboratory Trials," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1060-1071, December.
    6. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    7. Nian-Sheng Tang & Man-Lai Tang, 2002. "Exact Unconditional Inference for Risk Ratio in a Correlated 2 × 2 Table with Structural Zero," Biometrics, The International Biometric Society, vol. 58(4), pages 972-980, December.
    8. Hezhi Lu & Hua Jin & Zhining Wang & Chao Chen & Ying Lu, 2019. "Prior-free probabilistic interval estimation for binomial proportion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 522-542, June.
    Full references (including those not matched with items on IDEAS)

    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. Randy C. S. Lai & Jan Hannig & Thomas C. M. Lee, 2015. "Generalized Fiducial Inference for Ultrahigh-Dimensional Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 760-772, June.
    2. Xuhua Liu & Xingzhong Xu, 2016. "Confidence distribution inferences in one-way random effects model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 59-74, March.
    3. Roy, Anindya & Bose, Arup, 2009. "Coverage of generalized confidence intervals," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1384-1397, August.
    4. David R. Bickel, 2024. "Bayesian and frequentist inference derived from the maximum entropy principle with applications to propagating uncertainty about statistical methods," Statistical Papers, Springer, vol. 65(8), pages 5389-5407, October.
    5. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    6. Arisa Jiratampradab & Jiraphan Suntornchost & Thidaporn Supapakorn, 2025. "Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model," Mathematics, MDPI, vol. 13(1), pages 1-11, January.
    7. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    8. 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.
    9. Wang, Xiaofei & Wang, Bing Xing & Hong, Yili & Jiang, Pei Hua, 2021. "Degradation data analysis based on gamma process with random effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1200-1208.
    10. Yixuan Zou & Jan Hannig & Derek S. Young, 2021. "Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    11. Piero Veronese & Eugenio Melilli, 2015. "Fiducial and Confidence Distributions for Real Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 471-484, June.
    12. Gunnar Taraldsen, 2011. "Analysis of rounded exponential data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 977-986, February.
    13. 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.
    14. Jiratampradab Arisa & Supapakorn Thidaporn & Suntornchost Jiraphan, 2022. "Comparison of confidence intervals for variance components in an unbalanced one-way random effects model," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 149-160, December.
    15. Tang, Man-Lai & Qiu, Shi-Fang & Poon, Wai-Yin, 2012. "Confidence interval construction for disease prevalence based on partial validation series," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1200-1220.
    16. 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.
    17. Russell J. Bowater, 2017. "A defence of subjective fiducial inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 177-197, April.
    18. Xiaoyang Ma & David P. MacKinnon & Thomas Mathew & Brian Agan & George Luta & Ionut Bebu, 2025. "Generalized Inference for Mediation Analysis," Mathematics, MDPI, vol. 13(3), pages 1-13, January.
    19. Yuliang Yin & Bingbing Wang, 2016. "The Agreement between the Generalized Value and Bayesian Evidence in the One-Sided Testing Problem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, May.
    20. Tang, Man-Lai & Poon, Wai-Yin & Ling, Leevan & Liao, Yijie & Chui, Hang-Wai, 2011. "Approximate unconditional test procedure for comparing two ordered multinomials," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 955-963, February.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0272007. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.