IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i2p24-421d800597.html
   My bibliography  Save this article

Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data

Author

Listed:
  • Dewi Rahardja

    (Department of Defense, Fort Meade, MD 20755, USA
    Disclaimer Statement: This research represents the author’s own work and opinion. It does not reflect any policy nor represent the official position of the U.S. Department of Defense nor any other U.S. Federal Agency.)

Abstract

Previously, Rahardja (2020) paper (in the first reference list) developed a (pairwise) multiple comparison procedure (MCP) to determine which (proportions) pairs of Multiple Binomial Proportions (with under-reported data), the significant differences came from. Generally, such an MCP test (developed by Rahardja, 2020) is the second part of a two-stage sequential test. In this paper, we derived two omnibus tests (i.e., the overall equality of multiple proportions test) as the first part of the above two-stage sequential test (with under-reported data), in general. Using two likelihood-based approaches, we acquire two Wald-type (Omnibus) tests to compare Multiple Binomial Proportions (in the presence of under-reported data). Our closed-form algorithm is easy to implement and not computationally burdensome. We applied our algorithm to a vehicle-accident data example.

Suggested Citation

  • Dewi Rahardja, 2022. "Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data," Stats, MDPI, vol. 5(2), pages 1-14, April.
  • Handle: RePEc:gam:jstats:v:5:y:2022:i:2:p:24-421:d:800597
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/5/2/24/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2571-905X/5/2/24/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gordon J. Prescott & Paul H. Garthwaite, 2002. "A Simple Bayesian Analysis of Misclassified Binary Data with a Validation Substudy," Biometrics, The International Biometric Society, vol. 58(2), pages 454-458, June.
    2. Dewi Rahardja, 2019. "Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample," Stats, MDPI, vol. 2(1), pages 1-10, February.
    3. Dewi Rahardja, 2020. "Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data," Stats, MDPI, vol. 3(1), pages 1-12, March.
    4. Mary J. Morrissey & Donna Spiegelman, 1999. "Matrix Methods for Estimating Odds Ratios with Misclassified Exposure Data: Extensions and Comparisons," Biometrics, The International Biometric Society, vol. 55(2), pages 338-344, June.
    5. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
    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. Dewi Rahardja, 2019. "Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample," Stats, MDPI, vol. 2(1), pages 1-10, February.
    2. Stamey, James & Gerlach, Richard, 2007. "Bayesian sample size determination for case-control studies with misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2982-2992, March.
    3. Al-Kandari Noriah M. & Lahiri Partha, 2016. "Prediction of a Function of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    4. 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.
    5. Grace Y. Yi & Wenqing He, 2017. "Analysis of case-control data with interacting misclassified covariates," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-16, December.
    6. Gordon J. Prescott & Paul H. Garthwaite, 2002. "A Simple Bayesian Analysis of Misclassified Binary Data with a Validation Substudy," Biometrics, The International Biometric Society, vol. 58(2), pages 454-458, June.
    7. Robert H. Lyles, 2002. "A Note on Estimating Crude Odds Ratios in Case–Control Studies with Differentially Misclassified Exposure," Biometrics, The International Biometric Society, vol. 58(4), pages 1034-1036, December.
    8. Eirini-Christina Saloniki & Amanda Gosling, 2012. "Point identification in the presence of measurement error in discrete variables: application - wages and disability," Studies in Economics 1214, School of Economics, University of Kent.
    9. Briceön Wiley & Chris Elrod & Phil D. Young & Dean M. Young, 2021. "An integrated‐likelihood‐ratio confidence interval for a proportion based on underreported and infallible data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 290-298, August.
    10. Noriah M. Al-Kandari & Partha Lahiri, 2016. "Prediction Of A Function Of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    11. Stamey, James D. & Boese, Doyle H. & Young, Dean M., 2008. "Confidence intervals for parameters of two diagnostic tests in the absence of a gold standard," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1335-1346, January.
    12. Mohammad Ehsanul Karim & Paul Gustafson, 2016. "Hypothesis Testing for an Exposure–Disease Association in Case–Control Studies Under Nondifferential Exposure Misclassification in the Presence of Validation Data: Bayesian and Frequentist Adjustments," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 234-252, October.
    13. Rahardja, Dewi & Young, Dean M., 2010. "Credible sets for risk ratios in over-reported two-sample binomial data using the double-sampling scheme," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1281-1287, May.
    14. Robert H. Lyles & John M. Williamson & Hung-Mo Lin & Charles M. Heilig, 2005. "Extending McNemar's Test: Estimation and Inference When Paired Binary Outcome Data Are Misclassified," Biometrics, The International Biometric Society, vol. 61(1), pages 287-294, March.
    15. Marian Reiff & Erik Šoltés & Silvia Komara & Tatiana Šoltésová & Silvia Zelinová, 2022. "Segmentation and estimation of claim severity in motor third-party liability insurance through contrast analysis," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 17(3), pages 803-842, September.
    16. Dewi Rahardja & Ying Yang, 2015. "Maximum likelihood estimation of a binomial proportion using one-sample misclassified binary data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 272-280, August.
    17. Helmut Küchenhoff & Samuel M. Mwalili & Emmanuel Lesaffre, 2006. "A General Method for Dealing with Misclassification in Regression: The Misclassification SIMEX," Biometrics, The International Biometric Society, vol. 62(1), pages 85-96, March.
    18. Christina A. Holcroft & Donna Spiegelman, 1999. "Design of Validation Studies for Estimating the Odds Ratio of Exposure–Disease Relationships When Exposure Is Misclassified," Biometrics, The International Biometric Society, vol. 55(4), pages 1193-1201, December.
    19. Paul S. Albert & Aiyi Liu & Tonja Nansel, 2014. "Efficient logistic regression designs under an imperfect population identifier," Biometrics, The International Biometric Society, vol. 70(1), pages 175-184, March.
    20. Rahardja, Dewi & Young, Dean M., 2011. "Likelihood-based confidence intervals for the risk ratio using double sampling with over-reported binary data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 813-823, January.

    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:gam:jstats:v:5:y:2022:i:2:p:24-421:d:800597. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.