IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i7p3719-3729.html
   My bibliography  Save this article

Testing the equality of proportions for correlated otolaryngologic data

Author

Listed:
  • Tang, Nian-Sheng
  • Tang, Man-Lai
  • Qiu, Shi-Fang

Abstract

In otolaryngologic (or ophthalmologic) studies, each subject usually contributes information for each of two ears (or eyes), and the values from the two ears (or eyes) are generally highly correlated. Statistical procedures that fail to take into account the correlation between responses from two ears could lead to incorrect results. On the other hand, asymptotic procedures that overlook small sample designs, sparse data structures, or the discrete nature of data could yield unacceptably high type I error rates even when the intraclass correlation is taken into consideration. In this article, we investigate eight procedures for testing the equality of proportions in such correlated data. These test procedures will be implemented via the asymptotic and approximate unconditional methods. Our empirical results show that tests based on the approximate unconditional method usually produce empirical type I error rates closer to the pre-chosen nominal level than their asymptotic tests. Amongst these, the approximate unconditional score test performs satisfactorily in general situations and is hence recommended. A data set from an otolaryngologic study is used to illustrate our proposed methods.

Suggested Citation

  • Tang, Nian-Sheng & Tang, Man-Lai & Qiu, Shi-Fang, 2008. "Testing the equality of proportions for correlated otolaryngologic data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3719-3729, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3719-3729
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(07)00483-5
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. 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.
    2. Michael P. Fay & Barry I. Graubard, 2001. "Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators," Biometrics, The International Biometric Society, vol. 57(4), pages 1198-1206, 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. Keyi Mou & Zhiming Li & Changxing Ma, 2023. "Asymptotic Sample Size for Common Test of Relative Risk Ratios in Stratified Bilateral Data," Mathematics, MDPI, vol. 11(19), pages 1-17, October.
    2. Xueqing Zhang & Changxing Ma, 2023. "Testing the Homogeneity of Differences between Two Proportions for Stratified Bilateral and Unilateral Data across Strata," Mathematics, MDPI, vol. 11(19), pages 1-17, October.
    3. Guogen Shan & Changxing Ma, 2014. "Efficient tests for one sample correlated binary data with applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 175-188, June.
    4. Guogen Shan, 2020. "Exact confidence limits for proportion difference in clinical trials with bilateral outcome," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 515-525, September.
    5. Huipei Wang & Chang-Xing Ma, 2024. "Homogeneity Test of Ratios of Two Proportions in Stratified Bilateral and Unilateral Data," Mathematics, MDPI, vol. 12(17), pages 1-16, August.
    6. Eleftheraki, Anastasia G. & Kateri, Maria & Ntzoufras, Ioannis, 2009. "Bayesian analysis of two dependent 22 contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2724-2732, May.
    7. Shuyi Liang & Kai-Tai Fang & Xin-Wei Huang & Yijing Xin & Chang-Xing Ma, 2024. "Homogeneity tests and interval estimations of risk differences for stratified bilateral and unilateral correlated data," Statistical Papers, Springer, vol. 65(6), pages 3499-3543, August.

    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. 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.
    2. Barry I. Graubard & Thomas R. Fears, 2005. "Standard Errors for Attributable Risk for Simple and Complex Sample Designs," Biometrics, The International Biometric Society, vol. 61(3), pages 847-855, September.
    3. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    4. Ji-Hyun Lee & Michael J Schell & Richard Roetzheim, 2009. "Analysis of Group Randomized Trials with Multiple Binary Endpoints and Small Number of Groups," PLOS ONE, Public Library of Science, vol. 4(10), pages 1-9, October.
    5. 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.
    6. Haiyan Wang & Michael Akritas, 2010. "Inference from heteroscedastic functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 149-168.
    7. Galea, Manuel & de Castro, Mário, 2017. "Robust inference in a linear functional model with replications using the t distribution," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 134-145.
    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. Hsiu-Ting Yu & Mark Rooij, 2013. "Model Selection for the Trend Vector Model," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 338-369, October.
    10. Masahiko Gosho & Hisashi Noma & Kazushi Maruo, 2021. "Practical Review and Comparison of Modified Covariance Estimators for Linear Mixed Models in Small‐sample Longitudinal Studies with Missing Data," International Statistical Review, International Statistical Institute, vol. 89(3), pages 550-572, December.
    11. 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.
    12. Bing Lu & John S. Preisser & Bahjat F. Qaqish & Chirayath Suchindran & Shrikant I. Bangdiwala & Mark Wolfson, 2007. "A Comparison of Two Bias-Corrected Covariance Estimators for Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 63(3), pages 935-941, September.
    13. Olli Saarela & David A. Stephens & Erica E. M. Moodie & Marina B. Klein, 2015. "On Bayesian estimation of marginal structural models," Biometrics, The International Biometric Society, vol. 71(2), pages 279-288, June.
    14. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2019. "Transformed statistics for tests of conditional independence in J×K×L contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 193-208.
    15. 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.
    16. Slawa Rokicki & Jessica Cohen & Gunther Fink & Joshua Salomon & Mary Beth Landrum, 2018. "Inference with difference-in-differences with a small number of groups: a review, simulation study and empirical application using SHARE data," CHaRMS Working Papers 18-01, Centre for HeAlth Research at the Management School (CHaRMS).
    17. Lloyd, Chris J., 2007. "Efficient and exact tests of the risk ratio in a correlated 2x2 table with structural zero," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3765-3775, May.
    18. Tang, Nian-Sheng & Jiang, Shao-Ping, 2011. "Testing equality of risk ratios in multiple 2x2 tables with structural zero," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1273-1284, March.
    19. Steven Teerenstra & Bing Lu & John S. Preisser & Theo van Achterberg & George F. Borm, 2010. "Sample Size Considerations for GEE Analyses of Three-Level Cluster Randomized Trials," Biometrics, The International Biometric Society, vol. 66(4), pages 1230-1237, December.
    20. 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.

    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:eee:csdana:v:52:y:2008:i:7:p:3719-3729. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.