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Testing the equality of proportions for correlated otolaryngologic data

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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