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A general class of signed-rank tests for clustered data when the cluster size is potentially informative

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  • Somnath Datta
  • Jaakko Nevalainen
  • Hannu Oja

Abstract

Rank-based tests are alternatives to likelihood-based tests popularised by their relative robustness and underlying elegant mathematical theory. There has been a surge in research activities in this area in recent years since a number of researchers are working to develop and extend rank-based procedures to clustered-dependent data which include situations with known correlation structures (e.g. as in mixed effects models) as well as more general form of dependence. The purpose of this paper is to test the symmetry of a marginal distribution under clustered data. However, unlike most other papers in the area, we consider the possibility that the cluster size is a random variable whose distribution is dependent on the distribution of the variable of interest within a cluster. This situation typically arises when the clusters are defined in a natural way (e.g. not controlled by the experimenter or statistician) and in which the size of the cluster may carry information about the distribution of data values within a cluster. Under the scenario of an informative cluster size, attempts to use some form of variance-adjusted sign or signed-rank tests would fail since they would not maintain the correct size under the distribution of marginal symmetry. To overcome this difficulty, Datta and Satten [2008, ‘A Signed-Rank Test for Clustered Data’, Biometrics, 64, 501–507] proposed a Wilcoxon-type signed-rank test based on the principle of within-cluster resampling. In this paper, we study this problem in more generality by introducing a class of valid tests employing a general score function. Asymptotic null distribution of these tests is obtained. A simulation study shows that a more general choice of the score function can sometimes result in greater power than the Datta and Satten test; furthermore, this development offers the user a wider choice. We illustrate our tests using a real data example on spinal cord injury (SCI) patients.

Suggested Citation

  • Somnath Datta & Jaakko Nevalainen & Hannu Oja, 2012. "A general class of signed-rank tests for clustered data when the cluster size is potentially informative," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 797-808.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:797-808
    DOI: 10.1080/10485252.2012.672647
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    References listed on IDEAS

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    1. Datta, Somnath & Satten, Glen A., 2005. "Rank-Sum Tests for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 908-915, September.
    2. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    3. Werner, Carola & Brunner, Edgar, 2007. "Rank methods for the analysis of clustered data in diagnostic trials," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5041-5054, June.
    4. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
    5. Somnath Datta & Glen A. Satten, 2008. "A Signed-Rank Test for Clustered Data," Biometrics, The International Biometric Society, vol. 64(2), pages 501-507, June.
    6. Bernard Rosner & Robert J. Glynn & Mei-Ling Ting Lee, 2003. "Incorporation of Clustering Effects for the Wilcoxon Rank Sum Test: A Large-Sample Approach," Biometrics, The International Biometric Society, vol. 59(4), pages 1089-1098, December.
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    Cited by:

    1. Riina Lemponen & Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2012. "Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 977-991, December.
    2. Sandipan Dutta, 2022. "Robust Testing of Paired Outcomes Incorporating Covariate Effects in Clustered Data with Informative Cluster Size," Stats, MDPI, vol. 5(4), pages 1-13, December.
    3. Omer Ozturk & Asuman Turkmen, 2016. "Quantile inference based on clustered data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 867-893, October.

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