IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i8p1792-1812.html
   My bibliography  Save this article

Comparison of three-level cluster randomized trials using quantile dispersion graphs

Author

Listed:
  • S.P. Singh
  • S. Mukhopadhyay
  • A. Roy

Abstract

The purpose of this article is to evaluate and compare several three-level cluster randomized designs on the basis of their power functions. The power function of cluster designs depends on the intracluster correlations (ICCs), which are generally unknown at the planning stage. Thus, to compare these designs a prior knowledge of the ICCs is required. Three interval estimation methods are proposed for assigning joint confidence intervals to the two ICCs (corresponding to each cluster level). A detailed simulation study comparing the confidence intervals attained by the different techniques is given. The technique of quantile dispersion graphs is used for comparing the three-level cluster designs. For a given design, quantiles of the power function, are obtained for various effect sizes. These quantiles are functions of the unknown ICC coefficients. To address the dependence of the quantiles on the correlations, a confidence region is computed, and used as a parameter space. A three-level nested data set collected by the University of Michigan to study various school reforms on the achievements of students is used to illustrate the proposed methodology.

Suggested Citation

  • S.P. Singh & S. Mukhopadhyay & A. Roy, 2015. "Comparison of three-level cluster randomized trials using quantile dispersion graphs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1792-1812, August.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:8:p:1792-1812
    DOI: 10.1080/02664763.2015.1010491
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1010491
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1010491?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. S. Mukhopadhyay & S. W. Looney, 2009. "Quantile dispersion graphs to compare the efficiencies of cluster randomized designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1293-1305.
    2. Khuri, AndreI. & Lee, Juneyoung, 1998. "A graphical approach for evaluating and comparing designs for nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 27(4), pages 433-443, June.
    3. 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.
    4. Byoung Cheol Jung & André Khuri & Juneyoung Lee, 2008. "Comparison of designs for the three-fold nested random model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(6), pages 701-715.
    5. Moonseong Heo & Andrew C. Leon, 2008. "Statistical Power and Sample Size Requirements for Three Level Hierarchical Cluster Randomized Trials," Biometrics, The International Biometric Society, vol. 64(4), pages 1256-1262, December.
    6. Robinson, Kevin S. & Khuri, Andre I., 2003. "Quantile dispersion graphs for evaluating and comparing designs for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 47-62, May.
    7. A. I. Khuri, 1997. "Quantile dispersion graphs for analysis of variance estimates of variance components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 711-722.
    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. S. Mukhopadhyay & S. W. Looney, 2009. "Quantile dispersion graphs to compare the efficiencies of cluster randomized designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1293-1305.
    2. Kendra Davis‐Plourde & Monica Taljaard & Fan Li, 2023. "Sample size considerations for stepped wedge designs with subclusters," Biometrics, The International Biometric Society, vol. 79(1), pages 98-112, March.
    3. Kari Tokola & Andreas Lundell & Jaakko Nevalainen & Hannu Oja, 2014. "Design and cost optimization for hierarchical data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(2), pages 130-148, May.
    4. Anup Amatya & Dulal K. Bhaumik, 2018. "Sample size determination for multilevel hierarchical designs using generalized linear mixed models," Biometrics, The International Biometric Society, vol. 74(2), pages 673-684, June.
    5. Kadri Ulas Akay, 2014. "A graphical evaluation of logistic ridge estimator in mixture experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1217-1232, June.
    6. Juneyoung Lee & Andre Khuri, 1999. "Graphical technique for comparing designs for random models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 933-947.
    7. Mirjam Moerbeek & Maryam Safarkhani, 2018. "The Design of Cluster Randomized Trials With Random Cross-Classifications," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 159-181, April.
    8. Loeza-Serrano, S. & Donev, A.N., 2014. "Construction of experimental designs for estimating variance components," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1168-1177.
    9. Jia Liu & Zhan Zhao & Yongmin Mu & Xiaoping Zou & Dechun Zou & Jingbo Zhang & Shuo Chen & Lixin Tao & Xiuhua Guo, 2018. "Gender Differences in the Association between Serum Uric Acid and Prediabetes: A Six-Year Longitudinal Cohort Study," IJERPH, MDPI, vol. 15(7), pages 1-10, July.
    10. Heo, Moonseong & Xue, Xiaonan & Kim, Mimi Y., 2013. "Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical trials with random slopes," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 169-178.
    11. Tokola, K. & Larocque, D. & Nevalainen, J. & Oja, H., 2011. "Power, sample size and sampling costs for clustered data," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 852-860, July.
    12. Satoshi Usami, 2017. "Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 133-157, March.
    13. Robinson, Kevin S. & Khuri, Andre I., 2003. "Quantile dispersion graphs for evaluating and comparing designs for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 47-62, May.
    14. 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.
    15. Jamie Perin & John S. Preisser, 2017. "Alternating logistic regressions with improved finite sample properties," Biometrics, The International Biometric Society, vol. 73(2), pages 696-705, June.

    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:taf:japsta:v:42:y:2015:i:8:p:1792-1812. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.