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Calculating power for the comparison of dependent κ‐coefficients

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  • Hung‐Mo Lin
  • John M. Williamson
  • Stuart R. Lipsitz

Abstract

Summary. In the psychosocial and medical sciences, some studies are designed to assess the agreement between different raters and/or different instruments. Often the same sample will be used to compare the agreement between two or more assessment methods for simplicity and to take advantage of the positive correlation of the ratings. Although sample size calculations have become an important element in the design of research projects, such methods for agreement studies are scarce. We adapt the generalized estimating equations approach for modelling dependent κ‐statistics to estimate the sample size that is required for dependent agreement studies. We calculate the power based on a Wald test for the equality of two dependent κ‐statistics. The Wald test statistic has a non‐central χ2‐distribution with non‐centrality parameter that can be estimated with minimal assumptions. The method proposed is useful for agreement studies with two raters and two instruments, and is easily extendable to multiple raters and multiple instruments. Furthermore, the method proposed allows for rater bias. Power calculations for binary ratings under various scenarios are presented. Analyses of two biomedical studies are used for illustration.

Suggested Citation

  • Hung‐Mo Lin & John M. Williamson & Stuart R. Lipsitz, 2003. "Calculating power for the comparison of dependent κ‐coefficients," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 391-404, October.
    • Handle: RePEc:bla:jorssc:v:52:y:2003:i:4:p:391-404
    DOI: 10.1111/1467-9876.00412
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    References listed on IDEAS

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    1. Huiman X. Barnhart & John M. Williamson, 2002. "Weighted Least-Squares Approach for Comparing Correlated Kappa," Biometrics, The International Biometric Society, vol. 58(4), pages 1012-1019, December.
    2. R. Gonin & S. R. Lipsitz & G. M. Fitzmaurice & G. Molenberghs, 2000. "Regression modelling of weighted κ by using generalized estimating equations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 1-18.
    3. Lipsitz, Stuart R. & Fitzmaurice, Garrett M. & Sleeper, Lynn & Zhao, L. P., 1996. "Estimating the joint distribution of repeated binary responses: Some small sample results," Computational Statistics & Data Analysis, Elsevier, vol. 23(2), pages 219-227, December.
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    Cited by:

    1. Miao-Yu Tsai, 2012. "Assessing inter- and intra-agreement for dependent binary data: a Bayesian hierarchical correlation approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 173-187, March.

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