Science Journal of Applied Mathematics and Statistics

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An Approach of Power Estimation for Linear Mixed Models for Clinical Studies

Received: 10 April 2016    Accepted:     Published: 11 April 2016
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Abstract

This study aims to demonstrate a practical way of power estimation for linear mixed models in clinical studies. Approximation methods using z and t statistics are discussed and compared to the simulated results. It was found that the approximation methods generally provide a slight overestimation of power, relative to simulated results using the Kenward and Roger estimation of degree of freedom. However, results of approximation methods can be informative in certain scenarios. In conclusion, the z approximation and t approximation with a residual degree of freedom can be useful in certain situations. Simulation method can serve as a general solution.

DOI 10.11648/j.sjams.20160402.17
Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 2, April 2016)
Page(s) 59-63
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Power, Sample Size, Linear Mixed Model, Clinical Studies

References
[1] N. Laird and J. Ware. Random-effects models for longitudinal data. Biometrics. 38(4), pp 963-974, Dec 1982.
[2] A. Khuri. Linear Model Methodology. Taylor & Francis Group, 2010.
[3] A. Rencher and G. Schaalje. Linear Models in Statistics, 2nd Edition. John Wiley & Sons, Inc., Hoboken, New Jersey. 2008.
[4] C. McCulloch and S. Searle. Generalized, linear, and mixed models. John Wiley & Sons, Inc. 2001.
[5] G. Schaalje, J. McBride and G. Fellingham. Adequacy of Approximations to Distributions of Test Statistics in Complex Mixed Linear Models Journal of Agricultural, Biological, and Environmental Statistics Vol. 7, No. 4, pp 512-524, 2002.
[6] G. Liu and K. Liang. Sample Size Calculations for Studies with Correlated Observations. Biometrics Vol. 53, No. 3, pp 937-947, 1997.
[7] M. Kenward and J. Roger. Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood. Biometrics, Vol. 53, pp 983-997, 1997.
[8] S. Julious. Sample sizes for clinical trials with normal data. Stat Med. 23(12), pp 1921-1986. 2004.
[9] J. Lachin. Introduction to sample size determination and power analysis for clinical trials. Control Clin Trials. 2(2), pp 93-113, 1981.
[10] E. Vierron and B. Giraudeau. Sample size calculation for multicenter randomized trial: taking the center effect into account. Contemp Clin Trials. 28(4), pp 451-458, 2007.
[11] M. Heo, Y. Kim, X. Xue and M. Kim. Sample size requirement to detect an intervention effect at the end of follow-up in a longitudinal cluster randomized trial. Stat Med. 29(3), pp 382-390, Feb 2010.
[12] M. Kain, B. Bolker and M. McCoy. A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects. PeerJ. 3:e1226, Sep 2015.
[13] M. Candel and G. van Breukelen. Sample size calculation for treatment effects in randomized trials with fixed cluster sizes and heterogeneous intraclass correlations and variances. Stat Methods Med Res. 24(5), pp 557-573, Oct 2015.
[14] K. Lu, D. Mehrotra, G. Liu. Sample size determination for constrained longitudinal data analysis. Stat Med. 28(4), pp 679-699, 2009.
[15] S. Self and R. Mauritsen. Power/Sample Size Calculations for Generalized Linear Models Biometrics Vol. 44, No. 1, pp 79-86, 1988.
[16] Q. Dang, S. Mazumdar and P. Houckc. Sample Size and Power Calculations Based on Generalized Linear Mixed Models with Correlated Binary Outcomes. Comput Methods Programs Biomed. 91(2), pp 122–127, 2008.
[17] J. Chen, S. Stock and C. Deng. Sample Size Estimation Through Simulation of a Random Coefficient Model by Using SAS. PharmaSUG. 2008.
[18] T. Cook and D. DeMets. Introduction to Statistical Methods for Clinical Trials. Chapman and Hall/CRC, 2007.
[19] S. Chow, J. Shao and H. Wang. Sample Size Calculations in Clinical Research. CRC, 2003.
[20] F. Satterthwaite. An Approximate Distribution of Estimates of Variance Components. Biometrics Bulletin, Vol. 2, pp 110-114, 1946.
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    Weijia Feng. (2016). An Approach of Power Estimation for Linear Mixed Models for Clinical Studies. Science Journal of Applied Mathematics and Statistics, 4(2), 59-63. https://doi.org/10.11648/j.sjams.20160402.17

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    ACS Style

    Weijia Feng. An Approach of Power Estimation for Linear Mixed Models for Clinical Studies. Sci. J. Appl. Math. Stat. 2016, 4(2), 59-63. doi: 10.11648/j.sjams.20160402.17

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    AMA Style

    Weijia Feng. An Approach of Power Estimation for Linear Mixed Models for Clinical Studies. Sci J Appl Math Stat. 2016;4(2):59-63. doi: 10.11648/j.sjams.20160402.17

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  • @article{10.11648/j.sjams.20160402.17,
      author = {Weijia Feng},
      title = {An Approach of Power Estimation for Linear Mixed Models for Clinical Studies},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {2},
      pages = {59-63},
      doi = {10.11648/j.sjams.20160402.17},
      url = {https://doi.org/10.11648/j.sjams.20160402.17},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20160402.17},
      abstract = {This study aims to demonstrate a practical way of power estimation for linear mixed models in clinical studies. Approximation methods using z and t statistics are discussed and compared to the simulated results. It was found that the approximation methods generally provide a slight overestimation of power, relative to simulated results using the Kenward and Roger estimation of degree of freedom. However, results of approximation methods can be informative in certain scenarios. In conclusion, the z approximation and t approximation with a residual degree of freedom can be useful in certain situations. Simulation method can serve as a general solution.},
     year = {2016}
    }
    

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    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - This study aims to demonstrate a practical way of power estimation for linear mixed models in clinical studies. Approximation methods using z and t statistics are discussed and compared to the simulated results. It was found that the approximation methods generally provide a slight overestimation of power, relative to simulated results using the Kenward and Roger estimation of degree of freedom. However, results of approximation methods can be informative in certain scenarios. In conclusion, the z approximation and t approximation with a residual degree of freedom can be useful in certain situations. Simulation method can serve as a general solution.
    VL  - 4
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