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Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical trials with random slopes


  • Heo, Moonseong
  • Xue, Xiaonan
  • Kim, Mimi Y.


In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:169-178
    DOI: 10.1016/j.csda.2012.11.016

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    References listed on IDEAS

    1. Spyros Konstantopoulos, 2009. "Incorporating Cost in Power Analysis for Three-Level Cluster-Randomized Designs," Evaluation Review, , vol. 33(4), pages 335-357, August.
    2. repec:aph:ajpbhl:10.2105/ajph.2009.160879_1 is not listed on IDEAS
    3. Anindya Roy & Dulal K. Bhaumik & Subhash Aryal & Robert D. Gibbons, 2007. "Sample Size Determination for Hierarchical Longitudinal Designs with Differential Attrition Rates," Biometrics, The International Biometric Society, vol. 63(3), pages 699-707, September.
    4. 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.
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    Cited by:

    1. 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.


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