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Power calculation for cross‐sectional stepped wedge cluster randomized trials with variable cluster sizes

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  • Linda J Harrison
  • Tom Chen
  • Rui Wang

Abstract

Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW‐CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under‐powered study. We investigate the relative efficiency of a SW‐CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model—a commonly used approach for analyzing data from cluster randomized trials. When cluster sizes vary, the power of a SW‐CRT depends on the order in which clusters receive the intervention, which is determined through randomization. We first derive a variance formula that corresponds to any particular realization of the randomized sequence and propose efficient algorithms to identify upper and lower bounds of the power. We then obtain an “expected” power based on a first‐order approximation to the variance formula, where the expectation is taken with respect to all possible randomization sequences. Finally, we provide a variance formula for more general settings where only the cluster size arithmetic mean and coefficient of variation, instead of exact cluster sizes, are known in the design stage. We evaluate our methods through simulations and illustrate that the average power of a SW‐CRT decreases as the variation in cluster sizes increases, and the impact is largest when the number of clusters is small.

Suggested Citation

  • Linda J Harrison & Tom Chen & Rui Wang, 2020. "Power calculation for cross‐sectional stepped wedge cluster randomized trials with variable cluster sizes," Biometrics, The International Biometric Society, vol. 76(3), pages 951-962, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:951-962
    DOI: 10.1111/biom.13164
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    References listed on IDEAS

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    1. Rhoda, D.A. & Murray, D.M. & Andridge, R.R. & Pennell, M.L. & Hade, E.M., 2011. "Studies with staggered starts: Multiple baseline designs and group-randomized trials," American Journal of Public Health, American Public Health Association, vol. 101(11), pages 2164-2169.
    2. Fan Li & Elizabeth L. Turner & John S. Preisser, 2018. "Sample size determination for GEE analyses of stepped wedge cluster randomized trials," Biometrics, The International Biometric Society, vol. 74(4), pages 1450-1458, December.
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