Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method
Abstract
BACKGROUND: Cluster randomized trials are increasingly popular. In many of these trials, cluster sizes are unequal. This can affect trial power, but standard sample size formulae for these trials ignore this. Previous studies addressing this issue have mostly focused on continuous outcomes or methods that are sometimes difficult to use in practice. METHODS: We show how a simple formula can be used to judge the possible effect of unequal cluster sizes for various types of analyses and both continuous and binary outcomes. We explore the practical estimation of the coefficient of variation of cluster size required in this formula and demonstrate the formula's performance for a hypothetical but typical trial randomizing UK general practices. RESULTS: The simple formula provides a good estimate of sample size requirements for trials analysed using cluster-level analyses weighting by cluster size and a conservative estimate for other types of analyses. For trials randomizing UK general practices the coefficient of variation of cluster size depends on variation in practice list size, variation in incidence or prevalence of the medical condition under examination, and practice and patient recruitment strategies, and for many trials is expected to be approximately 0.65. Individual-level analyses can be noticeably more efficient than some cluster-level analyses in this context. CONCLUSIONS: When the coefficient of variation is <0.23, the effect of adjustment for variable cluster size on sample size is negligible. Most trials randomizing UK general practices and many other cluster randomized trials should account for variable cluster size in their sample size calculations.
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Assuming a mean cluster size of five patients per counselor, an intraclass correlation coefficient of 0.01, and a coefficient of variation of 0.30, 18 mental health counselors in each intervention arm and 90 participants per study arm are needed to detect a between-group difference on the GAD-7 with a medium effect size of d = 0.45, an alpha of 0.05 two-tailed, and a power of 0.80.
“Assuming a mean cluster size of five patients per counselor, an intraclass correlation coefficient of 0.01 [52] and a coefficient of variation of 0.30 [53], 18 mental health counselors in each intervention arm and 90 participants per study arm are needed to detect a between group difference on the GAD-7 with a medium effect size (d = 0.45) with an alpha of 0.05 (two-tailed) and a power of 0.80.”
From An Internet-based Acceptance and Commitment Therapy intervention for older adults with anxiety complaints: study protocol for a cluster randomized controlled trial. (2018) · cites this paper as [53]
The paper's section on estimating the coefficient of variation of cluster size supports using an estimated coefficient in cluster-trial sample-size calculations. It does not establish 0.30 for patients per mental health counselor; its illustrative general-practice trials had coefficients of 0.42–0.75. Citation [53] is attached to the 0.30 assumption, not to the sentence's GAD-7 sample-size result. (LLM, conf=0.82)
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References 29 · Cited by 529
Research works printed but not linked: 2
- Kerry SM, Bland JM. Sample size in cluster randomisation. BMJ 1998;316:549.
- Kerry SM, Bland JM. Unequal cluster sizes for trials in English and Welsh general practice: implications for sample size calculations. Stat Med 2001;20:377-90.
- Authors
- Eldridge, S. M., Ashby, D., & Kerry, S.
- Affiliations
- University of London (GB)
- Queen Mary University of London (GB)
- Corresponding author
- Eldridge, Sandra M
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2006-08-30
- Volume
- 35
- Issue
- 5
- Pages
- 1292-1300
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- OpenAlex
- W2153247789
- Cited by
- 529
- References
- 29
- Citations by year
- 2026: 27 · 2025: 41 · 2024: 28 · 2023: 31 · 2022: 41 · 2021: 29 · 2020: 44 · 2019: 36 · 2018: 42 · 2017: 35 · 2016: 29 · 2015: 24 · 2014: 25 · 2013: 24 · 2012: 28
- FWCI
- 4.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- sample size determination, unequal cluster sizes, individual-level analysis, binary outcomes, continuous outcomes, trial power
- MeSH terms
- Family Practice, Humans, Primary Health Care, Research Design, Cluster Analysis, Randomized Controlled Trials as Topic, Sample Size
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