Cluster randomized trials with a small number of clusters: which analyses should be used?
Abstract
Background: Cluster randomized trials (CRTs) are increasingly used to assess the effectiveness of health interventions. Three main analysis approaches are: cluster-level analyses, mixed-models and generalized estimating equations (GEEs). Mixed models and GEEs can lead to inflated type I error rates with a small number of clusters, and numerous small-sample corrections have been proposed to circumvent this problem. However, the impact of these methods on power is still unclear. Methods: We performed a simulation study to assess the performance of 12 analysis approaches for CRTs with a continuous outcome and 40 or fewer clusters. These included weighted and unweighted cluster-level analyses, mixed-effects models with different degree-of-freedom corrections, and GEEs with and without a small-sample correction. We assessed these approaches across different values of the intraclass correlation coefficient (ICC), numbers of clusters and variability in cluster sizes. Results: Unweighted and variance-weighted cluster-level analysis, mixed models with degree-of-freedom corrections, and GEE with a small-sample correction all maintained the type I error rate at or below 5% across most scenarios, whereas uncorrected approaches lead to inflated type I error rates. However, these analyses had low power (below 50% in some scenarios) when fewer than 20 clusters were randomized, with none reaching the expected 80% power. Conclusions: Small-sample corrections or variance-weighted cluster-level analyses are recommended for the analysis of continuous outcomes in CRTs with a small number of clusters. The use of these corrections should be incorporated into the sample size calculation to prevent studies from being underpowered.
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The empirical performance of some methods for generalized linear mixed models in terms of confidence interval coverage, type I error rates, and accuracy of standard error estimates has not been reported thoroughly, especially for cRCTs with a small number of clusters per condition.
“However, the empirical performance of some of those methods in terms of confidence interval coverage, type I error rates, and accuracy of standard error estimates has not been reported thoroughly, especially for cRCTs with a small number of clusters per condition [7, 8, 13].”
To mitigate the risk of inflating Type I error given the small number of clusters, the study will use the Kenward-Roger degrees of freedom correction.
“To mitigate the risk of inflating Type I error given the small number of clusters, we will use the Kenward-Roger degrees of freedom correction, which does not rely on the assumption of fixed cluster sizes [83].”
It was common for cluster RCTs to have too few clusters to achieve balance between intervention and control groups, and in some it was unclear whether clustering was adequately dealt with in the analysis.
“It was common for cluster RCTs to have too few clusters to achieve balance between intervention and control groups and in some it was unclear whether clustering was adequately dealt with in the analysis85.”
From A systematic review and meta-analysis of effects of early life non-cognitive skills on academic, psychosocial, cognitive and health outcomes (2018) · cites this paper as [85]
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- Authors
- Leyrat, C., Morgan, K. E., Leurent, B., & Kahan, B. C.
- Affiliations
- Inserm (FR)
- London School of Hygiene & Tropical Medicine (GB)
- Queen Mary University of London (GB)
- Corresponding author
- Leyrat, Clémence
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2017-08-23
- Volume
- 47
- Issue
- 1
- Pages
- 321-331
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- OpenAlex
- W2746185216
- Cited by
- 244
- References
- 31
- Citations by year
- 2026: 34 · 2025: 33 · 2024: 34 · 2023: 32 · 2022: 39 · 2021: 30 · 2020: 21 · 2019: 17 · 2018: 4
- FWCI
- 8.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- LSHTM Research Online (London School of Hygiene and Tropical Medicine) (acceptedVersion)
- Queen Mary Research Online (Queen Mary University of London) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- small number of clusters, type I error rate, statistical power, small sample correction, mixed models, generalized estimating equations, intraclass correlation coefficient, sample size determination, continuous outcomes
- MeSH terms
- Analysis of Variance, Computer Simulation, Data Interpretation, Statistical, Humans, Models, Statistical, Cluster Analysis, Randomized Controlled Trials as Topic, Sample Size
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