Cited by 245Statistical Methods in Clinical TrialsStatistical Methods and Bayesian InferenceAdvanced Causal Inference Techniques

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Cluster randomized trials with a small number of clusters: which analyses should be used?

Leyrat, Clémence, Morgan, Katy E, Leurent, Baptiste, Kahan, Brennan C·2018·International Journal of Epidemiology

DOI 10.1093/ije/dyx169

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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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Self-citation
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Sarkodie, S. K., Wason, J. M. S., & Grayling, M. J. (2024) · Statistics in Medicine · doi:10.1002/sim.10205 · Cited by 1
“3,23 To some researchers, 40 clusters are inadequate to yield precise estimates of the ICC in the frequentist framework.”
Effects of the dyadic FirstStep2Health intervention on parents’ behaviour and anthropometric outcomes: a secondary analysis of a cluster randomised trial
Ling, J., Kao, T. A., Robbins, L. B., Kerver, J. M., Zhang, N., & Shi, Y. (2024) · BMJ Open · doi:10.1136/bmjopen-2023-081578 · Cited by 1
Improving lung cancer decision-making using a conversation tool (iDECIDE): a stepped wedge pragmatic clinical trial
Disher, N. G., Dieckmann, N. F., Case, J., Rubim, F., Eden, K., Golden, S. E., Matlock, D. D., Coleman, C. A., Lyons, K. S., Saha, S., et al. (2025) · Future Oncology · doi:10.1080/14796694.2025.2475733 · Cited by 1
A cash transfer plus gender transformative economic empowerment intervention seeking to improve the wellbeing of caregivers of children and adolescents living with HIV in South Africa: a feasibility study protocol for a pilot cluster randomized trial
Govindasamy, D., Shai, N., Mwandacha, N., Carries, S., Sithole, N., Closson, K., Bhana, A., Sigwadhi, L. N., Washington, L., Gibbs, A., et al. (2025) · Pilot and Feasibility Studies · doi:10.1186/s40814-025-01643-3 · Cited by 3
“To account for the small number of clusters, the Satterthwaite correction will be applied to adjust the degrees of freedom in the linear mixed-effects models [39].”
Causal inference in randomized trials with partial clustering
Nugent, J. R., Kakande, E. R., Chamie, G., Kabami, J., Owaraganise, A., Havlir, D. V., Kamya, M. R., & Balzer, L. B. (2025) · Clinical Trials · doi:10.1177/17407745251333779 · Cited by 1
“Finally, as expected, implementing TMLE without aggregating the influence curve estimates in clusters led to significantly higher Type I error and lower coverage than the approach we proposed above (Supplemental Appendix 4.5).”
Influential
Electronic Patient-Reported Outcome Measure and Decision Support Tool Option for Early Intervention Service Quality: A Pilot Cluster-Randomized Pragmatic Trial
Kaelin, V. C., Rizk, S., Chen, Y., Dooling-Litfin, J. K., Papautsky, E. L., Leland, N. E., Murphy, N. J., McManus, B. M., Lage, C. R., Villegas, V. C., et al. (2026) · Advances in Rehabilitation Science and Practice · doi:10.1177/27536351261445239 · Cited by 1
“The between-within approach was used to adjust for small cluster numbers, 71,72 with intracluster correlation coefficients (ICC) estimated at each cluster level.”
Doll therapy in residential dementia care in China: protocol for an exploratory pilot and feasibility mixed-methods cluster randomized controlled trial
Cui, Z., Guan, R. M., Xue, T., Sun, Y., Tan, M. P., Said, M. A., & Cao, Y. (2026) · Frontiers in Public Health · doi:10.3389/fpubh.2026.1842340 · Cited by 1
“…agitation and support emotional regulation, social interaction, and purposeful activity, but the evidence base remains limited by small samples, variable intervention protocols, inconsistent outcome selection, and incomplete reporting of implementation fidelity and ethical safeguards (10–12).”
Emergency department reorganisation introducing increased autonomy: A mixed effects approach to evaluate the effects of a national policy
Tipsmark, L. S., Obel, B., Andersson, T., & Søgaard, R. (2023) · PLoS ONE · doi:10.1371/journal.pone.0283325 · Cited by 1
“Since the present analyses comprise only 21 clusters, small sample correction was applied using the t-distribution rather than the normal distribution to construct confidence intervals [31].”
Method
Statistical analysis plan for cluster randomised trial to evaluate a community-level complementary food safety and hygiene and nutrition intervention in Mali: the MaaCiwara study
Quinn, L., Martín, J., Asamane, E. A., Manaseki‐Holland, S., Lilford, R. J., Traoré, L., Thompson, J., Watson, S., & Hemming, K. (2024) · Trials · doi:10.1186/s13063-024-08328-x · Cited by 1
“No small sample correction will be included for the primary outcome analysis as the number of clusters is sufficiently large to maintain the type I error rate [15].”
Background
Developing a streamlined risk-adjusted cesarean section rate model for evaluation of obstetrical quality across hospitals by using EHRs: A provincial-scale multicenter retrospective study
Zhou, D., Zhong, W., Sun, Q., Fu, Q. J., Liu, P., Zhong, S., Li, G., Luo, B., Chen, X., Wang, J., et al. (2024) · Digital Health · doi:10.1177/20552076241284726 · Cited by 1
Inclusion of unexposed clusters improves the precision of fixed effects analysis of stepped-wedge cluster randomized trials with binary and count outcomes
Lee, K. M., Yang, G. M., & Cheung, Y. B. (2024) · BMC Medical Research Methodology · doi:10.1186/s12874-024-02379-z · Cited by 1
“The original analysis of the SW-CRT [31] used a fixed effects model to account for cluster effects, control for cluster-level confounders, and address concerns over the robustness of applying the mixed effects model to a SW-CRT with such a small number of clusters [14, 15].”
BackgroundMethod
A cluster randomized controlled trial of the effectiveness of a Parents Plus group-based parenting program to promote healthy lifestyles among children and their families
O’Dwyer, C., Davis, B. Á., O’Connor, M., Keating, A., Sharry, J., Looney, K., McDarby, F., Doran, A., Murphy, E., & Carr, A. (2025) · Archives of Public Health · doi:10.1186/s13690-025-01555-x · Cited by 2
“This may increase the risk of bias due to baseline differences, and potentially decrease the precision of the trial outcomes [47, 48].”
RCPNEOPERU trial: a cluster randomized pilot trial to assess traditional neonatal resuscitation compared to partially virtual training in remote areas
Delgado, C., Pomar, E. M. G., Velásquez, P., Sánchez, V., Shimabuku, R., & Huicho, L. (2025) · Jornal de Pediatria · doi:10.1016/j.jped.2025.04.008 · Cited by 1
Design and Analysis of Randomized Trials to Estimate Spatio-Temporally Heterogeneous Treatment Effects
Watson, S., & Smith, T. A. (2025) · Journal of the American Statistical Association · doi:10.1080/01621459.2025.2527424 · Cited by 1
“Many of the issues that we have outlined, such as biases in standard error estimators or complex correlation structures are mirrored in the cluster trial literature (Leyrat et al. 2018; Li et al. 2021).”
Ignoring Clustering and Nesting in Cluster Randomized Trials Renders Conclusions Unverifiable [Response to Letter]
Siraneh, Y., Woldie, M. K., & Birhanu, Z. (2022) · Risk Management and Healthcare Policy · doi:10.2147/rmhp.s392171 · Cited by 1
“However, these analysis yield low power (<50% in some cases) when fewer than 20 clusters are randomized with failure to reach the expected 80% power.(9) We found that the generalized linear mixed”
Background
Phase Transition Unbiased Estimation in High Dimensional SettingsPreprint
Guerrier, S., Karemera, M., Orso, S., & Victoria‐Feser, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.11541
“…Setting II (n = 50, mi = m = 5,∀i) reflects a possibly more frequent situation, Setting I concerns the case where n is small (and much smaller than m), a situation frequently encountered in Cluster Randomised Trials (see e.g. Huang et al., 2016; Leyrat et al., 2017, and the references therein).”
Background
A General Approach for Simulation-based Bias Correction in High Dimensional SettingsPreprint
Guerrier, S., Karemera, M., Orso, S., Victoria‐Feser, M., & Zhang, Y. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.13687
“…simulation settings, with, in Setting I, a small number of clusters (m = 5) and a large number of measurements per cluster (ni = 50 ∀i), a situation that is frequently encountered in cluster randomized trials (see e.g. Huang et al., 2016; Leyrat et al., 2017, and the references therein).”
Background
Statistical Methods for the Design and Analysis of Infectious Disease Studies
Kennedy‐Shaffer, L. (2020) · Digital Access to Scholarship at Harvard (DASH) (Harvard University)
Frequentist inference for cluster randomised trials with multiple primary outcomesPreprint
Watson, S., Akinyemi, J. O., & Hemming, K. (2021) · arXiv (Cornell University)
A comparative study of R functions for clustered data analysis
Wang, W., & Harhay, M. O. (2021) · Trials · doi:10.1186/s13063-021-05900-7
“The simulation scenarios in [26] include ρ = 0.001, 0.01, and 0.05, and n c = 4, 6, 8, 10, 20, 30, 40, and 200.”
BackgroundMethodInfluential
Evaluating De‐Implementation Interventions
Goulão, B., Verkerk, E. W., Thavorn, K., Presseau, J., & Taljaard, M. (2023) · doi:10.1002/9781119862758.ch10
Managing high cardiovascular disease risk among adults in Argentina using a multicomponent strategy linking key aspects of care: A two-arm cluster-randomized clinical trial (PRIMECare) protocol
Abrahams‐Gessel, S., Beratarrechea, A. G., Irazola, V. E., Gulayin, P., Gutiérrez, L., Mahoney, M., & Gaziano, T. A. (2023) · Contemporary Clinical Trials · doi:10.1016/j.cct.2023.107357
Authors’ Reply: Ambiguity in Statistical Analysis Methods and Nonconformity With Prespecified Commitment to Data Sharing in a Cluster Randomized Controlled Trial
ARGUELLO, D. J. (2024) · Journal of Medical Internet Research · doi:10.2196/57422
“The method adjusts for df to account for hierarchical complexity of data, including potential nesting and variable or small cluster sizes [3].”
Influential
Energy Conservation Education Intervention for People with End-Stage Kidney Disease Receiving Haemodialysis (Everest): A Cluster Randomised Control TrialPreprint
Sharma, S., Alexander, K. E., Green, T., Wu, M., & Bonner, A. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4785750 · Cited by 1
SupporTive Care At Home Research (STAHR) for patients with advanced cancer: Protocol for a cluster non-randomized controlled trial
Lee, D., Lee, S. Y., Yoo, S. H., Kim, K. H., Kim, M., Shin, J., Hwang, I. Y., Hwang, I. G., Baek, S. K., Kim, D. Y., et al. (2024) · PLoS ONE · doi:10.1371/journal.pone.0302011
Robust analysis of stepped wedge trials using composite likelihood models
Voldal, E. C., Kenny, A., Xia, F., Heagerty, P. J., & Hughes, J. P. (2024) · Statistics in Medicine · doi:10.1002/sim.10120
Population-Averaged and Conditional Relative Risks and Risk Differences from Generalised Linear Mixed ModelsPreprint
Watson, S. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4872695
Effectiveness of a modified behavioural activation treatment training program for primary medical staff to manage depressive symptoms among rural elderly in Hunan Province, China: study protocol for a cluster randomised controlled trial
Qin, N., Luo, Y., Wang, S., Li, Y., Li, J., Luo, J., Zhou, J., Zhang, Q., Xie, J., & Cheng, A. S. K. (2024) · BMJ Open · doi:10.1136/bmjopen-2024-086489
“41 Sensitivity analyses will involve comparing the results from ITT analysis with those from Per-Protocol analysis.”
Method
Analysis methods for covariate-constrained cluster randomized trials with time-to-event outcomes
Crisp, A. M., Halloran, M. E., Hitchings, M. D. T., Longini, I. M., & Dean, N. E. (2025) · BMC Medical Research Methodology · doi:10.1186/s12874-025-02465-w
The Cancer Tracking System (CATSystem): Study protocol of a randomized control trial to evaluate a systems level intervention for cervical cancer screening, treatment, referral and follow up in Kenya
Maloba, M., Finocchario‐Kessler, S., Wexler, C., Staggs, V. S., Maosa, N., Babu, S., Goggin, K., Hutton, D. W., Ganda, G., Mabeya, H., et al. (2025) · PLoS ONE · doi:10.1371/journal.pone.0318941
Inference for the treatment effect in staircase designs with continuous outcomes: a simulation study
Darzi, E. R., Grantham, K. L., Forbes, A. B., & Kasza, J. (2025) · BMC Medical Research Methodology · doi:10.1186/s12874-025-02567-5 · Cited by 1
“The cluster randomised trials literature often highlights concerns about the validity of sample size calculations and data analysis when standard methods are employed in trials with a “small” number of clusters [1, 26–28].”
Properties of adaptive, cluster-randomised controlled trials with few clusters: a simulation study
Nolan, E., Dizon, J., Oldmeadow, C. J., Holliday, E., Hall, A. E., & Barker, D. (2025) · Implementation Science · doi:10.1186/s13012-025-01443-6
“[22] found that a modelling method that performed best to analyse results from small trials, and was recommended previously [23], still failed to converge up to 40% of the time.”
Cluster-Randomized Trials in Surgery
Gouveia, K., Bzovsky, S., & Sprague, S. (2025) · Springer eBooks · doi:10.1007/978-3-031-87083-5_15
IMPLICATIONS OF CLINICAL-BIOLOGICAL FACTORS IN THE TREATMENT PLANNING OF PATIENTS WITH EXTENSIVE PARTIAL EDENTULISM: TWO-STEP CLUSTER ANALYSIS
Siminiuc, P., Agop-Forna, D., Dascălu, C. G., & Forna, N. C. (2025) · Romanian Journal of Oral Rehabilitation · doi:10.62610/rjor.2025.1.17.74
Promoting Healthier Meal Selection and Intake Among Children in Restaurants: Protocol for a Cluster-Randomized Trial
Anzman‐Frasca, S., Tauriello, S., Epstein, L. H., Ferrante, M. J., Gampp, A., Goldsmith, J., Haines, J., Leone, L. A., & Paluch, R. A. (2025) · JMIR Research Protocols · doi:10.2196/73618
“With only 6 unique locations being randomized in our trial, small cluster size adjustments will be applied to any models with the random effect of restaurant location retained, to improve type I error rates [34].”
The Get to Know Me Board in the Neonatal Intensive Care Unit: A Mixed-Methods Study
Byerly, C. L., Lévy, S., Thurman, P., & Moscou-Jackson, G. (2025) · American Journal of Critical Care · doi:10.4037/ajcc2025728
Commentary: Impact of resistance training intensity on body composition and nutritional intake among college women with overweight and obesity: a cluster randomized controlled trial
Keller, J. L., Deemer, S. E., Tanna, G. L. D., Pals, S. L., Fontaine, K. R., & Allison, D. B. (2025) · Frontiers in Public Health · doi:10.3389/fpubh.2025.1653392
Cluster‐Level Analyses to Estimate a Risk Difference in a Cluster Randomized Trial With Confounding Individual‐Level Covariates: A Simulation Study
Macedo, J. A. P., Giraudeau, B., & collaborators, T. E. (2025) · Statistics in Medicine · doi:10.1002/sim.70341
“For each number of clusters per arm, we specified several mean cluster sizes as 𝑛 (except when 𝑘 = 40forwhichonlyonemeanclustersizewasspecified)following the Leyrat et al. systematic review [20].”
Effectiveness and cost-effectiveness of a peer-delivered, relational, harm reduction intervention to improve mental health, quality of life, and related outcomes, for people experiencing homelessness and substance use problems: protocol for the ‘SHARPS’ cluster randomised controlled trial
Parkes, T., Carver, H., Boyd, J., Cotton, S. C., Breeman, S., Cooper, D., Forrest, M., Foster, R., Hawthorn, J., Hunt, K., et al. (2025) · Trials · doi:10.1186/s13063-025-09364-x
“A small sample approximation will be applied to the degrees of freedom, given the number of clusters [76].”
Additional file 1 of The effectiveness of the Structured Health Intervention For Truckers (SHIFT): a cluster randomised controlled trial (RCT)
Clemes, S., Varela-Mato, V., Bodicoat, D. H., Brookes, C. L., Chen, Y.-L., Edwardson, C. L., Gray, L. J., Guest, A. J., Johnson, V., Munir, F., et al. (2022) · Figshare · doi:10.6084/m9.figshare.19844692
Additional file 2 of The impact of improved water supply on cholera and diarrhoeal diseases in Uvira, Democratic Republic of the Congo: a protocol for a pragmatic stepped-wedge cluster randomised trial and economic evaluation
Gallandat, K., Jeandron, A., Ross, I., Mufitini Saidi, J., Bashige Rumedeka, B., Lumami Kapepula, V., Cousens, S. N., Allen, E., MacDougall, A. M., & Cumming, O. (2021) · Figshare · doi:10.6084/m9.figshare.14820914
Additional file 2 of Analysing cluster randomised controlled trials using GLMM, GEE1, GEE2, and QIF: results from four case studies
Offorha, B. C., Walters, S. J., & Jacques, R. (2024) · Figshare · doi:10.6084/m9.figshare.26653278
Additional file 1 of A comparative study of R functions for clustered data analysis
Wang, W., & Harhay, M. O. (2021) · Figshare · doi:10.6084/m9.figshare.17696299
Additional file 1 of Multiple imputation by predictive mean matching in cluster-randomized trials
Bailey, B. E., Andridge, R., & Shoben, A. B. (2020) · Figshare · doi:10.6084/m9.figshare.12050496
Additional file 2 of Mind the gap: covariate constrained randomisation can protect against substantial power loss in parallel cluster randomised trials
Kristunas, C., Michael, G., Gray, L. J., & Hemming, K. (2022) · Figshare · doi:10.6084/m9.figshare.19588608
Additional file 1 of Mind the gap: covariate constrained randomisation can protect against substantial power loss in parallel cluster randomised trials
Kristunas, C., Grayling, M., Gray, L. J., & Hemming, K. (2022) · Figshare · doi:10.6084/m9.figshare.19588605
Additional file 2 of Multiple imputation by predictive mean matching in cluster-randomized trials
Bailey, B. E., Andridge, R., & Shoben, A. B. (2020) · Figshare · doi:10.6084/m9.figshare.12050505

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
ORCID: Leyrat, Clémence
Morgan, Katy E
Leurent, Baptiste
Kahan, Brennan C
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
DOI: 10.1093/ije/dyx169
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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Cluster randomized trials with a small number of clusters: which analyses should be used?

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