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What is a clusterrandomised trial?
In a traditional randomised controlled trial (RCT), it is the individual patient that is allocated to an intervention or control group, and standard statistical analyses on participant outcomes are used to evaluate if the intervention was effective. The analyses conducted in an RCT are based on the assumption that all participants are completely independent (i.e. unlike each other, do not influence each other, and any outcomes measured on them are influenced by the intervention or usual care in the same way). In an RCT where the intervention is a drug this is quite straightforward to achieve. In some trials, however, interventions are not randomised to individuals but to intact groups, clusters or communities, either by choice or necessity. The clusters might be families, schools, factories, villages, cities, arbitrary geographical areas or some other predefined group. For generality we shall refer to all these types of studies as clusterrandomised trials (CRT).
Why would you want to do a cluster randomised trial?
In some studies, randomization at the individual patient level may not be feasible because the intervention is designed to be implemented at the group level or because the hypothesized mechanism of action of the intervention operates at the group level. For example, in trials of infectious disease interventions, treatment may be administered at the individual level but its effects observed among those in the wider community.^{1 }Randomisation at the individual level may also be undesirable for methodological reasons such as the need to avoid contamination, (for example, in trials of behavioural interventions), when individuals that may be in close proximity are randomised to competing interventions.^{2, 3} Finally, randomizing individuals may complicate the trial organization and implementation, for example, in a lowincome country setting special equipment, personnel, or permission from a senior political figure may need to be obtained in order to conduct the trial.^{4} The interventions may be delivered to the entire randomised group as a unit, or to individuals within each group, but all members of a group receive the same intervention; outcomes are then observed on individual cluster members (or subsamples of members) to evaluate the effect of the intervention.
How should clusters be randomised in a CRT?
Ideally potential participants should be identified before the randomisation of clusters begins. If this is not possible then an independent recruiter that is blinded to the allocation should be used. When randomising by cluster, (especially if there are only a small number of clusters), there is likely to be an imbalance in clusterlevel characteristics for intervention group comparisons. This can be prevented by matching or stratifying of clusters according to selected factors. Matching by baseline factors such as cluster size and geographic area is a common strategy in a CRT that intends to randomise a relatively small number of clusters. In stratified randomization, recruited clusters are assigned to groups according to clusterlevel characteristics that are thought to affect individual outcomes. Clusters are then randomised within strata to ensure a more even distribution of clusterlevel characteristics between intervention and control groups. By systematically randomizing within relatively homogeneous strata, the amount of variation within the sample is reduced, making inferential statistical testing more efficient.^{5}
What effect does clustering have on the sample size in a CRT?
In general, individuals within the same cluster tend to be more similar than individuals in a different cluster. As a consequence of this the information provided by a cluster randomised trial of a certain sample size is less than an individually randomised trial of the same sample size and so is less efficient from a statistical viewpoint. The key issue is that the sample size needs to take into account the correlation of individuals within a cluster. The intracluster correlation coefficient (ICC) is a statistical measure of the interdependence within each cluster and is calculated by dividing the variance between clusters by total variance, where total variance is the sum of between cluster variation and within cluster variation.^{6} The ICC is used to calculate a multiplying factor that is then applied to the usual sample size calculation, (that has been estimated assuming independence), in order to account for the clustering. This multiplying factor is known as the design effect (DE) and is essentially a ratio of the total number of subjects required using cluster randomisation to the number required using individual randomisation. The calculation of the DE is based on the ICC and the average cluster size.^{7} The DE needs to be estimated for all outcome variables to ensure that sample size is adequate for these outcomes. The ICC can usually be estimated from the available data using standard statistical methods, although the publication of estimates of ICCs from previous similar research can be used in sample size calculations.^{8 } In general, it is statistically more efficient to increase the number of clusters rather than increase the number of people within each cluster.^{9}
How should we analyse a CRT?
The key principle in the analysis of a CRT is that the analyses must take account of the correlation between individuals within a cluster. Failure to take account of the clustering of individuals in the analysis will underestimate the variability in the data and produce artificially narrow confidence intervals that can increase the chance of obtaining spuriously statistically significant results. A simple approach is to construct a summary statistic for each cluster and then analyse these summary values.^{10} However, this type of analysis is limited as it does not allow adjustment for other covariates and it also reduces the data set to the size of the number of clusters. Alternatively, statistical methods now exist that allow analysis at the level of the individual while accounting for the clustering in the data. These types of analyses can handle continuous, binary or categorical outcome at the individual level whilst simultaneously accounting for the clustering and are available in many standard statistical software packages.^{11}
Summary
When a researcher wishes to decide between designing an individual patient randomised trial or a CRT then the choice should be based on 3 key issues: 1) is the intervention a nondrug intervention such as an educational or behavioural intervention; 2) can the intervention only be delivered at the group level; 3) is there a risk of contamination when delivering the intervention. As is the case with an individually randomised trial, in order to detect moderate treatment effects reliably, researchers should aim to minimise bias and random error by ensuring that: a) the sample size is large enough to detect a clinically meaningful effect size; b) adequate randomisation is performed that ensure balance at baseline between the intervention groups being compared; c) there is blinding (also known as masking) of participants to the allocated intervention (and if this is not possible, as in many CRTs, then objective outcome assessments should be used); and d) intention to treat analyses are used by including all patients as randomised whether or not they received or completed the allocated intervention or not.^{12} CRTs are becoming more common in global health research and are potentially very useful. This short introduction should serve as a primer when a researcher is considering designing a CRT.
Derrick Bennett
Clinical Trial Service Unit and Epidemiological Studies Unit
Richard Doll Building, Old Road Campus, University of Oxford, OX3 7LF
References
1. Ayles HM, Sismanidis C, Beyers N, Hayes RJ, GodfreyFaussett P. ZAMSTAR, The Zambia South Africa TB and HIV Reduction Study: design of a 2 x 2 factorial community randomised trial. Trials 2008; 9:63.
2. COMMIT Research Group. Community intervention trial for smoking cessation (COMMIT): II. Changes in adult cigarette smoking prevalence. Am J Public Health 1995; 85(2):193200.
3. COMMIT Research Group. Community Intervention Trial for Smoking Cessation (COMMIT): I. cohort results from a fouryear community intervention. Am J Public Health 1995; 85(2):18392.
4. Hayes R, Mosha F, Nicoll A et al. A community trial of the impact of improved sexually transmitted disease treatment on the HIV epidemic in rural Tanzania: 1. Design. AIDS 1995; 9(8):91926.
5. Hahn S, Puffer S, Torgerson DJ, Watson J. Methodological bias in cluster randomised trials. BMC Med Res Methodol 2005; 5:10.
6. Kerry SM, Bland JM. The intracluster correlation coefficient in cluster randomisation. BMJ 1998; 316(7142):1455.
7. Kerry SM, Bland JM. Sample size in cluster randomisation. BMJ 1998; 316(7130):549.
8. Campbell MK, Elbourne DR, Altman DG. CONSORT statement: extension to cluster randomised trials. BMJ 2004; 328(7441):7028.
9. Hayes RJ, Bennett S. Simple sample size calculation for clusterrandomised trials. Int J Epidemiol 1999; 28(2):31926.
10. Kerry SM, Bland JM. Analysis of a trial randomised in clusters. BMJ 1998; 316(7124):54.
11. Mollison J, Simpson JA, Campbell MK, Grimshaw JM. Comparison of analytical methods for cluster randomised trials: an example from a primary care setting. J Epidemiol Biostat 2000; 5(6):33948.
12. Giraudeau B, Ravaud P. Preventing bias in cluster randomised trials. PLoS Med 2009; 6(5):e1000065.

Thank you, this is a wonderful article. Today, there are procedures for analysis of complex samples in several statistical packages so SAS, SPSS, etc.

Thank you for this excellent resource. We have some additional materials on ethical issues in CRTs available on Global Health Reviewers if they're of interest  please see https://globalhealthbioethics.tghn.org/topics/clusterrandomisedtrials/