Cluster randomised controlled trials (cluster RCT) in which existing groups (clusters) are recruited to a trial and randomly allocated to one treatment or another are potentially very valuable in health care because often changes cannot be applied to individuals. Examples might be staff education or changes in the organisation of care. Typically the clusters consist of teh group of patients or staff from a particular health provider or setting (for example a hospital unit, a general practice) and the cluster is the unit that is randomised.
I have on occasion seen studies in which there are two participating units, one of which is randomly allocated to receive an intervention described as a cluster RCT. In my view it is ridiculous to describe this as a cluster RCT and I struggle to see that randomisation adds much to the ability to make an inference - but if I am right, how many clusters are required before it is legitimate to call it a cluster RCT? Discus...
I find that rules of thumb are not particularly useful, and that it is much better to tailor the design to the problem that is at hand. That is do a power calculation. This is very useful with a good manual:
Optimal Design Software
The Optimal Design for Multi-Level and Longitudinal Research is a free stand-alone software program for performing statistical power calculations of impact evaluation studies, particularly group-randomized trials.
Suggested citation:
Raudenbush, S. W., et al. (2011). Optimal Design Software for Multi-level and Longitudinal Research (Version 3.01) [Software]. Available from www.wtgrantfoundation.org.
see https://sites.google.com/site/optimaldesignsoftware/home
A key issue is how to include covariates so as to increase power
Raudenbush, S. W., Martinez, A., & Spybrook, J. (2007). Strategies for Improving Precision in Group-Randomized Experiments. Educational Evaluation and Policy Analysis, 29(1), 5-29.
Bloom, H. S., Richburg-Hayes, L., & Black, A. R. (2007). Using Covariates to Improve Precision for Studies That Randomize Schools to Evaluate Educational Interventions. Educational Evaluation and Policy Analysis, 29(1), 30-59.
Raudenbush, S. W. (1997). Statistical Analysis and Optimal Design for Cluster Randomized Trials. Psychological Methods, 2(2), 173-185.
You could also adopt a simulation approach:
http://www.bristol.ac.uk/cmm/software/mlpowsim/
There is very good manual with that software.
Kelvyn Jones - I agree that there needs to be proper sample size calculation and the number of clusters is not sensibly arrived at by a rule of thumb. In many circumstances this might render my question moot but if, for example, the ICC is O then a cluster RCT with 2 clusters may look viable while sharing essentially all the design weaknesses of a non randomised trial of two groups.... is it right to even call it a cluster RCT n the first plac?
I would wish to use a cluster-based design not as a convenience to collect data but as a device to look at important and realistic heterogeneity between settings. If I had only two clusters I would use fixed effects (and not random effects) and I would be only able to infer to those two specific clusters, which would be not what I would be after. Two clusters would also mean that there is very little variation in the 'exposure' - you have a sample of two; and that seems pointless and lacking power to detect meaningful effect about things of interest.
Good discussion. Peter's question is if there is a minimum number of clusters required to call a study a cluster trial. Because the number of clusters is one aspect of the sample size of a cluster trial, we can also ask if there is a minimum number of randomized individuals to call it a typical parallel RCT. Would a study with perfect allocation concealment, triple blinding, etc. be an RCT if n = 2? (I think so, but a poorly designed one with a high potential for bias).
So my answer is that a k = 2 cluster trial is a cluster trial, but one with a high potential for biased inference.
I think part of the problem is that people have been taught that randomization automatically has magical bias-minimizing powers. It does, but those powers increase with n (and k), and with very small samples the magic doesn't work much better than eye of newt or tongue of toad.
Mark R Speechley you are probably correct and certainly, you make a more important bigger point about randomisation not magically solving all problems, the but my 'gut' says that something is fundamentally different when k (and as you say, n) is = to the number of groups in the trial.
In terms of the general point, there is a bigger issue in relation to cluster trials for the simple reason that it is less immediately obvious that there is a problem when 'n' is large whereas no one is likely to fail to notice the sample size issue with n=2!.
Peter, I agree with you entirely that some people might be spuriously impressed by large sample size in a study where two cities of 1,000,000 each were randomized in a cluster trial.
We were taught that a large number of small clusters is better (statistically, inferentially) than a small number of large clusters. I've always remembered this simple bit of advice and would approach a k = 2 cluster trial accordingly.
I still think there is confusion in the answers over the target of inference, if the setting makes a difference in the efficacy, I would want lots of settings to evaluate this variation.
Can we do a community based cluster RCT with just 2/3 clusters (such as villages/blocks in a colony). How does this fundamentally differ from the quasi-experimental study involving the same 2/3 cluster sites (except that in the quasi-study, we may choose the cluster receiving the intervention on administrative/feasibility considerations)?
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