A cluster randomized design is a trial design using clusters as experimental units, which considers the groups of participants as randomization units rather than individuals. If it's hard to give a treatment to individual patients in a community or social unit and does not affect the results in the standard care arm of the trial, the cluster randomization could be done. In clinical trials, the randomization units may be the intact social units as follows: a family, school, workplace, sports team, hospital, or community, all of which are called clusters.
Many aspects need to be considered when designing a cluster randomized trial (CRT). The total sample size of a CRT depends on the number and size of clusters. In other words, when one of these two parameters is confirmed, the other parameter will be confirmed using existing formulas. For example, when a feasible cluster size is confirmed, the corresponding number of clusters will be determined. When doing the sample size calculation and data analysis, the intra-cluster and inter-cluster variations must be under control. Basically, there is a higher similarity of subjects in the same cluster than those between clusters, and researchers usually use the intra-cluster correlation coefficient (ICC) to quantify this similarity. It's worthwhile to consider the ICC before trial design and data analysis, however, people always pay less attention to the calculation of cluster size. As a result, the observations in the cluster may not all make a real contribution to the power or precision of the trial when using an oversize cluster size.
As mentioned above, if only recruiting more individuals or accruing more data and keeping the number of clusters constant, then the increase in power will begin to level off (Figure 1). A point in time will be reached, and the contribution of the observation at this point of time is negligible, namely, "diminishing returns". Parameters such as type of outcome, target difference, proportion of participants with the outcome and ICC will affect this time point. Every observation in the trials with smaller ICCs makes more contributions to the overall power than the trials with larger ICCs, which means the power is stable and precise. Power is the ability to detect a target effect size and precision is the ability to measure the effect size within a sufficiently narrow confidence interval.
Figure 1. Power and precision curves with an ICC of 0.03. As cluster size increases, red curve shows the increases in power; green curve shows the increases in precision. Assumes a CRT with 10 clusters in each arm, designed to detect a difference between two proportions 0.6 and 0.45 at a two sided significance level of 5%.
There are of course limitations for cluster randomized design. Researchers usually focus on the number of clusters and cluster size. However, the financial cost, the social and ethical implications of participants should also be considered. That's why they should use unequal allocation ratios instead of a 1:1 allocation ratios with a costly intervention or ignore the power and precision curves examination in the case of unequal allocation. The sample size formulas we use is suitable for a relatively large number of clusters, so if the number of clusters is small, it's better to add one cluster to each arm at the 5% significance level. This allows the use of critical values from the normal distribution rather than from the t distribution.
In general, CRT design is usually used for the evaluation of non-drug interventions and particularly for the evaluation of educational and community level interventions. It has been widely used in healthcare system and large simple trials. Moreover, it is also useful in vaccine trials. For example, randomization of geographic areas can be used to capture indirect or herd effects of vaccination. It allows researchers to compare the incidence of disease in non-vaccinated individuals in the intervention group with the incidence of disease in the control group (Figure 2).
Figure 2. CRT: a fictional anti Flu-wv vaccine trial.
At CD BioSciences, we can help you to do the sample size and power calculation as well as the diminishing returns identification when designing a cluster randomized trial. If you have any questions, please feel free to contact us.
References:
1. Klar, N. (2013) ‘A practical guide to cluster randomised trials in health services research’, Journal of Biopharmaceutical Statistics, 23(3), 711-713.
2. Donner, A. (2010) ‘Some aspects of the design and analysis of cluster randomization trials’, Journal of the Royal Statistical Society, 47(1), 95-113.
3. Hemming, K., Girling, A. J., Sitch, A. J., Marsh, J., Lilford, R. J. (2011) ‘Sample size calculations for cluster randomised controlled trials with a fixed number of clusters’, BMC Medical Research Methodology, 11(1), 102.
4. Hemming, K., Eldridge, S., Forbes, G., Weijer, C., Taljaard, M. (2017) ‘How to design efficient cluster randomised trials’, Bmj, 358, j3064.