STATISTICS AND RESEARCH DESIGN

Cluster-randomized controlled trials: Part 1 Nikolaos Pandis, Associate Editor of Statistics and Research Design Bern, Switzerland, and Corfu, Greece

I

n certain situations, it is not possible to use patients as the randomization unit, so we must randomize to clusters (groups) consisting of a few, several, or many subjects who share some common characteristics. Clusters can be families, schools, communities, general practices, teeth in patients, or repeated measurements from the same participants over time. For example, in a trial involving oral health education delivered by the media, the unit of randomization might be entire towns, whereas randomizing persons would have been difficult and also inappropriate.1 In orthodontics, patients act in certain situations as clusters when they are contributing several teeth or when multiple measurements (repeated measures) over time are made on the same participants. Cluster randomization differs in sample calculation and data analysis from individually randomized trials, which assume that observations are independent. In cluster-randomized trials, observations are correlated with less information obtained per subject and a consequent loss of power compared with individual randomized trials. In clustered trials, an increase in the sample size is required to compensate for the loss of information (loss of precision or power) because of this data correlation.2 Imagine the following trial in which we want to evaluate the proportions of bond failures between 2 adhesives. In this scenario, a common option would be to randomize per patient, who will constitute a cluster; on average, each patient will contribute 20 teeth from premolar to premolar in nonextraction therapy. Some patients will receive adhesive A only, and some only adhesive B. Because the failures are not independent in patients, meaning that some patients will be more likely to break their appliances than others, the outcomes will tend to be correlated (clustered); therefore, the contribution of each tooth to the sample size is less than 1 because of the clustering effect (within-patient correlation of bond failures or no failures). Since the information contributed by each patient cluster is reduced, the required sample size must be increased by a factor

Am J Orthod Dentofacial Orthop 2012;142:276-7 0889-5406/$36.00 Copyright Ó 2012 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2012.04.007

276

related to the degree of correlation or the similarity of the outcomes within clusters. Two parameters indicate the degree of correlation between subjects within clusters: the intracluster correlation coefficient (ICC or r [rho]) and the betweencluster coefficient of variation (k). Furthermore, there are sample-size formulas available for cluster randomized designs that use either the ICC or k.1,2 There will be more on this in part 2. The ICC is 1 way to measure the degree of cluster variation and, like other correlation coefficients, can have a numeric value between
1 and 11. In practice, the values are usually positive, and a value of 0 means no clustering, whereas a value of 11 means that, within a cluster, the values are perfectly correlated. When the ICC 5 0, each participant within a cluster contributes the same amount of information as he or she would have contributed to an individually randomized trial. However, when the ICC 5 1, each cluster is considered as 1 individual. When the difference to be detected, the number of clusters, cluster sizes, and the significance levels remain constant, study power decreases as the ICC increases (Fig). The increased sample size required in clusterrandomized designs can be determined by the design effect, which is related to the ICC with the formula D 511ðm
1Þr where m is the number of subjects per cluster and r 5 ICC. The larger the ICC (with m the same), the larger the design effect, and the larger the required sample size for the clustered trial compared with an individually randomized trial with similar power. The design effect indicates the factor by which the sample size of an individually randomized trial must be increased to give the same power for a cluster-randomized design. In an example trial, when 2 adhesives, A and B, are compared, if we assume that the required number of teeth randomized to either intervention A or B is 500 per arm (a total of 25 patients per arm, assuming 20 teeth per patient), whereas in a cluster-randomized design with an ICC 5 .1 and using the design effect formula, we would have needed 1000 teeth 3 design effect. Design effect 511ðm
1Þr 511ð20
1Þ  :152:9

Statistics and research design

277

Fig. The graph shows how power decreases as the ICC increases for the various differences d (0.10, 0.20, 0.30) between treatment groups, at alpha 5 0.05 and for the same number of clusters (j 5 20) and participants per clusters (n 5 50).

Therefore, the required number of teeth would be 1000 3 2.9, or 2900, which would translate to 145 patients! Small values of ICC can have a dramatic effect on the required sample size. An intracluster correlation implies that there are differences between clusters, and another way to quantify the intracluster correlation is to measure the variability between clusters. This is done by the between-cluster coefficient of variation. In general, a coefficient of variation is a ratio of the data's standard deviation to its mean. The standard deviation can be larger than the mean, so, unlike ICC, values of k might be greater than 1. When planning a study, it might be easier to estimate the coefficient of variation rather than the ICC; this is because k is more directly related to the actual range of values.

CONCLUSIONS

1. 2. 3.

Clustering effects are common in orthodontics, but they are often ignored. In the presence of clustering effects, there is a loss of study power. Designs with clustering effects require larger sample sizes compared with designs with no clustering effects.

REFERENCES 1. Hayes RJ, Moulton LH. Cluster randomized trials. Interdisciplinary Statistic Series. Boca Raton, FL: Chapman & Hall/CRC; 2009. p. 15-23. 2. Killip S, Mahfoud Z, Pearce K. What is an intracluster correlation coefficient? Crucial concepts for primary care researchers. Ann Fam Med 2004;2:204-8.

American Journal of Orthodontics and Dentofacial Orthopedics

August 2012  Vol 142  Issue 2