Sample size calculations for cluster randomised controlled trials with a fixed number of clusters

Karla Hemming, Alan J Girling, Alice J Sitch, Jennifer Marsh, Richard J Lilford, Karla Hemming, Alan J Girling, Alice J Sitch, Jennifer Marsh, Richard J Lilford

Abstract

Background: Cluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied.

Methods: We systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided.

Results: For trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation (nI) and the estimated intra-cluster correlation (ρ). So, a simple rule is that the number of clusters (k) will be sufficient provided: [formula in text]. Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power.

Conclusions: Designing a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster.

Figures

Figure 1
Figure 1
Maximum achievable power for various different standardised effect sizes: limiting values as the cluster size approaches infinity.
Figure 2
Figure 2
Maximum achievable power to detect increases in 10 percentage points for various different baseline proportions (π1): limiting values as the cluster size approaches infinity.
Figure 3
Figure 3
Minimum detectable difference (effect size) at 80% power for continuous outcomes: limiting values as the cluster size approaches infinity.
Figure 4
Figure 4
Minimum detectable difference (π2) at 80% power various different baseline proportions (π1): limiting values as the cluster size approaches infinity.

References

    1. Murray DM. The Design and Analysis of Group-Randomized Trials. London: Oxford, University Press; 1998.
    1. Donner A, Klar N. Design and Analysis of Cluster Randomised Trials in Health Research. London: Arnold. 2000.
    1. Campbell MK, Thomson S, Ramsay CR, MacLennan GS, Grimshaw JM. Sample size calculator for cluster randomised trials. Computers in Biology and Medicine. 2004;34:113–125. doi: 10.1016/S0010-4825(03)00039-8.
    1. Donner A, Birkett N, Buck C. Randomization by cluster: sample size requirements and analysis. American Journal of Epidemiology. 1981;114:906–914.
    1. Kerry SM, Bland MJ. Sample size in cluster randomisation. BMJ. 1998;316:549.
    1. MacArthur C, Winter HR, Bick DE, Lilford RJ, Lancashire RJ, Knowles H. et al.Redesigning postnatal care: a randomised controlled trial of protocol-based midwifery-led care focused on individual womens physical and psychological health needs. Health Technology Assessment. 2003;7:37.
    1. MacArthur C, K KJ, Ingram L, Freemantle N, Dennis CL, Hamburger R, Antenatal peer support workers and breastfeeding initiation: a cluster randomised controlled trial. BMJ. 2009. p. 338.
    1. Pourshams A, Khademi H, Malekshah AF, Islami F, Nouraei M, Sadjadi AR. et al.Cohort profile: The Golestan Cohort Study - a prospective study of oesophagael cancer in northern Iran. International Journal of Epidemiology. 2009;39:52–59.
    1. Davies MJ, Heller S, Skinner TC, Campbell MJ, Carey ME, Cradock S. et al.Effectiveness of the diabetes education and self management for ongoing and newly diagnosed (DESMOND) programme for people with newly diagnosed type 2 diabetes: cluster randomised controlled trial. BMJ. 2008;336:491–495. doi: 10.1136/.
    1. Avery AJ, Rodgers S, Cantrill JA, Armstrong S, Elliott R, Howard R. et al.Protocol for the PINCER trial: a cluster randomised trial comparing the effectiveness of a pharmacist-led IT-based intervention with simple feedback in reducing rates of clinically important errors in medicines management in general practices. Trials. 2009;10:28. doi: 10.1186/1745-6215-10-28.
    1. Feng Z, Diehr P, Peterson A, McLerran D. Selected issues in group randomized trials. Annual Review of Public Health. 2001;22:167–87. doi: 10.1146/annurev.publhealth.22.1.167.
    1. Guittet L, Giraudea B, Ravaud P. A priori postulated and real power in cluster randomised triasl: mind the gap. BMC Medical Research Methodology. 2005;5:25. doi: 10.1186/1471-2288-5-25.
    1. Brown C, Hofer T, Johal A, Thomson R, Nicholl J, Franklin BD. et epistemology of patient safety research: a framework for study design and interpretation. Part 2. Study design. Qual Saf Health Care. 2008;17:163–169. doi: 10.1136/qshc.2007.023648.
    1. Armitage P, Berry G, Matthews JNS. Statistical methods in medical research. London: Blackwell Publishing; 2002.
    1. Kerry SM, Bland MJ. Sample size in cluster randomised trials: effect of coefficient of variation of cluster size and cluster analysis method. International Journal of Epidemiology. 2006;35:1292–1300. doi: 10.1093/ije/dyl129.
    1. Campbell MK, Fayers PM, Grimshaw JM. Determinants of the intracluster correlation coefficient in cluster randomized trials: the case of implementation research. Clinical Trials. 2005;2:99–107. doi: 10.1191/1740774505cn071oa.
    1. Lilford RJ, Johnson N. The alpha and beta errors in randomized trials. New England Journal of Medicine. 1990;322:780–781.
    1. Edwards SJ, Braunholtz D, Jackson J. Why underpowered trials are not necessarily unethical. Lancet. 2001;350:804–807.
    1. Medical Research Council. Cluster randomsied trials: methodological and ethical considerations; 2002.
    1. Yudkin PL, Moher M. Putting theory into practice: a cluster randomised trial with a small number of clusters. Statistics in Medicine. 2001;20:341–349. doi: 10.1002/1097-0258(20010215)20:3<341::AID-SIM796>;2-G.

Source: PubMed

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