title: Methods for sample size determination in cluster randomized trials.
abstract: BACKGROUND
  The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required.
  
  
  METHODS
  We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method.
  
  
  RESULTS
  We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs.
  
  
  CONCLUSIONS
  There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials.
authors.affiliation: Centre for Primary Care and Public Health, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK and c.m.rutterford@qmul.ac.uk.
authors.forename: Clare
authors.initials: C
authors.lastname: Rutterford
authors.affiliation: Hub for Trials Methodology Research, MRC Clinical Trials Unit at University College London, London, UK.
authors.forename: Andrew
authors.initials: A
authors.lastname: Copas
authors.affiliation: Centre for Primary Care and Public Health, Barts and the London School of Medicine and Dentistry, Queen Mary University of London, London, UK and.
authors.forename: Sandra
authors.initials: S
authors.lastname: Eldridge
mesh_terms: D006801:Humans; D010349:Patient Compliance; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D018401:Sample Size
keywords: Sample size; cluster randomization; design effect