title: Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient!
abstract: OBJECTIVE
  Simple guidelines for calculating efficient sample sizes in cluster randomized trials with unknown intraclass correlation (ICC) and varying cluster sizes.
  
  
  METHODS
  A simple equation is given for the optimal number of clusters and sample size per cluster. Here, optimal means maximizing power for a given budget or minimizing total cost for a given power. The problems of cluster size variation and specification of the ICC of the outcome are solved in a simple yet efficient way.
  
  
  RESULTS
  The optimal number of clusters goes up, and the optimal sample size per cluster goes down as the ICC goes up or as the cluster-to-person cost ratio goes down. The available budget, desired power, and effect size only affect the number of clusters and not the sample size per cluster, which is between 7 and 70 for a wide range of cost ratios and ICCs. Power loss because of cluster size variation is compensated by sampling 10% more clusters. The optimal design for the ICC halfway the range of realistic ICC values is a good choice for the first stage of a two-stage design. The second stage is needed only if the first stage shows the ICC to be higher than assumed.
  
  
  CONCLUSIONS
  Efficient sample sizes for cluster randomized trials are easily computed, provided the cost per cluster and cost per person are specified.
authors.affiliation: Department of Methodology and Statistics, CAPHRI School for Public Health and Primary Care, Maastricht University, Maastricht, The Netherlands. gerard.vbreukelen@maastrichtuniversity.nl
authors.forename: Gerard J P
authors.initials: GJ
authors.lastname: van Breukelen
authors.forename: Math J J M
authors.initials: MJ
authors.lastname: Candel
mesh_terms: D002017:Budgets; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D017408:Guidelines as Topic; D006801:Humans; D016032:Randomized Controlled Trials as Topic / Q000191:economics / Q000706:statistics & numerical data*; D018401:Sample Size