title: Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes.
abstract: BACKGROUND
  Cluster randomization design is increasingly used for the evaluation of health-care, screening or educational interventions. At the planning stage, sample size calculations usually consider an average cluster size without taking into account any potential imbalance in cluster size. However, there may exist high discrepancies in cluster sizes.
  
  
  METHODS
  We performed simulations to study the impact of an imbalance in cluster size on power. We determined by simulations to which extent four methods proposed to adapt the sample size calculations to a pre-specified imbalance in cluster size could lead to adequately powered trials.
  
  
  RESULTS
  We showed that an imbalance in cluster size can be of high influence on the power in the case of severe imbalance, particularly if the number of clusters is low and/or the intraclass correlation coefficient is high. In the case of a severe imbalance, our simulations confirmed that the minimum variance weights correction of the variation inflaction factor (VIF) used in the sample size calculations has the best properties.
  
  
  CONCLUSIONS
  Publication of cluster sizes is important to assess the real power of the trial which was conducted and to help designing future trials. We derived an adaptation of the VIF from the minimum variance weights correction to be used in case the imbalance can be a priori formulated such as "a proportion (gamma) of clusters actually recruit a proportion (tau) of subjects to be included (gamma < or = tau)".
authors.affiliation: Département d'Epidémiologie, Biostatistique et Recherche Clinique, Groupe Hospitalier Bichat-Claude Bernard (AP-HP), Université Xavier Bichat, Paris, France. guittetl@free.fr
authors.forename: Lydia
authors.initials: L
authors.lastname: Guittet
authors.forename: Philippe
authors.initials: P
authors.lastname: Ravaud
authors.forename: Bruno
authors.initials: B
authors.lastname: Giraudeau
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D016000:Cluster Analysis; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012107:Research Design; D018401:Sample Size; D016896:Treatment Outcome