title: Assessing potential sources of clustering in individually randomised trials.
abstract: BACKGROUND
  Recent reviews have shown that while clustering is extremely common in individually randomised trials (for example, clustering within centre, therapist, or surgeon), it is rarely accounted for in the trial analysis. Our aim is to develop a general framework for assessing whether potential sources of clustering must be accounted for in the trial analysis to obtain valid type I error rates (non-ignorable clustering), with a particular focus on individually randomised trials.
  
  
  METHODS
  A general framework for assessing clustering is developed based on theoretical results and a case study of a recently published trial is used to illustrate the concepts. A simulation study is used to explore the impact of not accounting for non-ignorable clustering in practice.
  
  
  RESULTS
  Clustering is non-ignorable when there is both correlation between patient outcomes within clusters, and correlation between treatment assignments within clusters. This occurs when the intraclass correlation coefficient is non-zero, and when the cluster has been used in the randomisation process (e.g. stratified blocks within centre) or when patients are assigned to clusters after randomisation with different probabilities (e.g. a surgery trial in which surgeons treat patients in only one arm). A case study of an individually randomised trial found multiple sources of clustering, including centre of recruitment, attending surgeon, and site of rehabilitation class. Simulations show that failure to account for non-ignorable clustering in trial analyses can lead to type I error rates over 20% in certain cases; conversely, adjusting for the clustering in the trial analysis gave correct type I error rates.
  
  
  CONCLUSIONS
  Clustering is common in individually randomised trials. Trialists should assess potential sources of clustering during the planning stages of a trial, and account for any sources of non-ignorable clustering in the trial analysis.
authors.affiliation: MRC Clinical Trials Unit, Aviation House, 125 Kingsway, London, WC2B 6NH, UK. brk@ctu.mrc.ac.uk
authors.forename: Brennan C
authors.initials: BC
authors.lastname: Kahan
authors.forename: Tim P
authors.initials: TP
authors.lastname: Morris
mesh_terms: D016000:Cluster Analysis; D006801:Humans; D008962:Models, Theoretical; D016032:Randomized Controlled Trials as Topic / Q000592:standards*; D013122:Spinal Diseases / Q000534:rehabilitation / Q000601:surgery