title: The use of random effects models to allow for clustering in individually randomized trials.
abstract: BACKGROUND
  We describe different forms of clustering that may occur in individually randomized trials, where the observed outcomes for different individuals cannot be regarded as independent. We propose random effects models to allow for such clustering, across a range of contexts and trial designs, and investigate their effect on estimation and interpretation of the treatment effect.
  
  
  METHODS
  We apply our proposed models to two individually randomized trials with potential for clustering, a trial of teleconsultation in hospital referral (the main outcome being offer of a further hospital appointment) and a trial of exercise therapy delivered by physiotherapists for low back pain (the outcome being a back pain score). Extensions to the methods include the possibility of explaining heterogeneity between clusters using cluster level characteristics and the potential dilution of cluster effects due to noncompliance.
  
  
  RESULTS
  In the teleconsultation trial, the odds ratio was significant (1.52, 95% CI 1.27 to 1.82) when clustering was ignored, but smaller and nonsignificant (1.36, 95% CI 0.85 to 2.13) when clustering by hospital consultant was taken into account. The 95% range of estimated treatment effects across consultants was from 0.21 to 8.76. This variability was only partially explained by the specialty of the consultant. In the back pain trial, although there was an overall benefit of exercise (change of - 0.51 points on the back pain score) and little evidence of clustering, the estimated treatment effects for different physiotherapists ranged from -1.26 to +0.26 points.
  
  
  CONCLUSIONS
  Clustering is an important issue in many individually randomized trials. Ignoring it can lead to underestimates of the uncertainty and too extreme P-values. Even when there is little apparent heterogeneity across clusters, it can still have a large impact on the estimation and interpretation of the treatment effect.
authors.affiliation: MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK. kj127@cam.ac.uk
authors.forename: Katherine J
authors.initials: KJ
authors.lastname: Lee
authors.forename: Simon G
authors.initials: SG
authors.lastname: Thompson
mesh_terms: D001416:Back Pain / Q000628:therapy; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D005081:Exercise Therapy; D006801:Humans; D015233:Models, Statistical; D026761:Physical Therapy Specialty; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D019114:Remote Consultation; D012107:Research Design; D016896:Treatment Outcome