title: Recommendations for the analysis of individually randomised controlled trials with clustering in one arm - a case of continuous outcomes.
abstract: In an individually randomised controlled trial where the treatment is delivered by a health professional it seems likely that the effectiveness of the treatment, independent of any treatment effect, could depend on the skill, training or even enthusiasm of the health professional delivering it. This may then lead to a potential clustering of the outcomes for patients treated by the same health professional, but similar clustering may not occur in the control arm. Using four case studies, we aim to provide practical guidance and recommendations for the analysis of trials with some element of clustering in one arm.
  
  
  
  Five approaches to the analysis of outcomes from an individually randomised controlled trial with clustering in one arm are identified in the literature. Some of these methods are applied to four case studies of completed randomised controlled trials with clustering in one arm with sample sizes ranging from 56 to 539. Results are obtained using the statistical packages R and Stata and summarised using a forest plot.
  
  
  
  The intra-cluster correlation coefficient (ICC) for each of the case studies was small (<0.05) indicating little dependence on the outcomes related to cluster allocations. All models fitted produced similar results, including the simplest approach of ignoring clustering for the case studies considered.
  
  
  
  A partially clustered approach, modelling the clustering in just one arm, most accurately represents the trial design and provides valid results. Modelling homogeneous variances between the clustered and unclustered arm is adequate in scenarios similar to the case studies considered. We recommend treating each participant in the unclustered arm as a single cluster. This approach is simple to implement in R and Stata and is recommended for the analysis of trials with clustering in one arm only. However, the case studies considered had small ICC values, limiting the generalisability of these results.
authors.affiliation: ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK.
authors.forename: Laura
authors.initials: L
authors.lastname: Flight
authors.affiliation: MRC Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge, CB2 0SR, UK.
authors.forename: Annabel
authors.initials: A
authors.lastname: Allison
authors.affiliation: ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK.
authors.forename: Munyaradzi
authors.initials: M
authors.lastname: Dimairo
authors.affiliation: ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK.
authors.forename: Ellen
authors.initials: E
authors.lastname: Lee
authors.affiliation: ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK.
authors.forename: Laura
authors.initials: L
authors.lastname: Mandefield
authors.affiliation: ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK. s.j.walters@sheffield.ac.uk.
authors.forename: Stephen J
authors.identifier: 0000-0001-9000-8126
authors.initials: SJ
authors.lastname: Walters
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D006801:Humans; D008962:Models, Theoretical; D017063:Outcome Assessment, Health Care / Q000379:methods / Q000592:standards / Q000706:statistics & numerical data*; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data*; D015203:Reproducibility of Results; D012107:Research Design / Q000592:standards; D018401:Sample Size
keywords: Clustering; Individually clustered randomised controlled trials; Randomised controlled trial; Statistical models; Therapist effects