title: An imbalance in cluster sizes does not lead to notable loss of power in cross-sectional, stepped-wedge cluster randomised trials with a continuous outcome.
abstract: The current methodology for sample size calculations for stepped-wedge cluster randomised trials (SW-CRTs) is based on the assumption of equal cluster sizes. However, as is often the case in cluster randomised trials (CRTs), the clusters in SW-CRTs are likely to vary in size, which in other designs of CRT leads to a reduction in power. The effect of an imbalance in cluster size on the power of SW-CRTs has not previously been reported, nor what an appropriate adjustment to the sample size calculation should be to allow for any imbalance. We aimed to assess the impact of an imbalance in cluster size on the power of a cross-sectional SW-CRT and recommend a method for calculating the sample size of a SW-CRT when there is an imbalance in cluster size.
  
  
  
  The effect of varying degrees of imbalance in cluster size on the power of SW-CRTs was investigated using simulations. The sample size was calculated using both the standard method and two proposed adjusted design effects (DEs), based on those suggested for CRTs with unequal cluster sizes. The data were analysed using generalised estimating equations with an exchangeable correlation matrix and robust standard errors.
  
  
  
  An imbalance in cluster size was not found to have a notable effect on the power of SW-CRTs. The two proposed adjusted DEs resulted in trials that were generally considerably over-powered.
  
  
  
  We recommend that the standard method of sample size calculation for SW-CRTs be used, provided that the assumptions of the method hold. However, it would be beneficial to investigate, through simulation, what effect the maximum likely amount of inequality in cluster sizes would be on the power of the trial and whether any inflation of the sample size would be required.
authors.affiliation: Diabetes Research Centre, University of Leicester, Leicester, UK. cak21@le.ac.uk.
authors.forename: Caroline A
authors.initials: CA
authors.lastname: Kristunas
authors.affiliation: Department of Health Sciences, University of Leicester, Leicester, UK.
authors.forename: Karen L
authors.initials: KL
authors.lastname: Smith
authors.affiliation: Department of Health Sciences, University of Leicester, Leicester, UK.
authors.forename: Laura J
authors.initials: LJ
authors.lastname: Gray
mesh_terms: D016000:Cluster Analysis; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012107:Research Design / Q000706:statistics & numerical data; D018401:Sample Size
keywords: Cluster randomised trial; Power; Sample size; Simulation study; Stepped wedge; Study design