title: Minimum number of clusters and comparison of analysis methods for cross sectional stepped wedge cluster randomised trials with binary outcomes: A simulation study.
abstract: Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters. The most common frameworks used to analyse data from these types of trials are generalised estimating equations and generalised linear mixed models. A topic of much research into these methods has been their application to cluster randomised trial data and, in particular, the number of clusters required to make reasonable inferences about the intervention effect. However, for stepped wedge trials, which have been claimed by many researchers to have a statistical power advantage over the parallel cluster randomised trial, the minimum number of clusters required has not been investigated.
  
  
  
  We conducted a simulation study where we considered the most commonly used methods suggested in the literature to analyse cross-sectional stepped wedge cluster randomised trial data. We compared the per cent bias, the type I error rate and power of these methods in a stepped wedge trial setting with a binary outcome, where there are few clusters available and when the appropriate adjustment for a time trend is made, which by design may be confounding the intervention effect.
  
  
  
  We found that the generalised linear mixed modelling approach is the most consistent when few clusters are available. We also found that none of the common analysis methods for stepped wedge trials were both unbiased and maintained a 5% type I error rate when there were only three clusters.
  
  
  
  Of the commonly used analysis approaches, we recommend the generalised linear mixed model for small stepped wedge trials with binary outcomes. We also suggest that in a stepped wedge design with three steps, at least two clusters be randomised at each step, to ensure that the intervention effect estimator maintains the nominal 5% significance level and is also reasonably unbiased.
authors.affiliation: School of Medicine and Public Health, Faculty of Health, University of Newcastle, Newcastle, NSW, Australia. daniel.barker@newcastle.edu.au.|CCEB, University of Newcastle, HMRI Building, Level 4 West, University Drive, Callaghan, NSW, 2308, Australia. daniel.barker@newcastle.edu.au.
authors.forename: Daniel
authors.identifier: 0000-0002-9707-4465
authors.initials: D
authors.lastname: Barker
authors.affiliation: School of Medicine and Public Health, Faculty of Health, University of Newcastle, Newcastle, NSW, Australia.|National Centre for Epidemiology and Population Health, Research School of Population Health, Australian National University, Canberra, Australia.
authors.forename: Catherine
authors.initials: C
authors.lastname: D'Este
authors.affiliation: Medical Statistics Group, ScHARR, University of Sheffield, Sheffield, UK.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Campbell
authors.affiliation: School of Medicine and Public Health, Faculty of Health, University of Newcastle, Newcastle, NSW, Australia.|Health Policy Analysis Pty Ltd, Sydney, NSW, Australia.
authors.forename: Patrick
authors.initials: P
authors.lastname: McElduff
mesh_terms: D015982:Bias; D016000:Cluster Analysis; D003198:Computer Simulation; D003430:Cross-Sectional Studies; D003627:Data Interpretation, Statistical; D023381:Endpoint Determination / Q000706:statistics & numerical data; D006801:Humans; D016014:Linear Models; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012107:Research Design / Q000706:statistics & numerical data; D013997:Time Factors; D016896:Treatment Outcome
keywords: Cluster randomised; Cross sectional; Simulation study; Statistical analysis; Stepped wedge