title: Cluster randomised crossover trials with binary data and unbalanced cluster sizes: application to studies of near-universal interventions in intensive care.
abstract: BACKGROUND
  Cluster randomised crossover trials have been utilised in recent years in the health and social sciences. Methods for analysis have been proposed; however, for binary outcomes, these have received little assessment of their appropriateness. In addition, methods for determination of sample size are currently limited to balanced cluster sizes both between clusters and between periods within clusters. This article aims to extend this work to unbalanced situations and to evaluate the properties of a variety of methods for analysis of binary data, with a particular focus on the setting of potential trials of near-universal interventions in intensive care to reduce in-hospital mortality.
  
  
  METHODS
  We derive a formula for sample size estimation for unbalanced cluster sizes, and apply it to the intensive care setting to demonstrate the utility of the cluster crossover design. We conduct a numerical simulation of the design in the intensive care setting and for more general configurations, and we assess the performance of three cluster summary estimators and an individual-data estimator based on binomial-identity-link regression.
  
  
  RESULTS
  For settings similar to the intensive care scenario involving large cluster sizes and small intra-cluster correlations, the sample size formulae developed and analysis methods investigated are found to be appropriate, with the unweighted cluster summary method performing well relative to the more optimal but more complex inverse-variance weighted method. More generally, we find that the unweighted and cluster-size-weighted summary methods perform well, with the relative efficiency of each largely determined systematically from the study design parameters. Performance of individual-data regression is adequate with small cluster sizes but becomes inefficient for large, unbalanced cluster sizes. When outcome prevalences are 6% or less and the within-cluster-within-period correlation is 0.05 or larger, all methods display sub-nominal confidence interval coverage, with the less prevalent the outcome the worse the coverage.
  
  
  CONCLUSIONS
  As with all simulation studies, conclusions are limited to the configurations studied. We confined attention to detecting intervention effects on an absolute risk scale using marginal models and did not explore properties of binary random effects models.
  
  
  CONCLUSIONS
  Cluster crossover designs with binary outcomes can be analysed using simple cluster summary methods, and sample size in unbalanced cluster size settings can be determined using relatively straightforward formulae. However, caution needs to be applied in situations with low prevalence outcomes and moderate to high intra-cluster correlations.
authors.affiliation: School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia Andrew.Forbes@monash.edu.
authors.forename: Andrew B
authors.initials: AB
authors.lastname: Forbes
authors.affiliation: School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC, Australia.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Akram
authors.affiliation: Centre for Outcome and Resource Evaluation (CORE), Australian and New Zealand Intensive Care Society (ANZICS), Carlton, VIC, Australia Australian and New Zealand Intensive Care Research Centre (ANZIC-RC), Monash University, Melbourne, VIC, Australia.
authors.forename: David
authors.initials: D
authors.lastname: Pilcher
authors.affiliation: Australian and New Zealand Intensive Care Research Centre (ANZIC-RC), Monash University, Melbourne, VIC, Australia.
authors.forename: Jamie
authors.initials: J
authors.lastname: Cooper
authors.affiliation: Australian and New Zealand Intensive Care Research Centre (ANZIC-RC), Monash University, Melbourne, VIC, Australia.
authors.forename: Rinaldo
authors.initials: R
authors.lastname: Bellomo
mesh_terms: D001315:Australia; D035843:Biomedical Research / Q000458:organization & administration*; D016000:Cluster Analysis; D003422:Critical Care / Q000458:organization & administration*; D018592:Cross-Over Studies; D006801:Humans; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D018401:Sample Size
keywords: Cluster randomised trial; binary data; crossover; intra-cluster correlation; sample size