title: Sample size calculation for stepped wedge and other longitudinal cluster randomised trials.
abstract: The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross-section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Centre for Primary Care & Public Health, Queen Mary University of London, London, U.K.. r.l.hooper@qmul.ac.uk.
authors.forename: Richard
authors.initials: R
authors.lastname: Hooper
authors.affiliation: Radboud Institute for Health Sciences, Radboud University Medical Centre, Nijmegen, The Netherlands.
authors.forename: Steven
authors.initials: S
authors.lastname: Teerenstra
authors.affiliation: Julius Center for Health Sciences and Primary Care, University Medical Centre Utrecht, Utrecht, The Netherlands.
authors.forename: Esther
authors.initials: E
authors.lastname: de Hoop
authors.affiliation: Centre for Primary Care & Public Health, Queen Mary University of London, London, U.K.
authors.forename: Sandra
authors.initials: S
authors.lastname: Eldridge
mesh_terms: D016000:Cluster Analysis; D018592:Cross-Over Studies; D006801:Humans; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D018401:Sample Size
keywords: clinical trial design; cluster randomised trial; intracluster correlation; sample size; stepped wedge