title: Use of the bootstrap in analysing cost data from cluster randomised trials: some simulation results.
abstract: BACKGROUND
  This work has investigated under what conditions confidence intervals around the differences in mean costs from a cluster RCT are suitable for estimation using a commonly used cluster-adjusted bootstrap in preference to methods that utilise the Huber-White robust estimator of variance. The bootstrap's main advantage is in dealing with skewed data, which often characterise patient costs. However, it is insufficiently well recognised that one method of adjusting the bootstrap to deal with clustered data is only valid in large samples. In particular, the requirement that the number of clusters randomised should be large would not be satisfied in many cluster RCTs performed to date.
  
  
  METHODS
  The performances of confidence intervals for simple differences in mean costs utilising a robust (cluster-adjusted) standard error and from two cluster-adjusted bootstrap procedures were compared in terms of confidence interval coverage in a large number of simulations. Parameters varied included the intracluster correlation coefficient, the sample size and the distributions used to generate the data.
  
  
  RESULTS
  The bootstrap's advantage in dealing with skewed data was found to be outweighed by its poor confidence interval coverage when the number of clusters was at the level frequently found in cluster RCTs in practice. Simulations showed that confidence intervals based on robust methods of standard error estimation achieved coverage rates between 93.5% and 94.8% for a 95% nominal level whereas those for the bootstrap ranged between 86.4% and 93.8%.
  
  
  CONCLUSIONS
  In general, 24 clusters per treatment arm is probably the minimum number for which one would even begin to consider the bootstrap in preference to traditional robust methods, for the parameter combinations investigated here. At least this number of clusters and extremely skewed data would be necessary for the bootstrap to be considered in favour of the robust method. There is a need for further investigation of more complex bootstrap procedures if economic data from cluster RCTs are to be analysed appropriately.
authors.affiliation: MRC Health Services Research Collaboration, Department of Social Medicine, University of Bristol, Canynge Hall, Whiteladies Road, Bristol BS8 2PR, UK. terry.flynn@bristol.ac.uk
authors.forename: Terry N
authors.initials: TN
authors.lastname: Flynn
authors.forename: Tim J
authors.initials: TJ
authors.lastname: Peters
mesh_terms: D000704:Analysis of Variance; D016000:Cluster Analysis; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D017048:Health Care Costs / Q000706:statistics & numerical data*; D006801:Humans; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D018401:Sample Size; D018709:Statistics, Nonparametric; D016896:Treatment Outcome