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Relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials
Author(s) -
van Breukelen Gerard J. P.,
Candel Math J. J. M.,
Berger Martijn P. F.
Publication year - 2006
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2740
Subject(s) - efficiency , statistics , cluster (spacecraft) , sample size determination , intraclass correlation , mathematics , randomization , cluster randomised controlled trial , cluster sampling , variance (accounting) , sample (material) , range (aeronautics) , randomized controlled trial , medicine , computer science , population , physics , surgery , environmental health , accounting , materials science , estimator , business , composite material , thermodynamics , programming language , psychometrics
Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance, patients within clinics or pupils within schools. Optimal sample sizes at the cluster (centre) and person level have been derived under the restrictive assumption of equal sample sizes per cluster. This paper addresses the relative efficiency of unequal versus equal cluster sizes in case of cluster randomization and person randomization within clusters. Starting from maximum likelihood parameter estimation, the relative efficiency is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the relative efficiency as a function of the mean and variance of cluster size and the intraclass correlation, which can be used for adjusting the sample size. The accuracy of this formula is checked against the numerical results and found to be quite good. It is concluded that the loss of efficiency due to variation of cluster sizes rarely exceeds 10 per cent and can be compensated by sampling 11 per cent more clusters. Copyright © 2006 John Wiley & Sons, Ltd.