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Stat Med. 2016 May 30;35(12):2000-15. doi: 10.1002/sim.6851. Epub 2016 Jan 12.

Repairing the efficiency loss due to varying cluster sizes in two-level two-armed randomized trials with heterogeneous clustering.

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Department of Methodology and Statistics, School for Public Health and Primary Care CAPHRI, Maastricht University, Maastricht, The Netherlands.


In two-armed trials with clustered observations the arms may differ in terms of (i) the intraclass correlation, (ii) the outcome variance, (iii) the average cluster size, and (iv) the number of clusters. For a linear mixed model analysis of the treatment effect, this paper examines the expected efficiency loss due to varying cluster sizes based upon the asymptotic relative efficiency of varying versus constant cluster sizes. Simple, but nearly cost-optimal, correction factors are derived for the numbers of clusters to repair this efficiency loss. In an extensive Monte Carlo simulation, the accuracy of the asymptotic relative efficiency and its Taylor approximation are examined for small sample sizes. Practical guidelines are derived to correct the numbers of clusters calculated under constant cluster sizes (within each treatment) when planning a study. Because of the variety of simulation conditions, these guidelines can be considered conservative but safe in many realistic situations.


asymptotic relative efficiency; cluster randomized trials; individually randomized group treatment; therapist effects; varying cluster sizes

[Indexed for MEDLINE]

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