The effect of heterogeneous variance on efficiency and power of cluster randomized trials with a balanced 2x2 factorial design

F. Lemme*, G.J.P. van Breukelen, M.J.J.M. Candel, M.P.F. Berger

*Corresponding author for this work

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Sample size calculation for cluster randomized trials (CRTs) with a 2x2 factorial design is complicated due to the combination of nesting (of individuals within clusters) with crossing (of two treatments). Typically, clusters and individuals are allocated across treatment conditions in a balanced fashion, which is optimal under homogeneity of variance. However, the variance is likely to be heterogeneous if there is a treatment effect. An unbalanced allocation is then more efficient, but impractical because the optimal allocation depends on the unknown variances. Focusing on CRTs with a 2x2 design, this paper addresses two questions: How much efficiency is lost by having a balanced design when the outcome variance is heterogeneous? How large must the sample size be for a balanced allocation to have sufficient power under heterogeneity of variance? We consider different scenarios of heterogeneous variance. Within each scenario, we determine the relative efficiency of a balanced design, as a function of the level (cluster, individual, both) and amount of heterogeneity of the variance. We then provide a simple correction of the sample size for the loss of power due to heterogeneity of variance when a balanced allocation is used. The theory is illustrated with an example of a published 2x2 CRT.
Original languageEnglish
Pages (from-to)574-593
JournalStatistical Methods in Medical Research
Issue number5
Publication statusPublished - 1 Jan 2015

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