The effect of heterogeneous variance on efficiency and power of cluster randomized trials with a balanced 2 × 2 factorial design.
Sample size calculation for cluster randomized trials (CRTs) with a [Formula: see text] 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 [Formula: see text] 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 2 x2 CRT.
Department of Methodology and Statistics, Maastricht University, The Netherlands francesca.lemme@maastrichtuniversity.nl.
Francesca
F
Lemme
Department of Methodology and Statistics, CAPHRI School for Public Health and Primary Care, Maastricht University, The Netherlands.
Gerard J P
GJ
van Breukelen
Department of Methodology and Statistics, CAPHRI School for Public Health and Primary Care, Maastricht University, The Netherlands.
Math J J M
MJ
Candel
Department of Methodology and Statistics, Maastricht University, The Netherlands.
Martijn P F
MP
Berger
D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D018401:Sample Size
2 × 2 factorial; Balanced design; cluster randomized trial; heterogeneous variance; optimal design