TY - JOUR
T1 - The effect of heterogeneous variance on efficiency and power of cluster randomized trials with a balanced 2x2 factorial design
AU - Lemme, F.
AU - van Breukelen, G.J.P.
AU - Candel, M.J.J.M.
AU - Berger, M.P.F.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
U2 - 10.1177/0962280215583683
DO - 10.1177/0962280215583683
M3 - Article
SN - 0962-2802
VL - 24
SP - 574
EP - 593
JO - Statistical Methods in Medical Research
JF - Statistical Methods in Medical Research
IS - 5
ER -