A priori postulated and real power in cluster randomized trials: mind the gap

Abstract

Background: Cluster randomization design is increasingly used for the evaluation of health-care, screening or educational interventions. The intraclass correlation coefficient (ICC) defines the clustering effect and be specified during planning. The aim of this work is to study the influence of the ICC on power in cluster randomized trials.

Methods: Power contour graphs were drawn to illustrate the loss in power induced by an underestimation of the ICC when planning trials. We also derived the maximum achievable power given a specified ICC.

Results: The magnitude of the ICC can have a major impact on power, and with low numbers of clusters, 80% power may not be achievable.

Conclusion: Underestimating the ICC during planning cluster randomized trials can lead to a seriously underpowered trial. Publication of a priori postulated and a posteriori estimated ICCs is necessary for a more objective reading: negative trial results may be the consequence of a loss of power due to a mis-specification of the ICC.

Figure 1

Real power of cluster randomized trials according to the discrepancy between the a priori postulated and a posteriori estimated intraclass correlation coefficients. The effect size to be detected is fixed at 0.25 and power at 80%. g is the number of clusters per arm, m is the average cluster size and N is the total number per intervention arm considering an a priori postulated ICC of 0.005 or 0.02.

Figure 2

Power contour graphs for several intraclass correlation coefficients (ICCs) and effect sizes*. Effect size is presented in columns and ICC in rows. In situations above or to the right of the red curve, the statistical power is greater than 90%. In situations between the red and blue curves, the statistical power is between 80% and 90%. In situations between the blue and red curves, the statistical power is between 60% and 80%. For vertical curves, increasing the cluster size is pointless. The number of subjects required, assuming individual randomization, is 24 to achieve a power of 40% to detect an effect size of 0.50, and 38, 28, 18 and 11 to achieve powers of 90%, 80%, 60% and 40%, respectively, to detect an effect size of 0.75, thus, the reason why curves are truncated. *Effect size = absolute difference between the two intervention-specific means divided by the S.D. of the response variable.

Figure 3

Theoretical maximal power assuming an infinite cluster size for several fixed numbers of clusters according to two different effect sizes *. *Effect size = absolute difference between the two intervention-specific means divided by the S.D. of the response variable.