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Table 2 Design effects, sample sizes and powers for stepped-wedge cluster randomised trials (SW-CRTs) with varying average cluster size, number of steps and cluster size inequality

From: An imbalance in cluster sizes does not lead to notable loss of power in cross-sectional, stepped-wedge cluster randomised trials with a continuous outcome

Average cluster size Number of steps DE used Actual power (%) Type of imbalance
None (CVā€‰=ā€‰0) Moderate Poisson Pareto 60:40 Pareto 70:30 Pareto 80:20
DE Sample size Power (%) CV DE Sample size Power (%) CV DE Sample size Power (%) CV DE Sample size Power (%) CV DE Sample size Power (%) CV DE Sample size Power (%)
10 4 Woertman et al. 81.8 0.535 440 81.9 0.314 0.535 440 80.1 0.320 0.535 440 81.9 0.428 0.535 440 81.7 0.909 0.538 440 80.3 1.603 0.538 440 82.0
Cluster weights - 0.535 440 - 0.314 0.584 480 85.5 0.320 0.586 480 84.2 0.428 0.627 520 87.7 0.909 0.948 760 95.8 1.603 1.820 1440 99.9
Min. var. weights - 0.535 440 - 0.317 0.568 480 85.5 0.313 0.569 480 84.2 0.420 0.593 480 84.9 0.889 0.787 640 92.2 1.622 1.362 1080 99.3
20 3 Woertman et al. 83.5 0.767 660 84.0 0.222 0.767 660 83.4 0.223 0.757 660 82.6 0.446 0.767 660 82.8 0.911 0.767 660 83.6 1.594 0.767 660 83.5
Cluster weights - 0.767 660 - 0.222 0.816 660 83.4 0.223 0.816 660 82.6 0.446 0.966 780 88.6 0.911 1.597 1260 97.7 1.594 3.308 2640 100.0
Min. var. weights - 0.767 660 - 0.222 0.790 660 83.4 0.223 0.793 660 82.6 0.405 0.844 720 87.6 0.999 1.232 1020 95.0 1.624 1.970 1560 99.2
4 Woertman et al. 82.5 0.572 480 83.3 0.222 0.572 480 82.5 0.225 0.572 480 82.3 0.445 0.572 480 82.6 0.957 0.572 480 82.4 1.647 0.572 480 84.2
Cluster weights - 0.572 480 - 0.222 0.622 560 87.9 0.225 0.623 560 87.1 0.445 0.770 640 91.2 0.957 1.488 1200 99.5 1.647 3.285 2640 100.0
Min. var. weights - 0.572 480 - 0.201 0.592 480 82.5 0.221 0.596 480 82.3 0.450 0.670 560 88.2 0.933 0.979 800 95.3 1.557 1.789 1440 99.8
5 Woertman et al. 83.6 0.464 400 82.0 0.221 0.464 400 84.3 0.224 0.464 400 84.0 0.444 0.464 400 83.5 0.939 0.464 400 84.0 1.689 0.464 400 84.5
Cluster weights - 0.464 400 - 0.221 0.512 500 89.9 0.224 0.514 500 90.5 0.444 0.661 600 94.4 0.939 1.345 1100 99.8 1.689 3.316 2700 100.0
Min. var. weights - 0.464 400 - 0.219 0.488 400 84.3 0.221 0.488 400 84.0 0.435 0.552 500 90.0 0.866 0.848 700 96.9 1.803 1.739 1400 100.0
6 Woertman et al. 85.8 0.392 360 83.6 0.221 0.392 360 84.8 0.222 0.392 360 86.0 0.449 0.392 360 85.2 0.994 0.392 360 85.2 1.682 0.392 360 86.8
Cluster weights - 0.392 360 - 0.221 0.441 360 84.8 0.222 0.442 360 86.0 0.449 0.594 480 93.1 0.994 1.380 1200 100.0 1.682 3.221 2640 100.0
Min. var. weights - 0.392 360 - 0.244 0.423 360 84.8 0.229 0.416 360 86.0 0.516 0.516 480 93.1 0.977 0.823 720 100.0 1.742 1.691 1440 100.0
7 Woertman et al. 81.7 0.341 280 79.3 0.220 0.341 280 81.5 0.222 0.341 280 81.3 0.492 0.341 280 81.1 0.971 0.341 280 82.4 1.631 0.341 280 83.4
Cluster weights - 0.341 280 - 0.220 0.390 420 93.3 0.222 0.391 420 93.6 0.492 0.583 560 97.9 0.971 1.284 1120 100.0 1.631 3.001 2380 100.0
Min. var. weights - 0.341 280 - 0.225 0.365 420 93.3 0.227 0.366 420 93.6 0.498 0.451 420 92.8 1.002 0.819 700 99.4 1.527 1.468 1260 100.0
8 Woertman et al. 90.2 0.303 320 87.3 0.219 0.303 320 89.6 0.223 0.303 320 88.9 0.471 0.303 320 89.6 0.997 0.303 320 89.3 1.672 0.303 320 90.4
Cluster weights - 0.303 320 - 0.219 0.351 320 89.6 0.223 0.352 320 88.9 0.471 0.524 480 96.9 0.997 1.297 1120 100.0 1.672 3.098 2560 100.0
Min. var. weights - 0.303 320 - 0.239 0.328 320 89.6 0.227 0.327 320 88.9 0.482 0.411 480 96.9 1.037 0.733 640 99.4 1.646 1.536 1280 100.0
30 4 Woertman et al. 81.4 0.589 480 81.8 0.180 0.589 480 81.2 0.182 0.589 480 81.8 0.468 0.589 480 81.8 0.963 0.589 480 82.0 1.673 0.589 480 83.7
Cluster weights - 0.589 480 - 0.180 0.638 600 88.5 0.182 0.639 600 89.0 0.468 0.918 840 96.0 0.963 1.980 1560 99.9 1.673 4.788 3840 100.0
Min. var. weights - 0.589 480 - 0.168 0.605 480 81.2 0.196 0.612 600 89.0 0.467 0.706 600 88.1 0.905 1.053 840 95.8 1.676 2.158 1800 100.0
40 4 Woertman et al. 80.8 0.599 480 79.7 0.155 0.599 480 81.7 0.156 0.599 480 81.3 0.499 0.599 480 80.4 1.021 0.599 480 80.4 1.574 0.599 480 83.6
Cluster weights - 0.599 480 - 0.155 0.647 640 90.3 0.156 0.647 640 90.5 0.499 1.097 960 97.8 1.021 2.684 2240 100.0 1.574 5.554 4480 100.0
Min. var. weights - 0.599 480 - 0.141 0.610 480 81.7 0.147 0.612 640 90.5 0.416 0.703 640 89.8 1.066 1.213 960 97.5 1.763 2.249 1920 100.0
  1. Design effects (DE) and sample sizes calculated, and power estimated, for SW-CRTs with an average cluster size of 10, 20, 30 or 40, the number of steps ranging from three to eight and increasing imbalance in cluster size, using the Woertman et al. [7] and two proposed adjusted DEs. The type I error, power, intracluster correlation coefficient (ICC) and effect size were 0.05, 80%, 0.05 and 0.2, respectively. CV, coefficient of variation in cluster size