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

Kristunas, Caroline A.; Smith, Karen L.; Gray, Laura J.

doi:10.1186/s13063-017-1832-8

Trials

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 (CV = 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

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

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