Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes

Table 3 Required sample size and empirical Type I error and power when using corrected variance inflation factors with an a priori hypothesized Pareto imbalance in cluster size – Effect size = 0.25

		No correction			Equal weights			Cluster size weights¹			Minimum variance weights
Intraclass correlation coefficient (ρ)	Number of clusters in each arm (g)	Sample size	Empirical probabilities		Sample size	Empirical probabilities		Sample size	Empirical probabilities		Sample size	Empirical probabilities
			Type I error	Power		Type I error	Power		Type I error	Power		Type I error	Power
0.005	5	485	0.0664	0.6432	1569	0.1028	0.8606	-	-	-	1037	0.0948	0.7992
	10	326	0.0566	0.6968	1057	0.0784	0.9386	515	0.0704	0.8106	464	0.0704	0.7806
	20	282	0.0486	0.7258	917	0.0624	0.9770	336	0.0450	0.7934	331	0.0458	0.7850
	40	265	0.0466	0.7572	861	0.0512	0.9918	287	0.0424	0.7842	286	0.0474	0.7706
0.02	10	629	0.0904	0.6236	2043	0.0638	0.8196	-	-	-	1731	0.0624	0.7968
	20	353	0.0660	0.6546	1147	0.0614	0.8924	1852	0.0576	0.9432	677	0.0752	0.7976
	40	290	0.0556	0.7008	942	0.0582	0.9486	435	0.0558	0.8092	401	0.0514	0.7960
0.05	20	743	0.0562	0.6256	2414	0.0564	0.8140	-	-	-	2165	0.0480	0.7976
	40	361	0.0604	0.6242	1173	0.0500	0.8598	-	-	-	770	0.0550	0.8048
0.10	40	652	0.0546	0.6006	2116	0.0542	0.8090	-	-	-	1881	0.0500	0.8036

Sample size calculations were performed considering type I and type II error rates fixed at 0.05 and 0.20, respectively.
¹ In some cases, 80% power was not reachable

ISSN: 1471-2288