Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcomes: a simulation study

Table 3 Comparison of root mean squared error

Design of CRTs			VIF⁴	% of missing data	Complete case analysis		Standard MI⁵		Within-cluster MI⁶
m¹	n²	ρ³	VIF⁴	% of missing data	GEE⁷	RELR⁸	GEE	RELR	GEE	RELR
5 ⁹ (S-Design)	500	0.001	1.499	0%	0.07	0.10
				15%	0.08	0.10	0.08	0.06	0.08	0.06
				30%	0.08	0.11	0.08	0.07	0.09	0.08
		0.01	5.99	0%	0.14	0.17
				15%	0.14	0.17	0.15	0.15	0.15	0.15
				30%	0.15	0.17	0.15	0.15	0.15	0.15
		0.05	25.95	0%	0.31	0.34
				15%	0.31	0.34	0.31	0.32	0.31	0.33
				30%	0.31	0.34	0.31	0.32	0.31	0.33
20 (L-Design)	50	0.01	1.49	0%	0.11	0.13
				15%	0.11	0.13	0.12	0.12	0.12	0.12
				30%	0.12	0.14	0.14	0.12	0.13	0.13
		0.05	3.45	0%	0.18	0.20
				15%	0.18	0.21	0.18	0.19	0.18	0.19
				30%	0.19	0.20	0.19	0.20	0.19	0.20
		0.1	5.90	0%	0.24	0.26
				15%	0.24	0.27	0.24	0.26	0.24	0.27
				30%	0.25	0.27	0.25	0.26	NA	NA
30 (L-Design)	30	0.05	2.45	0%	0.15	0.17
				15%	0.16	0.18	0.16	0.16	0.15	0.17
				30%	0.16	0.17	0.16	0.17	NA	NA
		0.1	3.90	0%	0.20	0.21
				15%	0.20	0.22	0.20	0.22	NA	NA
				30%	0.20	0.23	0.21	0.22	NA	NA
		0.2	6.80	0%	0.27	0.30
				15%	0.27	0.30	0.28	0.33	NA	NA
				30%	0.28	0.30	0.28	0.31	NA	NA

Root mean squared error is defined as the square root of the mean squared error, which is the average squared difference between the estimated treatment effect and the true parameter. The root mean squared errors obtained when 0% data are missing are considered as references for comparing with those obtained when 15% or 30% data are missing.
Note:1. m: Number of clusters per trial arm.2. n: Number of subjects per cluster.
3. ρ: Intracluster correlation coefficient; 4. VIF: Variance inflation factor, i.e. 1+(m-1)ρ; 5. Standard MI: Standard multiple imputation using logistic regression method.
6. Within-cluster MI: Within-cluster multiple imputation using logistic regression method, which is not applicable (NA) for some L-design of cluster randomized trials.
7. GEE: Generalized estimating equations.8. RELR: Random-effects logistic regression.
9. For CRTs with 5 clusters per arm, modified standard errors are provided.

ISSN: 1471-2288