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

Table 4 Comparison of coverage probability

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%	0.91	0.96
				15%	0.92	0.97	0.93	0.97	1.00	0.99
				30%	0.93	0.97	0.95	0.98	1.00	0.99
		0.01	5.99	0%	0.92	0.79
				15%	0.92	0.81	0.90	0.87	0.95	0.91
				30%	0.94	0.84	0.88	0.84	0.98	0.93
		0.05	25.95	0%	0.91	0.49
				15%	0.91	0.52	0.89	0.83	0.93	0.89
				30%	0.93	0.52	0.83	0.77	0.96	0.90
20 (L-Design)	50	0.01	1.49	0%	0.94	0.98
				15%	0.94	0.98	0.93	0.95	0.96	0.97
				30%	0.94	0.98	0.92	0.96	0.98	0.98
		0.05	3.45	0%	0.93	0.91
				15%	0.93	0.92	0.90	0.89	0.94	0.94
				30%	0.93	0.93	0.87	0.88	0.95	0.96
		0.1	5.90	0%	0.93	0.78
				15%	0.93	0.82	0.89	0.88	0.93	0.93
				30%	0.92	0.83	0.85	0.85	NA	NA
30 (L-Design)	30	0.05	2.45	0%	0.95	0.95
				15%	0.96	0.96	0.93	0.93	0.97	0.96
				30%	0.95	0.96	0.91	0.92	NA	NA
		0.1	3.90	0%	0.95	0.91
				15%	0.95	0.93	0.92	0.92	NA	NA
				30%	0.95	0.94	0.89	0.90	NA	NA
		0.2	6.80	0%	0.94	0.79
				15%	0.94	0.81	0.90	0.89	NA	NA
				30%	0.94	0.85	0.85	0.85	NA	NA

Coverage probability is defined as the proportion of times that the nominal 95% confidence interval contains the true treatment effect across all simulation replications. Coverage probabilities 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: Intra-cluster 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.