Comparison of Bayesian and classical methods in the analysis of cluster randomized controlled trials with a binary outcome: The Community Hypertension Assessment Trial (CHAT)

Table 2 Comparison of Nine Methods with and without Adjustment for Covariates

Unit of Analysis	Method of Analysis	Unadjusted for Covariates		Adjusted for Covariates
		OR	95% CI	OR	95% CI
Cluster	Un-weighted Regression	1.05	(0.59 1.87)	1.05	(0.60 1.84)
	Weighted Regression	1.27	(0.81 1.99)	1.27	(0.82 1.96)
	Random-effects Meta Regression	1.05	(0.60 1.85)	1.05	(0.61 1.82)
Individual	Standard Logistic Regression	1.14	(0.93 1.39)	1.17	(0.95 1.44)
	Robust Standard Error	1.14	(0.72 1.80)	1.17	(0.79 1.73)
	Generalized Estimating Equations **	1.14	(0.72 1.80)	1.15	(0.76 1.72)
	Modified GEE (1) ***	1.14	(0.71 1.83)
	Modified GEE (2) ****	1.14	(0.71 1.84)
	Random-effects Meta Analysis	1.09	(0.68 1.74)	1.12	(0.73 1.70)
	Random-effects Logistic Regression	1.10	(0.65 1.86)	1.13	(0.71 1.80)
	Bayesian Random-effects Regression	1.12	(0.64 1.95)	1.13	(0.68 1.87)

OR = odds ratio; CI = confidence interval
* For the cluster level analysis, include 'center' (i.e. Hamilton and Ottawa) as the covariate; for the individual level analysis, include 'diabetes at baseline', 'heart disease at baseline', and 'BP controlled at baseline' as the covariates.
** The intra-cluster correlation coefficient (ICC) estimated from GEE are 0.077 and 0.054 when unadjusted for covariates and adjusted for covariates respectively.
*** The confidence interval was calculated based on the corrected standard error which was equal to the sandwich standard error estimator multiply by , where J is the number of clusters in each arm.
**** The Confidence interval was calculated based on the quantiles from the t-distribution with 2(J-1) degrees of freedom instead of quantiles from the standard normal distribution.