Table 4.

Average percent bias, empirical SE, and CP of the 95 CI of , and across 1000 simulation replicates

No. of testing sites	Testing site size	Method
			Bias (SE)	CP	Bias (SE)	CP	Bias (SE)	CP	Bias (SE)	CP
50	30	IndCov	0.2 (0.134)	0.964	0.8 (0.110)	0.992	3.9 (0.124)	0.976	0.0 (0.071)	0.952
		ExchCov	0.6 (0.125)	0.958	2.5 (0.075)	0.971	1.1 (0.085)	0.952	0.4 (0.094)	0.958
		ExchTwoS	0.1 (0.066)	0.949	0.1 (0.067)	0.944	0.4 (0.075)	0.938	0.1 (0.053)	0.945
50	60	IndCov	0.1 (0.088)	0.965	0.7 (0.077)	0.991	4.1 (0.087)	0.980	0.0 (0.051)	0.950
		ExchCov	0.5 (0.085)	0.958	1.5 (0.055)	0.961	1.3 (0.057)	0.966	0.3 (0.067)	0.955
		ExchTwoS	0.1 (0.045)	0.955	0.1 (0.045)	0.956	0.8 (0.050)	0.939	0.0 (0.039)	0.946
100	30	IndCov	0.5 (0.089)	0.937	5.0 (0.079)	0.983	4.2 (0.086)	0.967	0.1 (0.048)	0.948
		ExchCov	0.2 (0.082)	0.949	3.6 (0.056)	0.958	2.2 (0.059)	0.945	0.3 (0.063)	0.957
		ExchTwoS	0.1 (0.046)	0.959	1.2 (0.051)	0.952	0.8 (0.055)	0.940	0.2 (0.037)	0.961
100	60	IndCov	0.4 (0.059)	0.953	5.1 (0.052)	0.978	3.8 (0.056)	0.969	0.1 (0.035)	0.939
		ExchCov	0.1 (0.057)	0.954	3.2 (0.039)	0.941	1.8 (0.040)	0.953	0.2 (0.045)	0.956
		ExchTwoS	0.2 (0.033)	0.948	0.9 (0.034)	0.940	0.4 (0.035)	0.955	0.0 (0.027)	0.950

A mixed-effects model is used to estimate the treatment probability and the effects of cluster-level unmeasured confounder on the treatment are generated from a skewed normal distribution with location parameter to be 1, scale parameter being 0.1 and shape parameter equals to 100. For the one-stage method, we consider the following situations: (1) using a working independent covariance matrix (IndCov); (2) using a working exchangeable covariance matrix for within subject correlation and assume independence between subjects (ExchCov). For the two-stage method, we consider using a working exchangeable covariance matrix for the first stage cluster-specific MSMs and combine the results using mixed-effects meta-analysis (ExchTwoS).