Table 2.

Balance tables from simulation study: Mean Pearson correlation between confounders and exposure across 500 bootstrapped samples for various propensity score regression specifications under three different simulation conditions.

Propensity score form	No differential confounding: W included				No differential confounding: W omitted				Differential confounding: W omitted
	X1	X2	X3	W	X1	X2	X3	W	X1	X2	X3	W
	(J, nj) = (200, 20)
Unadjusted	0.260	−0.595	0.131	−0.257	0.260	−0.596	0.131	−0.257	0.260	−0.596	0.131	−0.257
SLM	0.067	−0.096	0.062	−0.065	0.051	−0.077	0.046	−0.405	0.011	−0.039	0.011	−0.398
FEM	0.081	−0.142	0.063	−0.079	0.080	−0.141	0.063	−0.080	0.047	−0.123	0.024	−0.045
REM	0.074	−0.123	0.060	−0.073	0.073	−0.123	0.058	−0.120	0.041	−0.104	0.019	−0.102
	(J, nj) = (20, 200)
Unadjusted	0.315	−0.244	0.157	−0.303	0.315	−0.245	0.157	−0.303	0.315	−0.245	0.157	−0.303
SLM	0.032	−0.028	0.025	−0.038	0.020	−0.017	0.013	−0.356	0.002	−0.001	−0.002	−0.358
FEM	0.048	−0.043	0.041	−0.049	0.049	−0.042	0.042	−0.049	0.009	−0.010	0.005	−0.015
REM	0.047	−0.042	0.040	−0.049	0.047	−0.041	0.041	−0.051	0.009	−0.009	0.005	−0.022
	(J, nj) = (5, 800)
Unadjusted	0.323	−0.243	0.162	−0.266	0.323	−0.243	0.162	−0.266	0.323	−0.243	0.162	−0.266
SLM	0.011	−0.008	0.006	−0.017	0.006	−0.004	0.004	−0.310	0.006	−0.004	0.004	−0.310
FEM	0.012	−0.013	0.008	−0.011	0.012	−0.013	0.008	−0.011	0.012	−0.013	0.008	−0.011
REM	0.012	−0.013	0.007	−0.011	0.012	−0.013	0.007	−0.013	0.012	−0.013	0.007	−0.013

Abbreviations: SLM = single level model, FEM = fixed effects model, REM = random effects model, J = number of clusters, n_j = number of individuals in each cluster, W = cluster-level covariate.