Table 3.

Estimate of the treatment effect in the Scenario with a weak association between covariates and treatment, a strong association between covariates and outcome ( $T-Y+$), and a sample size of 1000.

		Bias		Std		RMSE		Coverage IC
Implementation	Approach	${\hat{\tau }}_{21}$	${\hat{\tau }}_{31}$	${\hat{\tau }}_{21}$	${\hat{\tau }}_{31}$	${\hat{\tau }}_{21}$	${\hat{\tau }}_{31}$	${\hat{\tau }}_{21}$	${\hat{\tau }}_{31}$
Cor.param.	Crude	0.564	0.819	0.173	0.192	0.590	0.841	0.125	0.009
	stan	0.001	0.002	0.081	0.082	0.081	0.082	0.984	0.986
	IPW	0.005	0.008	0.149	0.151	0.149	0.151	0.997	0.995
	match	0.037	0.039	0.110	0.110	0.116	0.117	0.983	0.979
	BCM	0.004	0.002	0.106	0.107	0.106	0.107	0.985	0.990
	TMLE	0.002	0.003	0.084	0.085	0.084	0.085	0.953	0.960
	OW	−0.001	0.002	0.111	0.115	0.111	0.115	0.999	0.998
	A-OW	0.001	0.002	0.083	0.084	0.083	0.084	0.940	0.943
Inc.param.	stan	0.046	0.057	0.096	0.097	0.107	0.112	0.922	0.905
	IPW	0.092	0.087	0.104	0.104	0.140	0.136	0.882	0.898
	match	0.032	0.034	0.097	0.099	0.102	0.105	0.953	0.955
	BCM	0.024	0.022	0.096	0.098	0.099	0.100	0.959	0.958
	TMLE	0.076	0.077	0.100	0.102	0.126	0.128	0.890	0.902
	OW	0.083	0.078	0.100	0.100	0.130	0.127	0.893	0.908
	A-OW	0.068	0.069	0.097	0.098	0.118	0.120	0.870	0.885
M.Learning	stan	0.001	0.005	0.084	0.085	0.084	0.085	0.926	0.941
	IPW	0.101	0.079	0.106	0.105	0.146	0.132	0.857	0.905
	match	0.034	0.019	0.108	0.108	0.113	0.110	0.940	0.954
	BCM	−0.003	0.001	0.099	0.101	0.099	0.101	0.960	0.965
	TMLE	0.004	0.007	0.085	0.086	0.085	0.086	0.957	0.955
	OW	0.091	0.070	0.102	0.102	0.137	0.124	0.868	0.907
	A-OW	0.002	0.006	0.084	0.085	0.085	0.086	0.933	0.941

Note: Cor.param=correct parametric models, Inc.param=incorrect parametric models, M.Learning=machine learning, Crude=Unadjusted, stan=standardization, IPW=inverse probability weighting, match=matching, BCM=bias-corrected matching, TMLE=targeted maximum likelihood, OW=overlap weights, A-OW=augmented overlap weights.