Table 4.

Estimate of the treatment effect in the Scenario with a strong 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	1.180	1.937	0.146	0.198	1.189	1.947	0.000	0.000
	stan	0.005	0.001	0.083	0.094	0.083	0.094	0.987	0.988
	IPW	0.079	0.075	0.612	0.614	0.617	0.618	0.841	0.866
	match	0.213	0.214	0.143	0.161	0.256	0.267	0.747	0.796
	BCM	0.039	0.007	0.131	0.147	0.136	0.147	0.976	0.983
	TMLE	0.006	0.002	0.102	0.118	0.102	0.118	0.951	0.959
	OW	0.012	0.006	0.131	0.142	0.131	0.143	0.990	0.990
	A-OW	0.006	0.003	0.096	0.107	0.096	0.107	0.948	0.959
Inc.param.	stan	−0.121	−0.039	0.098	0.113	0.155	0.120	0.785	0.928
	IPW	0.209	0.181	0.174	0.195	0.272	0.266	0.621	0.755
	match	0.132	0.118	0.121	0.136	0.179	0.180	0.799	0.869
	BCM	0.091	0.045	0.119	0.136	0.149	0.143	0.887	0.940
	TMLE	0.159	0.112	0.131	0.155	0.206	0.191	0.767	0.892
	OW	0.117	0.099	0.109	0.118	0.160	0.154	0.812	0.865
	A-OW	0.065	0.062	0.101	0.116	0.120	0.131	0.898	0.920
M.Learning	stan	0.005	0.014	0.090	0.105	0.090	0.106	0.938	0.940
	IPW	0.159	0.138	0.185	0.200	0.244	0.244	0.720	0.801
	match	0.124	0.111	0.122	0.138	0.174	0.177	0.819	0.875
	BCM	0.010	0.008	0.118	0.135	0.119	0.136	0.953	0.956
	TMLE	0.016	0.006	0.106	0.123	0.108	0.124	0.939	0.945
	OW	0.080	0.067	0.110	0.121	0.136	0.138	0.893	0.912
	A-OW ${}^{\ast }$	0.003	−0.001	0.098	0.108	0.098	0.108	0.937	0.952

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. *: in 1 replication, the confidence intervals could not be computed.