Table III.

Results of the 100,000 simulated randomized trials of size n = 1044 patients based on resampling from the PEARLS trial. For each of the seven adjusted estimators, relative efficiency is defined as the variance of the unadjusted estimator divided by the variance of the adjusted estimator.

Estimator	Bias	Variance	MSE	Rel.Efficiency
Scenario 1: Y and W dependent; zero average treatment effect
Unadjusted	−0.000087	0.00055	0.00055	1.000
IPW	−0.000071	0.00054	0.00054	1.020
Model standardization	−0.000075	0.00054	0.00054	1.020
DR-WLS	−0.000075	0.00054	0.00054	1.020
Tan	−0.000079	0.00054	0.00054	1.030
PLEASE	−0.000068	0.00054	0.00054	1.020
Rotnitzky et al.K=1	−0.000078	0.00054	0.00054	1.030
Gruber and van der Laan	−0.000080	0.00054	0.00054	1.020
Scenario 2: Y and W dependent; positive average treatment effect
Unadjusted	0.000052	0.00062	0.00062	1.000
IPW	0.000044	0.00061	0.00061	1.020
Model standardization	0.000040	0.00061	0.00061	1.020
DR-WLS	0.000048	0.00061	0.00061	1.020
Tan	0.000053	0.00061	0.00061	1.020
PLEASE	0.000070	0.00061	0.00061	1.020
Rotnitzky et al.K=1	0.000054	0.00061	0.00061	1.020
Gruber and van der Laan	0.000096	0.00061	0.00061	1.020
Scenario 3: Y and W independent; zero average treatment effect
Unadjusted	0.00011	0.00056	0.00056	1.000
IPW	0.00010	0.00056	0.00056	0.997
Model standardization	0.00010	0.00056	0.00056	0.997
DR-WLS	0.00010	0.00056	0.00056	0.997
Tan	0.00011	0.00056	0.00056	0.995
PLEASE	0.000091	0.00056	0.00056	0.992
Rotnitzky et al.K=1	0.00010	0.00056	0.00056	0.991
Gruber and van der Laan	0.00013	0.00056	0.00056	0.998
Scenario 4: Y and W independent; positive average treatment effect
Unadjusted	0.000011	0.00055	0.00055	1.000
IPW	0.0000034	0.00056	0.00056	0.997
Model standardization	0.0000023	0.00056	0.00056	0.997
DR-WLS	0.0000039	0.00056	0.00056	0.997
Tan	0.0000044	0.00056	0.00056	0.995
PLEASE	0.000018	0.00056	0.00056	0.993
Rotnitzky et al.K=1	0.000011	0.00056	0.00056	0.991
Gruber and van der Laan	0.000025	0.00055	0.00055	1.000