Table 4.

Simulation results comparing the efficient and compatible TML, IPTW, and EE estimators of ${\mathrm{\Psi }}_{CSDE}$ under the weak instrument simulation scenario and correct model specification for various sample sizes. 1,000 simulations. Bias and MSE values are averages across the simulations. The estimator standard error $\times \sqrt{n}$ should be compared to the efficiency bound, which is 1.13.

Estimand	Bias	%Bias	$\text{SE}\times \sqrt{n}$	95%CI Cov	MSE	% Out of Bounds
N=5000
TMLE compatible	−0.000	−0.08	1.13	73.50	0.001	0.00
TMLE, efficient	−0.000	−0.07	1.13	73.50	0.001	0.00
IPTW	0.016	8.14	19.29	98.70	0.045	0.10
EE	−0.000	−0.07	1.13	74.40	0.001	0.00
N=500
TMLE compatible	0.008	3.53	1.38	74.60	0.010	0.10
TMLE, efficient	0.008	3.55	1.38	74.50	0.010	0.10
IPTW	0.057	27.05	28.51	99.90	0.964	18.80
EE	0.008	3.69	1.40	75.30	0.010	0.10
N=100
TMLE compatible	0.048	22.19	344.04	86.49	3.302	4.10
TMLE, efficient	0.112	50.95	1226.43	88.51	3.550	469
IPTW	−1.14 ×1012	−5.11 ×1014	5.37 ×1028	100.00	1.24 ×1027	53.10
EE	0.042	19.40	53.66	88.50	0.740	3.30