Table 3.

Simulation results comparing estimators of ${\mathrm{\Psi }}_{CSDE}$ under various model misspecifications for sample size N=5,000. 1,000 simulations. Estimation methods compared include IPTW, EE, efficient TMLE, and compatible TMLE. 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 1.10. 95% CI Coverage as determined by bootstrapping is denoted in parentheses for scenarios in which the Z model is misspecified.

Estimand	Bias	%Bias	$\text{SE}\times \sqrt{n}$	95%CI Cov	MSE
M model misspecified, N=5,000
TMLE, compatible	0.000	0.02	1.05	94.30	0.000
TMLE, efficient	0.000	0.02	1.05	94.30	0.000
IPTW	−0.024	−11.28	5.32	99.40	0.003
EE	0.000	0.08	1.05	94.20	0.000
Y model misspecified, N=5,000
TMLE, compatible	0.000	0.09	1.14	95.60	0.000
TMLE, efficient	0.000	0.09	1.14	95.60	0.000
IPTW	0.003	1.45	6.53	98.70	0.005
EE	0.000	0.06	1.19	96.10	0.000
M and Y models misspecified, N=5,000
TMLE, compatible	0.096	44.90	1.06	0.00	0.009
TMLE, efficient	0.096	44.90	1.06	0.00	0.009
IPTW	−0.024	−11.28	5.32	99.40	0.003
EE	0.095	44.74	1.06	0.00	0.009
Z models misspecified, N=5,000
TMLE, compatible	0.001	0.28	1.16	87.50 (92.90)	0.000
TMLE, efficient	0.012	6.28	1.38	83.10 (92.60)	0.001
IPTW	0.003	1.45	6.53	98.70	0.005
EE	0.001	0.26	1.16	88.30 (92.80)	0.000
Z and Y models misspecified, N=5,000
TMLE, compatible	0.066	33.64	1.16	2.60 (47.00)	0.005
TMLE, efficient	0.041	20.72	1.42	45.70 (46.90)	0.002
IPTW	0.003	1.45	6.53	98.70	0.005
EE	0.071	36.09	1.23	2.10 (38.30)	0.005