TABLE A11.

Single Confounder Removal: simulation results for B(−X_j) using parametric estimation with n = 2000 under alternative settings;

Variable	1	2	3	4	5
Setting 5
Truth	0.0040	0.3000	0.0830	0.3040	0.3090
Estimate	0.0070	0.3060	0.0780	0.3050	0.3050
Bias	−0.0020	−0.0060	0.0050	0.0000	0.0040
ESE	0.0060	0.0300	0.0190	0.0310	0.0300
ASE	0.0067	0.0313	0.0193	0.0313	0.0312
Setting 6
Truth	0.1950	0.2810	0.2360	0.2580	0.0300
Estimate	0.1890	0.2850	0.2410	0.2520	0.0330
Bias	0.0050	−0.0040	−0.0040	0.0060	−0.0030
ESE	0.0360	0.0480	0.0390	0.0350	0.0170
ASE	0.0384	0.0487	0.0383	0.0356	0.0166
Setting 7
Truth	0.3960	0.2490	0.2180	0.1110	0.0270
Estimate	0.4050	0.2570	0.2150	0.1080	0.0140
Bias	−0.0090	−0.0080	0.0020	0.0020	0.0130
ESE	0.0410	0.0430	0.0330	0.0260	0.0100
ASE	0.0412	0.0426	0.0333	0.0253	0.0095
Setting 8
Truth	0.4300	0.1310	0.3430	0.0490	0.0480
Estimate	0.5130	0.0950	0.3500	0.0290	0.0130
Bias	−0.0830	0.0360	−0.0070	0.0190	0.0350
ESE	0.0910	0.0660	0.0840	0.0210	0.0110
ASE	0.0938	0.0764	0.0823	0.0269	0.0127

ESE = empirical standard error (standard deviation of estimates across the 1,000 replications); ASE = average standard error (average of standard error estimates across the 1,000 replications obtained using bootstrapping)