TABLE A7.

Single Confounder Removal: simulation results for B(−X_j) with n = 500 using parametric estimation;

Variable	1	2	3	4	5
Setting 1
Truth	0.3610	0.2300	0.1880	0.1950	0.0260
Estimate	0.3650	0.2220	0.1880	0.1970	0.0290
Bias	−0.0040	0.0080	0.0000	−0.0020	−0.0020
ESE	0.0760	0.0770	0.0600	0.0560	0.0240
ASE	0.0758	0.0750	0.0596	0.0547	0.0247
Setting 2
Truth	0.6090	0.0110	0.3170	0.0180	0.0460
Estimate	0.5940	0.0220	0.3060	0.0320	0.0470
Bias	0.0150	−0.0110	0.0110	−0.0140	−0.0010
ESE	0.0930	0.0190	0.0870	0.0260	0.0360
ASE	0.0955	0.0226	0.0877	0.0298	0.0365
Setting 3
Truth	0.3910	0.1920	0.0440	0.3010	0.0710
Estimate	0.4390	0.1780	0.0300	0.3210	0.0320
Bias	−0.0480	0.0150	0.0140	−0.0200	0.0390
ESE	0.0790	0.0610	0.0250	0.0870	0.0270
ASE	0.0852	0.0621	0.0297	0.0858	0.0299
Setting 4
Truth	0.3100	0.2150	0.1940	0.1970	0.0840
Estimate	0.3640	0.2250	0.1860	0.1960	0.0280
Bias	−0.0540	−0.0090	0.0080	0.0010	0.0550
ESE	0.0750	0.0770	0.0600	0.0570	0.0240
ASE	0.0769	0.0762	0.0604	0.0559	0.0251

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)