TABLE 2.

Results under Model 1b, with $\pi \left({\mathbf{X}}_i\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left(-0.3+0.2X_{1i}+0.6X_{5i}\right)/\left\{1+\mathrm{e}\mathrm{x}\mathrm{p}\left(-0.3+0.2X_{1i}+0.6X_{5i}\right)\right\}$ and L = 42

c	$n$	${\mu }_{\text{IPW}}$	${\mu }_{\text{AIPW}}$	${\mu }_{\text{CAIPW}}$	${\sigma }_{\text{IPW}}$	${\sigma }_{\text{AIPW}}$	${\sigma }_{\text{CAIPW}}$	$1-{\beta }_{\text{IPW}}/{\alpha }_{\text{IPW}}$	$1-{\beta }_{\text{AIPW}}/{\alpha }_{\text{AIPW}}$	$1-{\beta }_{\text{CAIPW}}/{\alpha }_{\text{CAIPW}}$
1.25	600	2.82	3.08	5.79	1.08	1.06	1.09	0.86	0.91	1.00
1.25	1000	3.82	4.03	7.56	1.03	1.02	1.14	0.98	0.99	1.00
0.75	600	1.85	2.09	3.71	1.08	1.06	1.05	0.57	0.67	0.97
0.75	1000	2.50	2.73	4.92	1.03	1.05	1.08	0.82	0.86	1.00
0.50	600	1.18	1.38	2.42	1.08	1.06	1.04	0.33	0.42	0.77
0.50	1000	1.68	1.87	3.27	1.06	1.05	1.04	0.53	0.58	0.95
0.00	600	−0.18	−0.03	−0.09	1.10	1.06	1.00	0.06	0.05	0.03
0.00	1000	−0.15	−0.03	−0.04	1.08	1.03	0.98	0.05	0.06	0.05
−0.50	600	−0.40	−0.22	−0.27	1.05	1.03	1.01	0.03	0.04	0.03
−0.50	1000	−0.33	−0.14	−0.19	1.03	0.97	0.98	0.03	0.03	0.03
−1.00	600	−0.32	−0.13	−0.14	1.07	1.10	1.07	0.02	0.06	0.05
−1.00	1000	−0.21	0.05	0.04	1.01	0.99	0.98	0.02	0.05	0.05

Note: Mean ($\mu$), standard deviation ($\sigma$), and power or type I error ($1-\beta /\alpha$) of the one-step value difference test statistic is based on 500 simulated data sets of n = {600, 1000}. Subscripts IPW, AIPW, and CAIPW specify whether the results are based on $T_{\text{IPW,SBT}}^S$,$T_{\text{AIPW, SBT}}^S$, or $T_{\text{CAIPW, SBT}}^S$, respectively. Largest standard error for $\mu$ and $\sigma$, and $1-\beta /\alpha$ is 0.05 and 0.08, and 0.02, respectively.