Table 2.

Results from testing for a difference in survival at time t = 2 years between the two treatment groups using a Kaplan Meier estimator, Δ̂_KM(t), the proposed estimator using Z information only, Δ̂^Z(t), T_𝕊 information only, ${\mathrm{\Delta ̂}}_{\mathrm{L}\mathrm{M}}^{T_{𝕊}}(t)$, Z and T_𝕊 information, ${\mathrm{\Delta ̂}}_{\mathrm{L}\mathrm{M}}^{\mathbf{W}}(t)$, and the augmented estimator, ${\mathrm{\Delta ̂}}_{\mathrm{A}\mathrm{U}\mathrm{G}}^{\mathbf{W}}(t)$ with corresponding empirical standard error (ESE), average of the standard error estimates from the perturbation-resampling method (ASE), efficiency relative to Ŝ_KM(t) with respect to MSE, and power.

	Δ̂KM(t)	Δ̂Z(t)	${\mathrm{\Delta ̂}}_{\mathrm{L}\mathrm{M}}^{T_{𝕊}}(t)$	${\mathrm{\Delta ̂}}_{\mathrm{L}\mathrm{M}}^{\mathrm{W}}(t)$	${\mathrm{\Delta ̂}}_{\mathrm{A}\mathrm{U}\mathrm{G}}^{\mathrm{W}}(t)$
Setting (i), no treatment difference
Estimate	−0.0002	−0.0002	−0.0004	−0.0001	0.0003
ESE	0.0323	0.0318	0.0316	0.0300	0.0282
ASE	0.0326	0.0308	0.0309	0.0291	0.0267
REMSE	-	1.12	1.12	1.26	1.49
α	0.0415	0.0462	0.0544	0.0467	0.0538
Setting (ii), small treatment difference
Estimate	0.0525	0.0519	0.0520	0.0523	0.0525
ESE	0.0318	0.0312	0.0312	0.0292	0.0276
ASE	0.0323	0.0305	0.0306	0.0287	0.0263
REMSE	-	1.12	1.11	1.27	1.51
Power	0.3740	0.4110	0.4060	0.4570	0.5200
Setting (iii), large treatment difference
Estimate	0.0954	0.0942	0.0947	0.0952	0.0952
ESE	0.0317	0.0312	0.0310	0.0288	0.0270
ASE	0.0320	0.0301	0.0303	0.0283	0.0259
REMSE	-	1.13	1.11	1.27	1.53
Power	0.8460	0.8690	0.8650	0.9090	0.9410