Table 3.

Averages and SEs for various estimators of the marginal survival functions S₁ and S₂ when the correct model (13) with θ = 4 is misspecified to the semiparametric normal model (4). The true marginal survival probabilities for both T₁ and T₂ are 0.850, 0.700 and 0.55, respectively.

		t1 = 0.1625			t1 = 0.3566			t1 = 0.5978
Censoring		bias	SE	MSE	bias	SE	MSE	Bias	SE	MSE
				(×10−3)			(×10−3)			(×10−3)
Censoring on T1 only	${\widehat{S}}_{\mathrm{E}}$	0.0%	0.036	1.3	0.0%	0.049	2.4	0.2%	0.063	3.9
	${\widehat{S}}_{\text{KM}}$	0.0%	0.036	1.3	0.1%	0.049	2.4	0.4%	0.064	4.1
	${\widehat{S}}_{\text{RE}}$	0.1%	0.036	1.3	0.2%	0.048	2.3	1.6%	0.060	3.7
	${\widehat{S}}_{\text{NT}}$	0.8%	0.031	1.0	2.7%	0.047	2.5	3.4%	0.065	4.6
			(0.036)			(0.050)			(0.062)
Univariate censoring	${\widehat{S}}_{\mathrm{E}}$	0.1%	0.043	1.8	0.1%	0.057	3.2	0.4%	0.071	5.0
censoring	${\widehat{S}}_{\text{KM}}$	0.0%	0.036	1.3	0.1%	0.049	2.4	0.4%	0.064	4.1
	${\widehat{S}}_{\text{RE}}$	0.1%	0.041	1.7	0.3%	0.054	2.9	1.1%	0.069	4.8
	${\widehat{S}}_{\text{NT}}$	0.6%	0.030	0.9	2.4%	0.046	2.4	3.4%	0.061	4.1
			(0.035)			(0.050)			(0.067)
Bivariate	${\widehat{S}}_{\mathrm{E}}$	−0.1%	0.048	2.3	0.1%	0.072	5.1	−0.4%	0.100	10.0
censoring	${\widehat{S}}_{\text{KM}}$	0.0%	0.035	1.2	0.3%	0.051	2.6	0.4%	0.064	4.1
	${\widehat{S}}_{\text{RE}}$	0.0%	0.047	2.2	0.6%	0.065	4.2	2.3%	0.069	4.9
	${\widehat{S}}_{\text{NT}}$	0.9%	0.031	1.0	1.9%	0.047	2.4	1.0%	0.063	4.0
			(0.035)			(0.051)			(0.065)

${\widehat{S}}_{\mathrm{E}}$, the empirical hazard rate estimator; ${\widehat{S}}_{\text{KM}}$, the Kaplan-Meier estimator; ${\widehat{S}}_{\text{RE}}$, the redistributed empirical estimator; ${\widehat{S}}_{\text{NT}}$, the semiparametric maximum likelihood estimator. SEs; empirical standard errors; for ${\widehat{S}}_{\text{NT}}$ the model based standard errors are displayed inside the brackets; only the estimates of the T₁-survival are reported, as similar patterns were observed for the estimates of the T₂-survival.