Table 4.

Comparison of the semiparametric normal transformation model (4) based SPMLE estimator and the IPCW estimator at various time pairs (t₁, t₂) under univariate censoring. The true underlying models are the semiparametric normal transformation model (4) with ρ = 0.5, i.e. the working model is correctly specified, and Clayton’;s model (13) with θ = 4, i.e. the working model is misspecified. The true bivariate survival probabilities at the specified points are 0.7577, 0.6415 and 0.5568, respectively, and the averages of the relative biases are listed in the table.

True Underlying Model		(t1; t2) = (0.1625, 0.1625)			(t1; t2) = (0.1625, 0.3566)			(t1; t2) = (0.3566, 0.3566)
		bias	SEe	MSE	bias	SEe	MSE	bias	SEe	MSE
				(×10−3)			(×10−3)			(×10−3)
Semiparametric Normal	${\widehat{S}}_{\text{NT}}$	0.1%	0.040	1.60	0.0%	0.049	2.40	0.1%	0.050	2.50
Transformation Model	${\widehat{S}}_{\text{IP}}$	−0.1%	0.043	1.85	−0.1%	0.052	2.70	0.0%	0.055	3.03
Clayton Model	${\widehat{S}}_{\text{NT}}$	2.6%	0.031	1.41	3.3%	0.039	1.98	2.1%	0.042	1.90
	${\widehat{S}}_{\text{IP}}$	0%	0.041	1.68	0.3%	0.051	2.61	0%	0.053	2.81

${\widehat{S}}_{\text{NT}}$, the semiparametric maximum likelihood estimator based on the semiparametric normal transformation model; ${\widehat{S}}_{\text{IP}}$, the inverse-probability-of-censoring-weighted estimator; SE_e, the empirical standard error; MSE, the mean squared error.