TABLE 3.

The mean percent (%) biases, average standard errors (ASE), empirical standard errors (ESE), and coverage probabilities (CP) are given for 1000 simulated datasets for the proposed method and naive method with β_X1 = log(1.5), β_Z1 = log(0.7), and β_Z2 = log(1.3); e is distributed as either a t with 4 df or as $.4\mathcal{N}(0,1)+.6\mathcal{N}(2,1.5)$

Sea = 0.80, Spb = 0.90			Proposed				Naive
e c	CR d	β	% Bias	ASE	ESE	CP	% Bias	ASE	ESE	CP
t e	0.90	β X1	−2.238	0.291	0.300	0.953	−94.50	0.031	0.031	0.000
		β Z1	0.622	0.152	0.157	0.951	−81.80	0.054	0.054	0.000
		β Z2	2.529	0.152	0.148	0.957	−76.70	0.054	0.053	0.033
	0.55	β X1	−0.646	0.140	0.153	0.940	−85.54	0.025	0.026	0.000
		β Z1	−2.362	0.072	0.072	0.950	−53.37	0.045	0.044	0.013
		β Z2	−3.303	0.071	0.072	0.950	−39.35	0.044	0.044	0.335
mix f	0.90	β X1	0.394	0.335	0.330	0.955	−95.64	0.027	0.028	0.000
		β Z1	−1.015	0.158	0.158	0.953	−83.29	0.054	0.055	0.000
		β Z2	−0.800	0.156	0.152	0.962	−75.25	0.054	0.056	0.055
	0.55	β X1	−1.081	0.156	0.151	0.958	−88.74	0.022	0.022	0.000
		β Z1	−2.415	0.074	0.070	0.958	−55.28	0.044	0.045	0.010
		β Z2	−2.083	0.073	0.070	0.964	−36.40	0.044	0.045	0.419
Se = 0.90, Sp = 0.80			Proposed				Naive
${\widehat{\mathit{\delta }}}_{\mathbf{(}\mathbf{1}\mathbf{)}}$	CR	β	% Bias	ASE	ESE	CP	% Bias	ASE	ESE	CP
t	0.90	β X1	−3.792	0.305	0.316	0.942	−96.91	0.025	0.025	0.000
		β Z1	1.848	0.160	0.165	0.948	−89.40	0.044	0.044	0.000
		β Z2	3.386	0.159	0.158	0.959	−86.97	0.044	0.044	0.000
	0.55	β X1	−1.119	0.141	0.159	0.933	−90.02	0.023	0.024	0.000
		β Z1	−1.666	0.073	0.073	0.940	−67.86	0.040	0.040	0.000
		β Z2	−3.048	0.072	0.074	0.944	−58.35	0.040	0.040	0.031
mix	0.90	β X1	−0.975	0.350	0.346	0.952	−97.65	0.022	0.024	0.000
		β Z1	−1.354	0.166	0.162	0.961	−90.94	0.043	0.044	0.000
		β Z2	0.585	0.164	0.160	0.955	−86.57	0.043	0.045	0.000
	0.55	β X1	−1.904	0.159	0.155	0.955	−92.26	0.020	0.021	0.000
		β Z1	−2.590	0.075	0.072	0.954	−69.29	0.040	0.040	0.000
		β Z2	−1.350	0.074	0.069	0.967	−56.67	0.040	0.039	0.036
Se = 1, Sp = 1			Truth
	CR	β	% Bias	ASE	ESE	CP
	0.90	β X1	0.002	0.108	0.106	0.959
		β Z1	0.034	0.108	0.109	0.951
		β Z2	1.032	0.107	0.106	0.961
	0.55	β X1	0.395	0.053	0.052	0.952
		β Z1	−0.462	0.052	0.052	0.948
		β Z2	−0.300	0.052	0.050	0.954

^aSe = Sensitivity.

^bSp = Specificity.

^ce refers to the distribution of the error.

^dCR = True censoring rate.

^et with 4 df.

^fMixture of two normals, that is, $.4\mathcal{N}(0,1)+.6\mathcal{N}(2,1.5)$.