Table 1.

Empirical characteristics of β̂₁ in 1000 simulations with n = 100 in the Assay-comparison study and n₁ = n₂ = 250 in the Main case-control study for models regressing D on the underlying X (True), the normalized X̃ (RC) and the raw error-prone W (Naïve).

${\tau }_1^2$	${\tau }_2^2$	δ2	eβ1	Bias			MSE			Coverage
				True	RC	Naïve	True	RC	Naïve	True	RC	Naïve
0.1	0.1	0	2.0	0.02	0.01	−0.05	0.03	0.03	0.03	0.96	0.96	0.94
	0.5			0.02	−0.01	−0.15	0.03	0.03	0.04	0.96	0.96	0.81
	1.0			0.02	−0.02	−0.24	0.03	0.04	0.07	0.96	0.96	0.56
0.5	0.5			0.02	−0.02	−0.22	0.03	0.04	0.07	0.96	0.96	0.62
	1.0			0.02	−0.03	−0.29	0.03	0.04	0.10	0.96	0.95	0.35
1.0	1.0			0.02	−0.05	−0.34	0.03	0.05	0.13	0.96	0.94	0.19
0.1	0.1		5.0	0.05	0.00	−0.10	0.06	0.06	0.06	0.96	0.96	0.90
	0.5			0.05	−0.08	−0.34	0.06	0.06	0.15	0.96	0.93	0.54
	1.0			0.05	−0.14	−0.54	0.06	0.08	0.32	0.96	0.88	0.16
0.5	0.5			0.05	−0.15	−0.51	0.06	0.08	0.29	0.96	0.87	0.20
	1.0			0.05	−0.21	−0.67	0.06	0.10	0.47	0.96	0.81	0.04
1.0	1.0			0.05	−0.26	−0.79	0.06	0.13	0.64	0.96	0.74	0.00
0.1	0.1	0.5	2.0	0.02	0.01	−0.08	0.03	0.03	0.03	0.96	0.96	0.92
	0.5			0.02	−0.01	−0.18	0.03	0.03	0.05	0.96	0.96	0.74
	1.0			0.02	−0.02	−0.26	0.03	0.04	0.09	0.96	0.96	0.45
0.5	0.5			0.02	−0.02	−0.24	0.03	0.04	0.08	0.96	0.96	0.54
	1.0			0.02	−0.03	−0.31	0.03	0.04	0.11	0.96	0.95	0.28
1.0	1.0			0.02	−0.05	−0.35	0.03	0.05	0.14	0.96	0.94	0.16
0.1	0.1		5.0	0.05	0.00	−0.19	0.06	0.06	0.08	0.96	0.96	0.82
	0.5			0.05	−0.08	−0.42	0.06	0.06	0.21	0.96	0.93	0.35
	1.0			0.05	−0.14	−0.62	0.06	0.08	0.41	0.96	0.88	0.06
0.5	0.5			0.05	−0.15	−0.56	0.06	0.08	0.34	0.96	0.87	0.13
	1.0			0.05	−0.21	−0.72	0.06	0.10	0.54	0.96	0.81	0.02
1.0	1.0			0.05	−0.26	−0.81	0.06	0.13	0.68	0.96	0.74	0.00
0.1	0.1	1.0	2.0	0.02	0.01	−0.17	0.03	0.03	0.05	0.96	0.96	0.79
	0.5			0.02	−0.01	−0.25	0.03	0.03	0.08	0.96	0.96	0.51
	1.0			0.02	−0.02	−0.32	0.03	0.04	0.11	0.96	0.96	0.24
0.5	0.5			0.02	−0.02	−0.29	0.03	0.04	0.10	0.96	0.96	0.34
	1.0			0.02	−0.03	−0.35	0.03	0.04	0.13	0.96	0.95	0.16
1.0	1.0			0.02	−0.05	−0.38	0.03	0.05	0.16	0.96	0.94	0.08
0.1	0.1		5.0	0.05	0.00	−0.39	0.06	0.06	0.18	0.96	0.96	0.42
	0.5			0.05	−0.08	−0.59	0.06	0.06	0.37	0.96	0.93	0.08
	1.0			0.05	−0.14	−0.75	0.06	0.08	0.58	0.96	0.88	0.01
0.5	0.5			0.05	−0.15	−0.67	0.06	0.08	0.47	0.96	0.87	0.03
	1.0			0.05	−0.21	−0.81	0.06	0.10	0.68	0.96	0.81	0.00
1.0	1.0			0.05	−0.26	−0.88	0.06	0.13	0.79	0.96	0.74	0.00

Note: ${\tau }_1^2$ and ${\tau }_2^2$ are the measurement error variances from Lab 1 and Lab 2, respectively; δ₂ is the mean of the measurement error from Lab 2, and Lab 1 is regarded as the reference(i.e., δ₁ = 0); e^β₁ is the odds ratio of one increment increase of X from the underlying logistic regression model.