Table 4.

Simulation results for Poisson regression: E(Y|X) = exp(β₀ + β₁X), where X = L + U_b; W = L + U_c; β = (0.5, ln(2))′; M = 1 − 2L + V; Q = −1 + 2X + ∊; θ is the proportion of the calibration data; L ~ N(0.5,1); U_b ~ N(0,${\sigma }_b^2$) is the Berkson error; U_c ~ N(0,${\sigma }_c^2$) is the classical error; V ~ N(0,1); ∊ ~ N(0,1); n = 500; Naive, “naive” regression replacing X by W;RC1, Regression calibration approach replacing X by its conditional expectation given W; RC2, Regression calibration approach replacing X by its conditional expectation given W and Q, M in the calibration sample; SIMEX, simulation extrapolation procedure; EEE, Expected estimating equation method.

				${\sigma }_c^2$ = 0.3					${\sigma }_c^2$ = 0.5
θ	${\sigma }_b^2$	β		Naive	RC1	RC2	SIMEX	EEE	Naive	RC1	RC2	SIMEX	EEE
0.5	0.2	β 0	Bias	0.183	0.103	0.075	0.010	0.002	0.242	0.124	0.086	0.022	−0.001
			SD	0.048	0.054	0.053	0.058	0.056	0.046	0.053	0.053	0.058	0.053
			ASE	0.046	0.052	0.051	0.055	0.053	0.046	0.057	0.056	0.059	0.057
			CP	0.048	0.481	0.670	0.927	0.935	0.005	0.420	0.686	0.917	0.962
		β 1	Bias	−0.159	0.000	−0.006	−0.012	−0.001	−0.230	0.007	−0.004	−0.030	0.004
			SD	0.037	0.057	0.051	0.045	0.048	0.035	0.066	0.056	0.047	0.051
			ASE	0.033	0.055	0.049	0.043	0.045	0.032	0.065	0.056	0.046	0.051
			CP	0.023	0.942	0.929	0.917	0.932	0.003	0.957	0.940	0.877	0.942
	0.4	β 0	Bias	0.230	0.149	0.103	0.003	0.001	0.289	0.172	0.120	0.005	−0.001
			SD	0.048	0.054	0.054	0.055	0.054	0.051	0.063	0.061	0.061	0.061
			ASE	0.049	0.056	0.055	0.057	0.057	0.050	0.060	0.059	0.061	0.061
			CP	0.003	0.262	0.524	0.929	0.952	0.000	0.234	0.453	0.935	0.950
		β 1	Bias	−0.161	−0.001	−0.010	−0.006	−0.001	−0.231	0.001	−0.015	−0.013	0.000
			SD	0.039	0.061	0.055	0.047	0.049	0.038	0.074	0.061	0.049	0.054
			ASE	0.037	0.061	0.054	0.048	0.050	0.036	0.070	0.059	0.050	0.056
			CP	0.038	0.942	0.935	0.935	0.957	0.003	0.952	0.919	0.922	0.950
0.7	0.2	β 0	Bias	0.181	0.100	0.054	0.004	−0.002	0.242	0.127	0.069	0.021	0.003
			SD	0.046	0.050	0.050	0.054	0.052	0.044	0.053	0.052	0.057	0.054
			ASE	0.046	0.051	0.050	0.053	0.052	0.046	0.053	0.053	0.057	0.055
			CP	0.040	0.498	0.802	0.942	0.942	0.003	0.323	0.762	0.942	0.960
		β 1	Bias	−0.160	0.002	−0.002	−0.010	0.001	−0.230	0.001	−0.007	−0.030	−0.001
			SD	0.035	0.054	0.047	0.043	0.044	0.032	0.055	0.046	0.042	0.044
			ASE	0.034	0.051	0.044	0.042	0.042	0.032	0.057	0.048	0.043	0.046
			CP	0.018	0.928	0.938	0.940	0.960	0.000	0.960	0.960	0.887	0.943
	0.4	β 0	Bias	0.226	0.148	0.078	−0.002	−0.002	0.293	0.177	0.093	0.006	0.003
			SD	0.049	0.056	0.056	0.060	0.059	0.051	0.061	0.058	0.058	0.059
			ASE	0.050	0.054	0.053	0.056	0.055	0.049	0.057	0.056	0.060	0.058
			CP	0.018	0.235	0.678	0.927	0.939	0.000	0.175	0.603	0.939	0.942
		β 1	Bias	−0.158	−0.002	−0.007	−0.007	0.001	−0.234	−0.001	−0.012	−0.012	−0.002
			SD	0.038	0.056	0.048	0.046	0.045	0.038	0.066	0.054	0.048	0.050
			ASE	0.037	0.054	0.048	0.045	0.045	0.036	0.061	0.052	0.048	0.050
			CP	0.041	0.937	0.942	0.934	0.947	0.000	0.934	0.929	0.924	0.939

Note: SD denotes the sample standard deviation of the estimates; ASE is the average of the estimated standard errors; CP represents the coverage probability of the 95% confidence intervals.