Table 2.

Simulation results for the general measurement error model with skewed distributions for the model covariates as well as the subject-specific and random error. For 1000 simulated data sets, the mean bias, empirical standard deviation (SD), bootstrap standard deviation (BSD), root mean squared error (RSME) and estimated 95% coverage probability (CP) are given for β = log 1.5, log 3.

	Moderate Subject-Specific Bias					Strong Subject-Specific Bias
β = log 1.5	Bias	SD	BSD	RMSE	CP	Bias	SD	BSD	RMSE	CP
True	0.002	0.020	0.020	0.020	94.6	0.002	0.020	0.020	0.020	94.6
Naive	−0.082	0.022	0.022	0.085	3.8	−0.072	0.042	0.034	0.083	45.4
RC	−0.025	0.099	0.079	0.102	86.9	−0.045	0.089	0.069	0.099	88.7
RRC	0.016	0.096	0.121	0.097	93.7	0.044	0.076	0.071	0.088	82.1
CS B	0.012	0.048	0.050	0.050	94.9	0.012	0.048	0.050	0.050	94.9
CS W	0.028	0.061	0.060	0.067	93.5	0.054	0.075	0.076	0.092	88.4
NP B	0.011	0.057	0.061	0.058	96.2	0.011	0.057	0.061	0.058	96.2
NP W	0.008	0.055	0.061	0.057	96.6	0.009	0.056	0.060	0.057	96.4

β = log 3	Bias	SD	BSD	RMSE	CP	Bias	SD	BSD	RMSE	CP
True	0.003	0.038	0.037	0.038	94.5	0.003	0.038	0.037	0.038	94.5
Naive	−0.491	0.032	0.029	0.492	0.0	−0.590	0.051	0.038	0.592	0.0
RC	−0.343	0.193	0.152	0.394	44.4	−0.458	0.157	0.122	0.485	0.7
RRC	−0.077	0.197	0.201	0.211	94.3	−0.116	0.167	0.161	0.203	90.9
CS B	0.136	0.160	0.184	0.210	99.0	0.136	0.160	0.184	0.210	99.0
CS W	0.138	0.226	0.225	0.265	94.9	0.112	0.231	0.249	0.257	98.0
NP B	0.068	0.210	0.243	0.221	96.6	0.068	0.210	0.242	0.221	96.6
NP W	0.059	0.195	0.234	0.204	97.3	0.064	0.209	0.237	0.219	96.6

True: Cox regression with true X; Naive: Cox regression with unadjusted Q; RC: ordinary regression calibration; RRC: risk set regression calibration; CS B: CS from Tsiatis and Davidian (2001) using biomarker W data only; CS W: weighted combination of CS using Q only and W only; NP B: NP equation from Huang and Wang (2000) using only W; NP W: weighted combination of NP using Q only and W only.