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. Author manuscript; available in PMC: 2013 Apr 10.
Published in final edited form as: Biometrics. 2013 Feb 4;69(1):80–90. doi: 10.1111/j.1541-0420.2012.01833.x

Table 2.

Simulation Study B Non-Normal Measurement Error with Normal or Non-Normal True Covariate Results for Slope Parameter β1 – Sample Size n=200, Validation Sample Size m=70

M MD Emp-SD IQ-SD 95% CI F M MD Emp-SD IQ-SD 95% CI F
X ~ N (0, 1) and ε ~ DBLEXP(γ)
γ = 0.5
γ = 1.0
Naive 0.6378 0.6287 0.1609 0.1517 0.334 0 0.4659 0.4598 0.1370 0.1349 0.039 0
RECS 1.0684 0.9986 0.3611 0.3264 0.948 0 1.1362 1.0089 0.5714 0.4335 0.933 6
N&S 1.0471 1.0126 0.2970 0.3293 0.888 0 0.9625 1.0099 0.2794 0.2872 0.845 11
SIMEX - Q 0.8905 0.8641 0.2438 0.2276 0.871 0 0.7205 0.6970 0.2289 0.2165 0.629 0
H&W 1.0770 0.9848 0.4523 0.3202 0.951 0 0.9886 0.8985 0.4636 0.3336 0.942 1
MCMC η =100 1.2987 1.2613 0.3796 0.4360 0.970 0 1.1476 1.0940 0.3785 0.4483 0.990 0
X ~ N (0, 1) and ε ~ MODCHI(γ)
γ = 0.5
γ = 1.0
Naive 0.6822 0.6793 0.1706 0.1672 0.467 0 0.5196 0.5146 0.1547 0.1552 0.126 0
RECS 1.0555 1.0348 0.2981 0.2775 0.959 0 1.0869 1.0345 0.3970 0.3546 0.966 0
N&S 1.1449 1.1451 0.3230 0.3808 0.857 4 1.1232 1.1779 0.2711 0.2319 0.805 18
SIMEX - Q 0.9678 0.9500 0.2624 0.2617 0.890 0 0.8320 0.8234 0.2711 0.2765 0.747 0
H&W 1.0260 0.9809 0.3822 0.2861 0.956 2 0.9640 0.8949 0.4753 0.3069 0.927 3
MCMC η =100 1.2154 1.1673 0.3372 0.2999 0.920 0 1.1502 1.1252 0.2996 0.2924 0.980 0
X ~ MODCHI (1) and ε ~ MODCHI (γ)
γ = 0.5
γ = 1.0
Naive 0.5461 0.5348 0.1709 0.1662 0.250 0 0.3917 0.3824 0.1448 0.1402 0.063 0
RECS 1.1279 1.0479 0.4989 0.4415 0.938 0 1.1272 1.0319 0.5784 0.5316 0.932 0
N&S 1.2750 1.3552 0.4993 0.6506 0.672 51 1.0147 1.1508 0.4306 0.5522 0.545 212
SIMEX - Q 0.8175 0.7884 0.2870 0.2713 0.791 0 0.6396 0.6176 0.2602 0.2498 0.490 0
H&W 0.9610 0.8409 0.5507 0.3729 0.912 6 0.8084 0.6995 0.5894 0.4255 0.846 13
MCMC η =100 1.0279 1.0105 0.4865 0.4735 0.970 0 0.8416 0.8245 0.4370 0.4278 0.930 0

SIMEX results are based on B = 100, λ = (0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9) and the simex R library

L - linear extrapolation; Q - quadratic extrapolation; NL - non-linear extrapolation of Cook and Stefanski (1994)

M - empirical mean; MD - empirical median; Emp-SD - empirical standard deviation; IQ-SD - inter-quartile dispersion; 95% CI - empirical coverage rate of 95% Wald confidence interval (or HPD interval, for MCMC); F - number of samples with no solution