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. 2016 Jul 13;184(3):249–258. doi: 10.1093/aje/kww068

Table 1.

Results From a Single-Time-Interval Simulation Study With 27 Scenarios (Rows) in Which Sample Size (N), the Magnitude of the Confounder L (α1), and the Standard Deviation of Measurement Error σδ are Varied in Marginal Structural Models Including an Error-Free L and an Uncorrected Error-Prone L*

α1, N, and Scenario Error Deviation (σδ) Model Using SIMEX-Corrected L*
Direct Correction
 Indirect Correction
Bias (β1) Relative MSEa MCSE 95% Bootstrap Coverageb Bias (β1) Relative MSEa MCSE 95% Bootstrap Coverageb
0.25
 100
  A 0.25 −0.006 1.000 0.219 0.950 −0.007 1.000 0.220 0.953
  B 0.75 0.008 0.933 0.288 0.963 0.004 0.944 0.290 0.960
  C 1.25 0.099 0.780 0.355 0.950 0.089 0.792 0.360 0.957
 500
  D 0.25 0.008 1.000 0.099 0.943 0.008 1.000 0.099 0.943
  E 0.75 0.030 0.472 0.127 0.943 0.026 0.472 0.128 0.943
  F 1.25 0.127 0.385 0.156 0.890 0.120 0.375 0.158 0.900
 1,000
  G 0.25 0.002 1.000 0.076 0.943 0.002 1.000 0.076 0.943
  H 0.75 0.022 0.370 0.099 0.920 0.018 0.370 0.100 0.920
  I 1.25 0.115 0.329 0.120 0.787 0.110 0.318 0.122 0.817
0.50
 100
  J 0.25 −0.005 1.016 0.251 0.963 −0.008 1.016 0.251 0.967
  K 0.75 0.028 0.723 0.326 0.963 0.002 0.764 0.337 0.960
  L 1.25 0.214 0.506 0.388 0.937 0.170 0.525 0.417 0.960
 500
  M 0.25 0.005 0.933 0.117 0.937 0.001 0.933 0.118 0.937
  N 0.75 0.035 0.271 0.146 0.930 0.008 0.271 0.152 0.950
  O 1.25 0.222 0.256 0.173 0.730 0.181 0.217 0.186 0.830
 1,000
  P 0.25 −0.003 0.875 0.085 0.917 −0.007 0.875 0.085 0.920
  Q 0.75 0.025 0.178 0.111 0.907 −0.002 0.178 0.115 0.927
  R 1.25 0.211 0.216 0.132 0.603 0.170 0.171 0.141 0.750
0.75
 100
  S 0.25 0.025 1.009 0.335 0.943 0.015 1.009 0.335 0.943
  T 0.75 0.055 0.755 0.452 0.947 −0.013 0.792 0.467 0.967
  U 1.25 0.327 0.479 0.499 0.890 0.220 0.486 0.559 0.930
 500
  V 0.25 −0.002 0.955 0.147 0.937 −0.015 1.000 0.148 0.943
  W 0.75 0.025 0.245 0.190 0.920 −0.056 0.298 0.205 0.947
  X 1.25 0.304 0.231 0.215 0.647 0.186 0.168 0.256 0.860
 1,000
  Y 0.25 0.000 0.833 0.102 0.937 −0.014 0.917 0.103 0.923
  Z 0.75 0.026 0.139 0.135 0.920 −0.056 0.182 0.147 0.907
  AA 1.25 0.302 0.199 0.155 0.443 0.184 0.116 0.183 0.787

Abbreviations: MCSE, Monte Carlo standard error; MSE, mean squared error; SIMEX, simulation-extrapolation.

a MSEs are relative to those computed using a naive model including an error-prone L* with an identical parameter set.

b Bootstrap coverage was computed using the nonparametric bootstrap percentiles approach.