Table 2.

Results^a From a 2-Time-Interval Simulation Study With 4 Scenarios (Rows) in Which the Magnitude of the Confounder L (α₁) and the Standard Deviation of Measurement Error σ_δ are Varied in Marginal Structural Models Including an Error-Free L and an Uncorrected Error-Prone L^*

α1 and Scenario	Error Deviation (σδ)	Model Using SIMEX-Corrected ${\mathit{L}}_{\mathbf{1}}{}^{\mathbf{\ast }}$, ${\mathit{L}}_{\mathbf{2}}{}^{\mathbf{\ast }}$
		Direct Correction							Indirect Correction
		Bias		Relative MSEb		MCSE		95% Bootstrap Coveragec	Bias		Relative MSEb		MCSE		95% Bootstrap Coveragec
		β1	β2	β1	β2	β1	β2	(β1, β2)	β1	β2	β1	β2	β1	β2	(β1, β2)
0.50
1	0.25	−0.003	0.009	1.000	1.000	0.097	0.107	0.923, 0.970	−0.006	0.007	1.000	1.000	0.097	0.107	0.927, 0.970
2	1.25	0.187	0.154	0.263	0.552	0.112	0.114	0.600, 0.760	0.158	0.145	0.218	0.507	0.118	0.117	0.717, 0.793
0.75
3	0.25	0.008	0.013	1.000	0.950	0.126	0.137	0.907, 0.933	−0.001	0.008	1.000	0.950	0.127	0.138	0.913, 0.933
4	1.25	0.249	0.213	0.240	0.565	0.127	0.141	0.527, 0.650	0.162	0.189	0.151	0.522	0.150	0.158	0.783, 0.720

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

^a A sample size of n = 1,000 was used for all simulations.

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

^c Bootstrap coverage was computed using the nonparametric bootstrap percentiles approach.