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. Author manuscript; available in PMC: 2013 Nov 1.
Published in final edited form as: Epidemiology. 2012 Nov;23(6):879–888. doi: 10.1097/EDE.0b013e31826c2bb9

Table 3.

Simulation results for the direct and indirect effects - negative binomial Y, logistic regression X-model (incorrectly fit), (n = 200)

Mediator Scenario Effect True Integration Approach Empirical Approach
Bias Relative
Bias
(%)		 SE of
Bias		 CP1
(%)		 CP2
(%)		 Bias Relative
Bias
(%)		 SE of
Bias		 CP1
(%)		 CP2
(%)
N 1a D 1.82 −0.010 −0.53 0.010 94.4 94.6 −0.011 −0.54 0.010 94.4 94.7
I 0.00 0.003 - 0.002 94.4 97.8 0.020 - 0.004 17.5 98.5
1b D 0.00 −0.029 - 0.026 94.8 95.7 −0.028 - 0.026 94.8 95.4
I 1.78 0.048 2.74 0.018 93.8 93.7 0.13 7.17 0.025 61.3 93.8
1c D 3.09 −0.043 −1.37 0.039 94.5 95.8 −0.054 −1.70 0.040 93.7 95.5
I 3.23 0.093 2.86 0.031 92.8 92.8 0.22 6.61 0.041 71.1 91.3
1d D 3.44 −0.12 −3.39 0.053 92.6 96.3 −0.13 −3.72 0.053 92.5 95.7
I 3.59 0.097 2.57 0.041 92.7 92.0 1.04 28.5 0.056 67.1 95.8
C 2a D 1.06 −0.014 −1.28 0.008 93.6 94.1 −0.013 −1.21 0.008 93.4 94.0
I 0.00 <0.001 - 0.001 97.5 99.9 0.004 - 0.002 21.0 99.4
2b D 0.00 −0.004 - 0.014 94.2 95.2 −0.013 - 0.022 94.2 95.0
I 1.21 −0.75 −61.7 0.009 31.3 24.6 −0.10 −10.5 0.24 63.8 70.5
2c D 1.25 −0.38 −30.2 0.015 84.9 86.2 −0.049 −4.13 0.030 89.9 92.8
I 1.21 −0.76 −62.6 0.009 28.7 22.6 −0.51 −42.5 0.40 66.8 70.5
2d D 1.43 −0.49 −33.7 0.021 85.8 91.3 −0.068 −4.76 0.041 91.1 94.8
I 1.42 −0.93 −65.3 0.012 33.8 28.1 0.035 7.68 0.45 72.0 87.9
B 3a D 2.32 0.024 1.05 0.011 94.3 94.5 0.021 0.91 0.011 94.1 94.5
I 0.00 0.002 - 0.002 94.1 98.4 0.014 - 0.003 11.7 98.3
3b D 0.00 −0.009 - 0.030 93.9 94.6 0.003 - 0.027 93.9 94.5
I 1.47 0.78 53.1 0.022 78.0 93.7 −0.050 −3.45 0.025 28.8 92.1
3c D 0.56 0.029 5.36 0.016 93.4 93.9 0.003 0.54 0.015 93.9 94.4
I 0.56 0.21 37.3 0.009 89.4 97.2 <0.001 0.05 0.007 46.1 97.7
3d D 0.61 −0.003 −0.47 0.020 95.0 94.6 −0.028 −4.57 0.019 95.7 95.1
I 0.58 0.26 45.5 0.011 88.8 97.4 0.22 38.0 0.013 38.4 99.0

Mediator: N = normal; C = chi-square; B = beta

Effect: D = (Natural) direct effect for exposed, D1(1); I = (Natural) indirect effect for exposed, I1(0)

CP1: bootstrap percentile CI coverage probability

CP2: standard CI coverage probability

“<0.001” implies less than 0.001 in absolute value