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. Author manuscript; available in PMC: 2018 Sep 1.
Published in final edited form as: Stat Methods Med Res. 2017 Jan 8;27(9):2756–2774. doi: 10.1177/0962280216686131

Table 2.

Simulation results with a post-treatment confounder

D’n M N Z NDE
ND^E
 NDE RMSE Cov.
rr^
 NME
NM^E
 NME RMSE Cov.
rr^
 NTE
NT^E
 NTE RMSE Cov.
rr^
Poi N 100 1 0.706 0.702 0.011 97.0 0.605 0.260 0.262 0.006 98.7 0.354 0.828 0.844 0.018 97.8 0.792
0 0.568 0.582 0.016 97.2 0.571 0.122 0.142 0.020 95.3 0.199
500 1 0.709 0.704 0.006 95.1 1.000 0.264 0.258 0.007 98.7 0.950 0.833 0.834 0.004 96.7 1.000
0 0.569 0.576 0.008 95.5 1.000 0.124 0.130 0.006 93.9 0.950
B 100 1 0.721 0.710 0.016 96.8 0.430 0.307 0.279 0.029 93.8 0.412 0.907 0.900 0.013 97.3 0.664
0 0.600 0.622 0.025 96.7 0.376 0.186 0.190 0.005 90.9 0.456
500 1 0.721 0.714 0.009 97.8 0.991 0.313 0.300 0.013 95.2 1.000 0.910 0.909 0.005 98.1 1.000
0 0.598 0.609 0.013 96.9 0.982 0.189 0.195 0.007 92.8 1.000
NB N 100 1 0.696 0.709 0.018 97.1 0.363 0.252 0.267 0.017 96.3 0.246 0.817 0.854 0.039 97.6 0.548
0 0.565 0.587 0.024 96.2 0.336 0.120 0.145 0.025 93.6 0.113
500 1 0.698 0.699 0.005 98.0 0.982 0.253 0.251 0.004 95.6 0.934 0.820 0.829 0.010 98.3 0.998
0 0.566 0.578 0.013 98.1 0.983 0.122 0.130 0.008 91.7 0.920
B 100 1 0.756 0.752 0.016 95.0 0.319 0.262 0.234 0.029 91.4 0.185 0.908 0.906 0.015 97.2 0.471
0 0.647 0.672 0.029 96.2 0.283 0.152 0.154 0.004 89.8 0.222
500 1 0.751 0.743 0.011 99.0 0.949 0.252 0.239 0.013 87.7 0.938 0.899 0.892 0.009 99.1 0.997
0 0.647 0.653 0.008 98.4 0.933 0.147 0.150 0.003 84.6 0.929
ZIP N 100 1 0.760 0.700 0.061 99.0 0.129 0.309 0.252 0.057 80.5 0.144 0.897 0.866 0.035 99.0 0.248
0 0.589 0.614 0.028 97.9 0.125 0.138 0.167 0.028 89.3 0.088
500 1 0.765 0.656 0.109 95.4 0.790 0.295 0.220 0.076 70.5 0.706 0.902 0.798 0.104 95.7 0.955
0 0.607 0.579 0.029 95.7 0.846 0.138 0.142 0.005 81.2 0.704
B 100 1 0.889 0.826 0.065 99.6 0.210 0.317 0.295 0.023 87.0 0.092 1.084 1.030 0.056 99.6 0.414
0 0.767 0.736 0.034 99.3 0.192 0.195 0.204 0.010 93.3 0.201
500 1 0.915 0.809 0.106 97.8 0.902 0.331 0.291 0.040 85.2 0.985 1.106 1.011 0.096 98.2 0.988
0 0.776 0.720 0.056 98.9 0.905 0.192 0.202 0.010 87.5 0.991
ZINB N 100 1 0.853 0.834 0.032 99.1 0.123 0.414 0.400 0.019 87.4 0.181 1.091 1.076 0.030 99.7 0.353
0 0.677 0.676 0.018 99.0 0.165 0.238 0.242 0.010 89.0 0.073
500 1 0.830 0.761 0.070 98.2 0.659 0.411 0.333 0.079 84.6 0.708 1.062 0.961 0.103 98.5 0.917
0 0.651 0.628 0.026 97.2 0.787 0.232 0.200 0.033 84.5 0.432
B 100 1 0.829 0.817 0.074 99.1 0.133 0.365 0.217 0.198 91.3 0.051 1.067 1.079 0.075 99.2 0.253
0 0.702 0.861 0.257 99.0 0.106 0.238 0.262 0.025 94.4 0.093
500 1 0.809 0.741 0.071 98.2 0.570 0.372 0.337 0.036 87.8 0.874 1.066 0.993 0.077 98.3 0.869
0 0.695 0.656 0.042 97.7 0.600 0.258 0.252 0.007 92.6 0.924

D’n: distribution; M: mediator; N: sample size; NDE: natural direct effect; NME: natural mediation effect; NTE: natural total effect; RMSE: root mean squared error; Cov: 95% CI coverage; rr: empirical rejection rate of the test; Poi: Poisson, NB: negative binomial; ZIP: zero-inflated Poisson; ZINB: zero-inflated negative binomial; N: normal; B: binary