Table 1. . Bias, Relative bias and variance of naive estimators of total effect, natural direct effect, natural indirect effect and proportion mediated for simulation scenario I assuming sensitivity = (0.70, 0.80, 0.90, 0.95), and specificity = 1.
| H1(β1a ≠ 0, ϑ2b ≠ 0) | True |
SN = 0.70 |
SN = 0.80 |
SN = 0.90 |
SN = 0.95 |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bias | Rel. bias | Var | Bias | Rel. bias | Var | Bias | Rel. bias | Var | Bias | Rel. bias | Var | ||
| TE |
-194 |
77.6 |
-0.40 |
990 |
58.2 |
-0.30 |
1013 |
32.98 |
-0.17 |
1305 |
19.4 |
-0.10 |
1397 |
| NDE |
-149 |
74.5 |
-0.50 |
1090 |
59.6 |
-0.40 |
1176 |
37.25 |
-0.25 |
1942 |
20.86 |
-0.14 |
1952 |
| NIE |
-45 |
-1.80 |
0.04 |
149 |
-0.9 |
0.02 |
193 |
-2.7 |
0.06 |
270 |
-2.25 |
0.05 |
330 |
| PM |
0.24 |
0.16 |
0.67 |
0.04 |
0.12 |
0.50 |
0.02 |
0.072 |
0.30 |
0.02 |
0.04 |
0.17 |
0.01 |
|
H0(β1a ≠ 0, ϑ2b = 0) | |||||||||||||
| TE |
-150 |
60.0 |
-0.40 |
990 |
45.0 |
-0.30 |
998 |
25.5 |
-0.17 |
1019 |
15.0 |
-0.10 |
1045 |
| NDE |
-150 |
75.0 |
-0.50 |
1090 |
59.6 |
-0.40 |
1177 |
37.5 |
-0.25 |
1305 |
20.86 |
-0.14 |
1398 |
| NIE |
0 |
-16 |
-16/0 |
127 |
-14 |
-14/0 |
174 |
-11 |
-11/0 |
225 |
-6 |
-6/0 |
319 |
| PM | 0 | 0.21 | 0.21/0 | 0.02 | 0.15 | 0.15/0 | 0.03 | 0.10 | 0.10/0 | 0.03 | 0.05 | 0.05/0 | 0.37 |
†Exposure-mediator association from Equation 3.
‡Mediator-outcome association from Equation 2.
NDE: Natural direct effect; NIE: Natural indirect effect; PM: Proportion mediated; SN: Sensitivity; SP: Specificity; TE: total effect; var: Variance.