Table 2 Comparison of approaches for the estimation of natural effects on the odds ratio scale for Scenario 2 with a continuous mediator (based on 1000 data sets of size \(n=1000\))
Effect | Approach | True value | Mean | Bias | Relative bias (%) | SD | RMSE | CP (%) delta | CP (%) boot |
|---|---|---|---|---|---|---|---|---|---|
NDE | Approx_Naive | 1.622 | 1.840 | 0.218 | 13.445 | 0.285 | 0.358 | 88.1 | 86.6 |
Approx_C | 1.622 | 1.727 | 0.105 | 6.450 | 0.258 | 0.278 | 92.8 | 93.3 | |
Approx_IPW | 1.622 | 1.752 | 0.130 | 8.028 | 0.266 | 0.296 | 92.4 | 91.6 | |
Exact_Naive | 1.622 | 1.505 | -0.117 | -7.240 | 0.209 | 0.240 | 89.6 | 90.1 | |
Exact_IPW | 1.622 | 1.652 | 0.030 | 1.835 | 0.238 | 0.239 | 94.7 | 94.7 | |
Unified | 1.622 | 1.719 | 0.097 | 5.978 | 0.254 | 0.272 | 93.6 | - | |
NIE | Approx_Naive | 1.585 | 1.903 | 0.318 | 20.080 | 0.192 | 0.372 | 62.6 | 51.9 |
Approx_C | 1.585 | 1.547 | -0.038 | -2.385 | 0.108 | 0.114 | 98.7 | 92.0 | |
Approx_IPW | 1.585 | 1.653 | 0.068 | 4.296 | 0.130 | 0.147 | 98.5 | 92.0 | |
Exact_Naive | 1.585 | 1.737 | 0.152 | 9.611 | 0.124 | 0.197 | 79.6 | 76.5 | |
Exact_IPW | 1.585 | 1.592 | 0.007 | 0.431 | 0.108 | 0.108 | 99.0 | 95.1 | |
Unified | 1.585 | 1.525 | -0.060 | -3.797 | 0.095 | 0.113 | 88.1 | - | |
TE | Approx_Naive | 2.571 | 3.507 | 0.936 | 36.411 | 0.680 | 1.157 | 68.4 | 64.1 |
Approx_C | 2.571 | 2.659 | 0.089 | 3.460 | 0.361 | 0.372 | 98.1 | 94.8 | |
Approx_IPW | 2.571 | 2.886 | 0.316 | 12.280 | 0.433 | 0.536 | 94.1 | 87.2 | |
Exact_Naive | 2.571 | 2.605 | 0.034 | 1.332 | 0.346 | 0.348 | 94.9 | 94.3 | |
Exact_IPW | 2.571 | 2.619 | 0.049 | 1.892 | 0.351 | 0.354 | 97.1 | 95.0 | |
Unified | 2.571 | 2.610 | 0.040 | 1.540 | 0.347 | 0.349 | 95.2 | - |