Table 10 Comparison of approaches for the estimation of natural effects on the odds ratio scale for Scenario 5 with a binary 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 | 3.023 | 3.949 | 0.926 | 30.648 | 0.596 | 1.101 | 61.8 | 58.2 |
Approx_C | 3.023 | 3.808 | 0.785 | 25.979 | 0.596 | 0.986 | 71.7 | 69.1 | |
Approx_IPW | 3.023 | 3.870 | 0.847 | 28.034 | 0.599 | 1.038 | 67.8 | 63.9 | |
Exact_Naive | 3.023 | 2.529 | -0.494 | -16.346 | 0.560 | 0.747 | 83.3 | 85.6 | |
Exact_IPW | 3.023 | 3.063 | 0.040 | 1.336 | 0.533 | 0.535 | 95.0 | 94.6 | |
Unified | 3.023 | 3.811 | 0.788 | 26.058 | 0.598 | 0.989 | 72.8 | - | |
NIE | Approx_Naive | 2.213 | 1.838 | -0.375 | -16.948 | 0.134 | 0.398 | 23.5 | 21.5 |
Approx_C | 2.213 | 1.785 | -0.428 | -19.327 | 0.130 | 0.447 | 23.0 | 16.9 | |
Approx_IPW | 2.213 | 1.842 | -0.371 | -16.752 | 0.135 | 0.395 | 29.7 | 25.6 | |
Exact_Naive | 2.213 | 2.759 | 0.546 | 24.670 | 0.518 | 0.752 | 77.5 | 78.5 | |
Exact_IPW | 2.213 | 2.238 | 0.025 | 1.148 | 0.266 | 0.268 | 96.6 | 94.9 | |
Unified | 2.213 | 1.780 | -0.433 | -19.566 | 0.129 | 0.452 | 15.0 | - | |
TE | Approx_Naive | 6.690 | 7.233 | 0.543 | 8.124 | 1.053 | 1.185 | 93.8 | 92.3 |
Approx_C | 6.690 | 6.762 | 0.073 | 1.087 | 0.934 | 0.937 | 97.0 | 95.6 | |
Approx_IPW | 6.690 | 7.099 | 0.409 | 6.119 | 1.022 | 1.100 | 95.2 | 94.1 | |
Exact_Naive | 6.690 | 6.761 | 0.071 | 1.063 | 0.933 | 0.935 | 96.0 | 95.6 | |
Exact_IPW | 6.690 | 6.773 | 0.083 | 1.239 | 0.942 | 0.945 | 96.6 | 95.5 | |
Unified | 6.690 | 6.746 | 0.056 | 0.844 | 0.930 | 0.932 | 95.9 | - |