Table 7 Comparison of approaches for the estimation of natural effects on the odds ratio scale for Scenario 2 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 | 3.529 | 5.629 | 2.100 | 59.510 | 1.197 | 2.417 | 41.3 | 35.1 |
Approx_C | 3.529 | 4.890 | 1.361 | 38.566 | 1.011 | 1.696 | 68.7 | 64.0 | |
Approx_IPW | 3.529 | 5.039 | 1.510 | 42.795 | 1.061 | 1.846 | 63.5 | 56.5 | |
Exact_Naive | 3.529 | 2.733 | -0.796 | -22.544 | 0.399 | 0.890 | 55.0 | 57.4 | |
Exact_IPW | 3.529 | 3.617 | 0.088 | 2.504 | 0.545 | 0.552 | 95.1 | 94.9 | |
Unified | 3.529 | 4.897 | 1.368 | 38.767 | 1.011 | 1.701 | 71.5 | - | |
NIE | Approx_Naive | 1.460 | 2.486 | 1.026 | 70.293 | 0.254 | 1.057 | 0.0 | 0.0 |
Approx_C | 1.460 | 1.097 | -0.362 | -24.816 | 0.151 | 0.392 | 57.3 | 35.5 | |
Approx_IPW | 1.460 | 1.581 | 0.121 | 8.281 | 0.151 | 0.194 | 97.2 | 87.6 | |
Exact_Naive | 1.460 | 1.929 | 0.469 | 32.154 | 0.135 | 0.488 | 1.5 | 1.2 | |
Exact_IPW | 1.460 | 1.472 | 0.013 | 0.869 | 0.116 | 0.117 | 99.0 | 95.6 | |
Unified | 1.460 | 1.097 | -0.362 | -24.823 | 0.150 | 0.392 | 51.4 | - | |
TE | Approx_Naive | 5.151 | 14.039 | 8.888 | 172.557 | 3.546 | 9.570 | 0.6 | 0.5 |
Approx_C | 5.151 | 5.258 | 0.107 | 2.073 | 0.729 | 0.736 | 99.8 | 95.8 | |
Approx_IPW | 5.151 | 7.899 | 2.748 | 53.351 | 1.496 | 3.129 | 61.6 | 32.7 | |
Exact_Naive | 5.151 | 5.253 | 0.102 | 1.979 | 0.718 | 0.725 | 95.5 | 95.5 | |
Exact_IPW | 5.151 | 5.301 | 0.150 | 2.911 | 0.740 | 0.755 | 97.8 | 95.3 | |
Unified | 5.151 | 5.264 | 0.113 | 2.202 | 0.722 | 0.731 | 95.8 | - |