Table 2 Performance of confounding-adjustment methods across confounding and skewness scenarios in the simulation study with maximum Monte Carlo standard errors (SE) provided in the table footnote (see Supplementary Table 3 for all Monte Carlo SEs)
From: Confounding-adjustment methods for the causal difference in medians
Confounding | Skewness scenario | Method | Absolute bias | Relative bias (%) | Empirical SE | Model SE | Error SE (%) | Coverage (%) |
|---|---|---|---|---|---|---|---|---|
Weak | 1 | Unadjusted | 0.090 | 10.07 | 0.369 | 0.381 | 3.21 | 94.60 |
QR | 0.059 | 6.63 | 0.384 | 0.375 | -2.24 | 94.80 | ||
IPW estimator | -0.004 | -0.48 | 0.442 | 0.454 | 2.78 | 94.90 | ||
Weighted QR | -0.023 | -2.53 | 0.440 | 0.453 | 2.98 | 95.20 | ||
G-comp (MC) | -0.026 | -2.91 | 0.308 | 0.298 | -3.18 | 93.70 | ||
G-comp (approx) | -0.026 | -2.90 | 0.308 | 0.298 | -3.16 | 93.60 | ||
Weak | 2 | Unadjusted | 0.123 | 10.08 | 0.526 | 0.528 | 0.32 | 94.90 |
QR | 0.099 | 8.13 | 0.540 | 0.517 | -4.35 | 94.20 | ||
IPW estimator | 0.050 | 4.09 | 0.625 | 0.640 | 2.43 | 93.70 | ||
Weighted QR | 0.023 | 1.91 | 0.621 | 0.636 | 2.54 | 94.20 | ||
G-comp (MC) | 0.006 | 0.48 | 0.436 | 0.420 | -3.60 | 94.00 | ||
G-comp (approx) | 0.006 | 0.45 | 0.436 | 0.420 | -3.62 | 93.90 | ||
Weak | 3 | Unadjusted | 0.160 | 10.00 | 0.684 | 0.727 | 6.27 | 95.60 |
QR | 0.114 | 7.14 | 0.693 | 0.695 | 0.31 | 94.70 | ||
IPW estimator | 0.019 | 1.17 | 0.806 | 0.870 | 7.94 | 95.00 | ||
Weighted QR | -0.020 | -1.23 | 0.803 | 0.864 | 7.62 | 95.20 | ||
G-comp (MC) | -0.016 | -1.00 | 0.550 | 0.563 | 2.47 | 95.20 | ||
G-comp (approx) | -0.015 | -0.97 | 0.550 | 0.563 | 2.40 | 95.10 | ||
Weak | 4 | Unadjusted | 0.193 | 10.09 | 0.833 | 0.894 | 7.24 | 96.80 |
QR | 0.133 | 6.95 | 0.864 | 0.842 | -2.62 | 95.50 | ||
IPW estimator | 0.123 | 6.45 | 1.032 | 1.098 | 6.40 | 95.30 | ||
Weighted QR | 0.081 | 4.22 | 1.017 | 1.091 | 7.24 | 95.50 | ||
G-comp (MC) | 0.062 | 3.25 | 0.695 | 0.712 | 2.40 | 95.00 | ||
G-comp (approx) | 0.063 | 3.28 | 0.694 | 0.710 | 2.20 | 94.90 | ||
Strong | 1 | Unadjusted | 0.171 | 20.17 | 0.391 | 0.398 | 1.66 | 93.20 |
QR | 0.098 | 11.58 | 0.398 | 0.390 | -2.10 | 94.30 | ||
IPW estimator | 0.003 | 0.31 | 0.441 | 0.466 | 5.75 | 95.40 | ||
Weighted QR | -0.017 | -1.95 | 0.440 | 0.464 | 5.33 | 95.30 | ||
G-comp (MC) | -0.023 | -2.65 | 0.308 | 0.306 | -0.93 | 94.10 | ||
G-comp (approx) | -0.023 | -2.67 | 0.308 | 0.306 | -0.86 | 94.10 | ||
Strong | 2 | Unadjusted | 0.240 | 20.05 | 0.544 | 0.568 | 4.40 | 94.00 |
QR | 0.117 | 9.81 | 0.556 | 0.556 | -0.03 | 95.00 | ||
IPW estimator | 0.030 | 2.55 | 0.621 | 0.673 | 8.34 | 96.00 | ||
Weighted QR | 0.004 | 0.33 | 0.617 | 0.670 | 8.61 | 95.40 | ||
G-comp (MC) | -0.025 | -2.08 | 0.446 | 0.441 | -1.22 | 94.30 | ||
G-comp (approx) | -0.025 | -2.10 | 0.446 | 0.440 | -1.22 | 94.00 | ||
Strong | 3 | Unadjusted | 0.307 | 20.11 | 0.729 | 0.734 | 0.72 | 93.50 |
QR | 0.219 | 14.39 | 0.726 | 0.709 | -2.32 | 93.70 | ||
IPW estimator | 0.117 | 7.68 | 0.847 | 0.897 | 5.89 | 95.40 | ||
Weighted QR | 0.082 | 5.35 | 0.843 | 0.891 | 5.77 | 95.50 | ||
G-comp (MC) | 0.076 | 4.97 | 0.570 | 0.579 | 1.62 | 95.10 | ||
G-comp (approx) | 0.075 | 4.93 | 0.569 | 0.579 | 1.75 | 95.20 | ||
Strong | 4 | Unadjusted | 0.420 | 20.02 | 1.004 | 1.052 | 4.76 | 95.10 |
QR | 0.189 | 8.98 | 1.002 | 0.993 | -0.88 | 94.50 | ||
IPW estimator | 0.038 | 1.81 | 1.189 | 1.252 | 5.37 | 95.50 | ||
Weighted QR | -0.009 | -0.43 | 1.180 | 1.241 | 5.19 | 95.50 | ||
G-comp (MC) | -0.028 | -1.34 | 0.759 | 0.806 | 6.11 | 95.40 | ||
G-comp (approx) | -0.028 | -1.32 | 0.760 | 0.791 | 4.12 | 95.70 |