FW | -0.300 | 10.798 | 93.849 | 42.547 | 1.005 |  | -0.588 | 12.476 | 93.353 | 50.758 | 1.039 |  | -0.555 | 11.617 | 93.651 | 47.476 | 1.043 |  | -0.358 | 8.568 | 93.651 | 33.456 | 0.996
Non-probability sample ($S_{A}$)
UW | 44.057 | 44.254 | 0.000 | 16.239 | 0.993 |  | 45.304 | 45.566 | 0.000 | 19.086 | 0.998 |  | 42.865 | 43.094 | 0.000 | 17.834 | 1.026 |  | 35.889 | 36.043 | 0.000 | 12.980 | 0.992
FW | 0.170 | 4.160 | 95.139 | 16.418 | 1.007 |  | -0.039 | 4.564 | 95.139 | 18.010 | 1.006 |  | 0.158 | 4.328 | 95.635 | 17.384 | 1.025 |  | 0.142 | 3.739 | 95.635 | 14.658 | 1.000
Non-robust method
Model specification: QR–True
IPSW | -2.157 | 10.471 | 92.857 | 42.950 | 1.069 |  | -2.257 | 10.919 | 92.956 | 43.494 | 1.038 |  | -1.980 | 10.273 | 92.857 | 41.675 | 1.054 |  | -2.058 | 9.476 | 94.246 | 38.427 | 1.059
Model specification: QR–False
IPSW | 30.837 | 31.398 | 0.099 | 23.746 | 1.025 |  | 29.353 | 30.150 | 0.694 | 27.671 | 1.024 |  | 28.686 | 29.364 | 0.496 | 25.303 | 1.029 |  | 29.823 | 30.082 | 0.000 | 16.020 | 1.038
Doubly robust methods
Model specification: QR–True, PM–True
GPPP | -0.329 | 9.828 | 93.452 | 39.581 | 1.027 |  | -0.491 | 11.391 | 92.361 | 45.621 | 1.022 |  | -0.279 | 10.520 | 93.948 | 42.782 | 1.037 |  | -0.347 | 8.042 | 93.552 | 31.670 | 1.005
PSPP | -0.331 | 9.825 | 93.552 | 39.571 | 1.028 |  | -0.497 | 11.397 | 92.460 | 45.574 | 1.021 |  | -0.275 | 10.517 | 93.849 | 42.718 | 1.036 |  | -0.353 | 8.030 | 93.452 | 31.655 | 1.006
LWP | -0.318 | 9.819 | 93.452 | 39.545 | 1.027 |  | -0.468 | 11.408 | 92.560 | 45.582 | 1.020 |  | -0.278 | 10.516 | 93.849 | 42.698 | 1.036 |  | -0.249 | 8.029 | 93.552 | 31.664 | 1.006
AIPW | -0.344 | 9.827 | 93.254 | 39.557 | 1.027 |  | -0.500 | 11.402 | 92.560 | 45.548 | 1.020 |  | -0.313 | 10.522 | 93.651 | 42.663 | 1.034 |  | -0.380 | 8.020 | 93.651 | 31.635 | 1.007
Model specification: QR–True, PM–False
GPPP | -0.243 | 9.885 | 93.651 | 39.576 | 1.021 |  | -0.446 | 11.315 | 92.758 | 45.663 | 1.030 |  | -0.181 | 10.569 | 93.948 | 42.585 | 1.028 |  | -0.248 | 8.029 | 93.452 | 31.783 | 1.010
PSPP | -0.293 | 9.889 | 93.552 | 39.552 | 1.020 |  | -0.514 | 11.319 | 92.758 | 45.628 | 1.029 |  | -0.272 | 10.575 | 93.948 | 42.539 | 1.026 |  | -0.368 | 8.036 | 93.552 | 31.802 | 1.010
LWP | -0.306 | 9.892 | 93.651 | 39.546 | 1.020 |  | -0.523 | 11.309 | 92.659 | 45.595 | 1.029 |  | -0.305 | 10.573 | 93.849 | 42.463 | 1.024 |  | -0.290 | 8.028 | 93.651 | 31.771 | 1.010
AIPW | -0.288 | 9.902 | 93.452 | 39.494 | 1.017 |  | -0.476 | 11.304 | 92.659 | 45.534 | 1.028 |  | -0.289 | 10.563 | 93.750 | 42.418 | 1.024 |  | -0.422 | 8.042 | 93.651 | 31.768 | 1.009
Model specification: QR–False, PM–True
GPPP | -0.027 | 8.255 | 93.651 | 33.254 | 1.027 |  | -0.268 | 8.722 | 93.552 | 34.618 | 1.012 |  | -0.050 | 8.168 | 93.948 | 32.870 | 1.026 |  | -0.187 | 7.194 | 94.048 | 28.743 | 1.019
PSPP | 0.664 | 8.282 | 93.552 | 33.140 | 1.024 |  | 0.324 | 8.716 | 93.353 | 34.499 | 1.010 |  | 0.514 | 8.163 | 94.345 | 32.827 | 1.027 |  | 0.297 | 7.201 | 93.948 | 28.654 | 1.016
LWP | -0.052 | 8.262 | 93.750 | 33.260 | 1.026 |  | -0.296 | 8.754 | 93.552 | 34.672 | 1.010 |  | -0.084 | 8.174 | 93.948 | 32.824 | 1.024 |  | -0.211 | 7.029 | 94.841 | 28.203 | 1.024
AIPW | -2.397 | 13.400 | 94.048 | 53.981 | 1.044 |  | -2.748 | 14.221 | 93.948 | 57.030 | 1.042 |  | -2.459 | 13.296 | 94.742 | 53.741 | 1.049 |  | -2.081 | 10.389 | 94.345 | 42.436 | 1.063
Model specification: QR–False, PM–False
GPPP | 30.818 | 31.348 | 0.099 | 22.751 | 1.010 |  | 29.492 | 30.201 | 0.496 | 26.142 | 1.025 |  | 28.797 | 29.405 | 0.298 | 24.074 | 1.032 |  | 29.590 | 29.893 | 0.000 | 16.838 | 1.012
PSPP | 30.815 | 31.347 | 0.099 | 22.752 | 1.008 |  | 29.486 | 30.196 | 0.496 | 26.129 | 1.023 |  | 28.792 | 29.401 | 0.298 | 24.082 | 1.032 |  | 29.580 | 29.879 | 0.000 | 16.685 | 1.009
LWP | 30.840 | 31.366 | 0.099 | 22.408 | 0.999 |  | 29.484 | 30.195 | 0.397 | 26.043 | 1.020 |  | 28.791 | 29.397 | 0.198 | 23.909 | 1.027 |  | 29.853 | 30.103 | 0.000 | 15.380 | 1.014
AIPW | 30.885 | 31.393 | 0.099 | 22.123 | 1.003 |  | 29.522 | 30.224 | 0.298 | 25.858 | 1.018 |  | 28.836 | 29.433 | 0.198 | 23.739 | 1.026 |  | 29.903 | 30.143 | 0.000 | 15.305 | 1.027

  * •

UW: Unweighted; FW: Fully weighted; GPPP: Gaussian Process of Propensity
Prediction; PSPP: Penalized Spline of Propensity Prediction; LWP: Linear-in-
weight prediction; AIPW: Augmented Inverse Propensity Weighting;

Table 10: Comparing the performance of the bias adjustment methods in the
simulation study for the _binary_ outcome with $(n_{A},n_{R})=(500,500)$ and
$\gamma_{1}=0.3$

| $LIN$ |  | $CUB$ |  | $EXP$ |  | $SIN$
---|---|---|---|---|---|---|---
Measure | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE
Probability sample ($S_{R}$)
UW | -41.047 | 41.487 | 0.000 | 19.213 | 0.813 |  | -44.574 | 45.028 | 0.000 | 20.730 | 0.828 |  | -42.945 | 43.406 | 0.000 | 20.084 | 0.812 |  | -34.898 | 35.315 | 0.000 | 17.395 | 0.820
FW | -0.335 | 10.901 | 93.552 | 42.588 | 0.997 |  | -0.575 | 12.433 | 92.560 | 50.551 | 1.038 |  | -0.570 | 11.625 | 93.254 | 47.208 | 1.037 |  | -0.326 | 8.522 | 94.544 | 33.469 | 1.002
Non-probability sample ($S_{A}$)
UW | 44.575 | 44.964 | 0.000 | 22.956 | 0.992 |  | 46.016 | 46.554 | 0.000 | 26.997 | 0.976 |  | 43.285 | 43.785 | 0.000 | 25.219 | 0.974 |  | 36.188 | 36.468 | 0.000 | 18.343 | 1.037
FW | 0.188 | 5.912 | 95.238 | 23.269 | 1.004 |  | 0.094 | 6.541 | 94.742 | 25.533 | 0.995 |  | 0.038 | 6.316 | 95.734 | 24.616 | 0.994 |  | 0.156 | 5.027 | 95.337 | 20.785 | 1.055
Non-robust method
Model specification: QR–True
IPSW | -2.243 | 11.249 | 92.659 | 45.293 | 1.048 |  | -2.251 | 11.567 | 92.758 | 46.382 | 1.042 |  | -2.284 | 11.271 | 92.262 | 44.587 | 1.030 |  | -2.216 | 10.028 | 93.155 | 40.735 | 1.062
Model specification: QR–False
IPSW | 31.049 | 31.894 | 1.290 | 28.822 | 1.008 |  | 29.561 | 30.735 | 6.151 | 33.381 | 1.011 |  | 28.698 | 29.785 | 5.060 | 31.006 | 0.992 |  | 30.014 | 30.449 | 0.000 | 20.837 | 1.036
Doubly robust methods
Model specification: QR–True, PM–True
GPPP | -0.304 | 10.252 | 93.948 | 40.870 | 1.017 |  | -0.278 | 11.735 | 94.246 | 47.397 | 1.030 |  | -0.374 | 10.829 | 95.040 | 44.445 | 1.047 |  | -0.276 | 8.244 | 93.254 | 32.312 | 1.000
PSPP | -0.312 | 10.254 | 93.849 | 40.855 | 1.016 |  | -0.309 | 11.731 | 94.246 | 47.293 | 1.028 |  | -0.401 | 10.822 | 94.940 | 44.352 | 1.046 |  | -0.297 | 8.219 | 93.452 | 32.270 | 1.002
LWP | -0.241 | 10.233 | 94.048 | 40.783 | 1.016 |  | -0.239 | 11.747 | 94.147 | 47.290 | 1.027 |  | -0.373 | 10.819 | 94.643 | 44.304 | 1.045 |  | -0.021 | 8.216 | 93.750 | 32.302 | 1.003
AIPW | -0.334 | 10.246 | 94.147 | 40.796 | 1.016 |  | -0.340 | 11.717 | 94.147 | 47.183 | 1.027 |  | -0.487 | 10.837 | 94.444 | 44.240 | 1.042 |  | -0.349 | 8.213 | 93.353 | 32.233 | 1.002
Model specification: QR–True, PM–False
GPPP | -0.022 | 10.274 | 93.552 | 40.822 | 1.013 |  | -0.232 | 11.714 | 93.353 | 47.716 | 1.039 |  | -0.065 | 10.868 | 93.651 | 44.175 | 1.036 |  | -0.030 | 8.185 | 93.651 | 32.685 | 1.018
PSPP | -0.161 | 10.277 | 93.452 | 40.787 | 1.012 |  | -0.368 | 11.703 | 93.353 | 47.627 | 1.038 |  | -0.276 | 10.853 | 93.849 | 44.023 | 1.035 |  | -0.291 | 8.197 | 93.651 | 32.673 | 1.017
LWP | -0.189 | 10.269 | 93.552 | 40.775 | 1.013 |  | -0.403 | 11.701 | 93.254 | 47.504 | 1.036 |  | -0.367 | 10.855 | 93.849 | 43.904 | 1.032 |  | -0.108 | 8.174 | 93.948 | 32.588 | 1.017
AIPW | -0.180 | 10.278 | 93.155 | 40.695 | 1.010 |  | -0.327 | 11.655 | 93.056 | 47.403 | 1.037 |  | -0.312 | 10.815 | 94.048 | 43.809 | 1.033 |  | -0.372 | 8.203 | 93.452 | 32.545 | 1.013
Model specification: QR–False, PM–True
GPPP | -0.074 | 8.802 | 93.353 | 34.932 | 1.012 |  | -0.108 | 9.361 | 94.147 | 37.706 | 1.027 |  | -0.099 | 8.807 | 94.444 | 35.413 | 1.025 |  | -0.271 | 7.442 | 93.452 | 29.490 | 1.011
PSPP | 1.298 | 8.884 | 93.750 | 34.903 | 1.013 |  | 1.242 | 9.401 | 94.742 | 37.718 | 1.032 |  | 1.110 | 8.819 | 94.742 | 35.405 | 1.032 |  | 0.675 | 7.426 | 93.948 | 29.415 | 1.014
LWP | -0.113 | 8.812 | 93.056 | 34.873 | 1.009 |  | -0.168 | 9.391 | 93.750 | 37.675 | 1.023 |  | -0.169 | 8.795 | 94.742 | 35.309 | 1.024 |  | -0.325 | 7.269 | 93.651 | 29.004 | 1.018
AIPW | -2.559 | 14.081 | 95.139 | 57.536 | 1.060 |  | -2.702 | 15.082 | 94.643 | 61.474 | 1.056 |  | -2.527 | 14.254 | 93.849 | 57.570 | 1.046 |  | -2.289 | 11.031 | 94.048 | 45.025 | 1.064
Model specification: QR–False, PM–False
GPPP | 31.065 | 31.834 | 0.595 | 27.121 | 0.994 |  | 29.748 | 30.772 | 2.679 | 31.444 | 1.019 |  | 28.823 | 29.783 | 2.778 | 29.269 | 0.995 |  | 29.821 | 30.265 | 0.000 | 20.999 | 1.037
PSPP | 31.076 | 31.846 | 0.595 | 27.108 | 0.993 |  | 29.738 | 30.764 | 2.877 | 31.423 | 1.017 |  | 28.818 | 29.779 | 2.579 | 29.258 | 0.994 |  | 29.783 | 30.231 | 0.000 | 20.989 | 1.032
LWP | 31.060 | 31.825 | 0.595 | 26.790 | 0.985 |  | 29.720 | 30.751 | 2.877 | 31.231 | 1.009 |  | 28.806 | 29.764 | 2.480 | 29.036 | 0.988 |  | 30.003 | 30.404 | 0.000 | 19.992 | 1.035
AIPW | 31.111 | 31.865 | 0.595 | 26.638 | 0.986 |  | 29.743 | 30.769 | 2.877 | 31.144 | 1.008 |  | 28.847 | 29.804 | 2.877 | 28.960 | 0.985 |  | 30.078 | 30.482 | 0.000 | 20.037 | 1.033

  * •

UW: Unweighted; FW: Fully weighted; GPPP: Gaussian Process of Propensity
Prediction; PSPP: Penalized Spline of Propensity Prediction; LWP: Linear-in-
weight prediction; AIPW: Augmented Inverse Propensity Weighting;

Table 11: Comparing the performance of the bias adjustment methods in the
simulation study for the _binary_ outcome with $(n_{A},n_{R})=(500,1,000)$ and
$\gamma_{1}=0.6$

| $LIN$ |  | $CUB$ |  | $EXP$ |  | $SIN$
---|---|---|---|---|---|---|---
Measure | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE
Probability sample ($S_{R}$)
UW | -40.760 | 41.085 | 0.000 | 13.610 | 0.673 |  | -44.127 | 44.513 | 0.000 | 14.703 | 0.642 |  | -42.643 | 43.014 | 0.000 | 14.229 | 0.644 |  | -34.513 | 34.804 | 0.000 | 12.322 | 0.700
FW | 0.256 | 9.389 | 92.758 | 37.069 | 1.007 |  | 0.371 | 11.344 | 93.254 | 45.111 | 1.014 |  | 0.101 | 10.820 | 92.758 | 41.488 | 0.978 |  | 0.095 | 7.111 | 93.849 | 28.415 | 1.019
Non-probability sample ($S_{A}$)
UW | 86.387 | 86.546 | 0.000 | 20.970 | 1.019 |  | 93.225 | 93.459 | 0.000 | 26.157 | 1.011 |  | 86.223 | 86.433 | 0.000 | 24.102 | 1.021 |  | 63.287 | 63.420 | 0.000 | 16.349 | 1.015
FW | 0.131 | 7.764 | 95.238 | 30.716 | 1.009 |  | 0.046 | 8.475 | 94.841 | 32.731 | 0.985 |  | -0.118 | 8.148 | 94.147 | 32.023 | 1.002 |  | -0.025 | 7.263 | 95.734 | 28.730 | 1.009
Non-robust method
Model specification: QR–True
IPSW | -3.227 | 13.982 | 93.353 | 56.871 | 1.066 |  | -3.152 | 14.463 | 92.460 | 57.679 | 1.042 |  | -3.082 | 13.955 | 92.758 | 55.562 | 1.041 |  | -3.285 | 12.805 | 92.956 | 52.146 | 1.074
Model specification: QR–False
IPSW | 53.562 | 54.137 | 0.000 | 31.653 | 1.025 |  | 50.993 | 51.855 | 0.000 | 37.317 | 1.010 |  | 49.050 | 49.812 | 0.000 | 34.351 | 1.009 |  | 51.063 | 51.358 | 0.000 | 21.820 | 1.012
Doubly robust methods
Model specification: QR–True, PM–True
GPPP | 0.337 | 9.267 | 94.742 | 37.662 | 1.037 |  | 0.357 | 11.473 | 93.254 | 44.914 | 0.999 |  | 0.391 | 10.659 | 94.444 | 42.397 | 1.015 |  | 0.313 | 7.382 | 93.056 | 28.939 | 1.000
PSPP | 0.307 | 9.265 | 94.742 | 37.616 | 1.036 |  | 0.312 | 11.436 | 93.254 | 44.827 | 1.000 |  | 0.383 | 10.639 | 94.742 | 42.158 | 1.011 |  | 0.277 | 7.361 | 93.056 | 28.724 | 0.996
LWP | 0.887 | 9.303 | 95.139 | 37.769 | 1.040 |  | 0.679 | 11.588 | 93.452 | 45.211 | 0.997 |  | 0.563 | 10.697 | 94.544 | 42.513 | 1.015 |  | 2.122 | 7.827 | 93.552 | 29.736 | 1.006
AIPW | 0.242 | 9.280 | 94.940 | 37.601 | 1.033 |  | 0.147 | 11.439 | 93.254 | 44.799 | 0.999 |  | -0.006 | 10.682 | 94.444 | 42.023 | 1.003 |  | 0.133 | 7.387 | 92.956 | 28.793 | 0.994
Model specification: QR–True, PM–False
GPPP | 1.021 | 9.354 | 94.643 | 38.386 | 1.053 |  | 0.790 | 11.546 | 92.857 | 45.111 | 0.999 |  | 0.739 | 10.591 | 94.444 | 42.842 | 1.034 |  | 1.411 | 7.633 | 93.948 | 29.422 | 1.000
PSPP | 0.469 | 9.290 | 94.147 | 38.002 | 1.044 |  | 0.322 | 11.365 | 93.056 | 44.503 | 0.999 |  | 0.285 | 10.541 | 94.147 | 42.234 | 1.022 |  | 0.298 | 7.440 | 93.452 | 29.029 | 0.996
LWP | 0.282 | 9.303 | 94.048 | 37.791 | 1.036 |  | 0.296 | 11.384 | 92.857 | 44.395 | 0.995 |  | 0.206 | 10.517 | 94.048 | 41.911 | 1.016 |  | 0.650 | 7.450 | 94.048 | 29.049 | 0.998
AIPW | 0.335 | 9.278 | 93.948 | 37.612 | 1.034 |  | 0.472 | 11.339 | 93.155 | 44.319 | 0.997 |  | 0.396 | 10.522 | 93.750 | 41.799 | 1.014 |  | 0.072 | 7.418 | 93.651 | 28.780 | 0.989
Model specification: QR–False, PM–True
GPPP | 0.279 | 7.814 | 95.635 | 32.201 | 1.051 |  | 0.515 | 9.122 | 94.048 | 35.787 | 1.002 |  | 0.337 | 8.482 | 94.742 | 34.458 | 1.037 |  | 0.259 | 6.655 | 93.552 | 26.511 | 1.017
PSPP | 4.350 | 9.046 | 93.948 | 33.320 | 1.071 |  | 4.859 | 10.448 | 92.857 | 37.065 | 1.022 |  | 4.419 | 9.750 | 94.048 | 35.700 | 1.047 |  | 2.881 | 7.177 | 93.155 | 26.425 | 1.025
LWP | 0.031 | 7.792 | 95.238 | 31.935 | 1.045 |  | 0.010 | 9.015 | 93.849 | 35.327 | 0.999 |  | -0.070 | 8.411 | 94.544 | 33.866 | 1.027 |  | 0.116 | 6.618 | 93.353 | 26.025 | 1.003
AIPW | -3.794 | 17.578 | 94.940 | 70.650 | 1.050 |  | -4.091 | 19.231 | 94.246 | 75.598 | 1.026 |  | -3.969 | 17.898 | 95.536 | 70.722 | 1.033 |  | -3.231 | 13.525 | 94.345 | 54.283 | 1.054
Model specification: QR–False, PM–False
GPPP | 46.258 | 46.727 | 0.000 | 26.958 | 1.041 |  | 43.406 | 44.150 | 0.000 | 31.503 | 0.995 |  | 42.182 | 42.813 | 0.000 | 29.504 | 1.027 |  | 46.251 | 46.541 | 0.000 | 20.569 | 1.011
PSPP | 46.229 | 46.695 | 0.000 | 26.939 | 1.043 |  | 43.369 | 44.112 | 0.000 | 31.478 | 0.995 |  | 42.150 | 42.779 | 0.000 | 29.486 | 1.028 |  | 46.153 | 46.445 | 0.000 | 20.470 | 1.004
LWP | 46.320 | 46.787 | 0.000 | 26.826 | 1.038 |  | 43.358 | 44.107 | 0.000 | 31.488 | 0.992 |  | 42.145 | 42.777 | 0.000 | 29.429 | 1.024 |  | 48.246 | 48.528 | 0.000 | 20.352 | 0.994
AIPW | 46.840 | 47.297 | 0.000 | 26.698 | 1.038 |  | 43.745 | 44.481 | 0.000 | 31.341 | 0.992 |  | 42.734 | 43.354 | 0.000 | 29.297 | 1.022 |  | 50.152 | 50.439 | 0.000 | 21.149 | 1.003

  * •

UW: Unweighted; FW: Fully weighted; GPPP: Gaussian Process of Propensity
Prediction; PSPP: Penalized Spline of Propensity Prediction; LWP: Linear-in-
weight prediction; AIPW: Augmented Inverse Propensity Weighting;

Table 12: Comparing the performance of the bias adjustment methods in the
simulation study for the _binary_ outcome with $(n_{A},n_{R})=(1,000,500)$ and
$\gamma_{1}=0.6$

| $LIN$ |  | $CUB$ |  | $EXP$ |  | $SIN$
---|---|---|---|---|---|---|---
Measure | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE
Probability sample ($S_{R}$)
UW | -41.047 | 41.487 | 0.000 | 19.213 | 0.813 |  | -44.574 | 45.028 | 0.000 | 20.730 | 0.828 |  | -42.945 | 43.406 | 0.000 | 20.084 | 0.812 |  | -34.898 | 35.315 | 0.000 | 17.395 | 0.820
FW | -0.326 | 10.847 | 93.552 | 42.776 | 1.006 |  | -0.675 | 12.615 | 92.758 | 51.013 | 1.033 |  | -0.509 | 11.780 | 93.353 | 47.385 | 1.027 |  | -0.403 | 8.536 | 93.849 | 33.518 | 1.002
Non-probability sample ($S_{A}$)
UW | 84.864 | 84.948 | 0.000 | 14.914 | 1.009 |  | 91.029 | 91.148 | 0.000 | 18.565 | 1.016 |  | 84.651 | 84.761 | 0.000 | 17.102 | 1.007 |  | 62.735 | 62.802 | 0.000 | 11.602 | 1.017
FW | 0.203 | 5.406 | 95.536 | 21.575 | 1.018 |  | 0.015 | 5.762 | 95.933 | 22.988 | 1.017 |  | 0.090 | 5.638 | 95.437 | 22.508 | 1.018 |  | 0.231 | 5.039 | 95.337 | 20.205 | 1.023
Non-robust method
Model specification: QR–True
IPSW | -3.783 | 15.498 | 90.179 | 62.509 | 1.061 |  | -3.878 | 15.620 | 89.782 | 62.778 | 1.058 |  | -3.599 | 15.118 | 90.675 | 60.239 | 1.046 |  | -3.782 | 14.133 | 91.964 | 57.700 | 1.080
Model specification: QR–False
IPSW | 52.198 | 52.687 | 0.000 | 28.997 | 1.032 |  | 49.275 | 50.008 | 0.000 | 34.156 | 1.021 |  | 47.956 | 48.604 | 0.000 | 31.095 | 1.002 |  | 50.472 | 50.655 | 0.000 | 17.591 | 1.042
Doubly robust methods
Model specification: QR–True, PM–True
GPPP | -0.261 | 9.930 | 94.643 | 40.048 | 1.029 |  | -0.448 | 11.556 | 93.552 | 46.462 | 1.026 |  | -0.204 | 10.641 | 94.444 | 43.177 | 1.035 |  | -0.335 | 8.120 | 93.056 | 32.132 | 1.010
PSPP | -0.276 | 9.928 | 94.643 | 40.018 | 1.028 |  | -0.482 | 11.562 | 93.452 | 46.369 | 1.024 |  | -0.172 | 10.636 | 94.643 | 43.046 | 1.032 |  | -0.314 | 8.105 | 93.452 | 32.015 | 1.008
LWP | -0.010 | 9.904 | 94.940 | 39.981 | 1.029 |  | -0.272 | 11.604 | 93.552 | 46.460 | 1.021 |  | -0.072 | 10.646 | 94.643 | 43.106 | 1.032 |  | 0.617 | 8.144 | 94.345 | 32.321 | 1.015
AIPW | -0.313 | 9.942 | 94.544 | 40.021 | 1.027 |  | -0.535 | 11.589 | 93.452 | 46.411 | 1.022 |  | -0.346 | 10.660 | 94.444 | 42.987 | 1.029 |  | -0.396 | 8.128 | 93.353 | 32.166 | 1.010
Model specification: QR–True, PM–False
GPPP | 0.112 | 9.911 | 94.544 | 40.299 | 1.037 |  | -0.195 | 11.524 | 94.048 | 46.627 | 1.032 |  | -0.101 | 10.628 | 93.750 | 43.280 | 1.038 |  | 0.391 | 8.149 | 93.651 | 32.036 | 1.004
PSPP | -0.165 | 9.926 | 94.444 | 40.142 | 1.031 |  | -0.429 | 11.490 | 93.552 | 46.458 | 1.032 |  | -0.299 | 10.611 | 93.849 | 43.080 | 1.036 |  | -0.240 | 8.113 | 94.147 | 31.929 | 1.004
LWP | -0.258 | 9.942 | 94.345 | 40.075 | 1.028 |  | -0.475 | 11.489 | 93.849 | 46.395 | 1.031 |  | -0.297 | 10.567 | 93.948 | 42.907 | 1.036 |  | -0.094 | 8.127 | 93.849 | 31.970 | 1.003
AIPW | -0.210 | 9.956 | 93.552 | 39.995 | 1.025 |  | -0.298 | 11.469 | 93.849 | 46.334 | 1.030 |  | -0.230 | 10.601 | 94.147 | 42.867 | 1.031 |  | -0.412 | 8.136 | 93.651 | 31.864 | 1.000
Model specification: QR–False, PM–True
GPPP | 0.021 | 8.403 | 93.849 | 33.606 | 1.020 |  | 0.028 | 8.886 | 94.246 | 35.807 | 1.027 |  | 0.084 | 8.297 | 94.643 | 33.793 | 1.039 |  | -0.331 | 7.326 | 93.452 | 29.197 | 1.017
PSPP | 2.302 | 8.643 | 94.841 | 33.926 | 1.038 |  | 2.340 | 9.163 | 93.948 | 36.205 | 1.042 |  | 2.233 | 8.580 | 94.643 | 34.188 | 1.052 |  | 1.294 | 7.406 | 93.452 | 29.067 | 1.016
LWP | -0.093 | 8.411 | 93.651 | 33.554 | 1.017 |  | -0.196 | 8.926 | 93.948 | 35.751 | 1.021 |  | -0.119 | 8.295 | 94.345 | 33.557 | 1.032 |  | -0.269 | 7.155 | 92.659 | 28.604 | 1.020
AIPW | -4.750 | 18.998 | 94.742 | 77.083 | 1.069 |  | -5.189 | 20.238 | 95.139 | 81.947 | 1.068 |  | -4.784 | 18.933 | 94.643 | 77.221 | 1.075 |  | -3.902 | 14.639 | 92.560 | 60.317 | 1.090
Model specification: QR–False, PM–False
GPPP | 46.307 | 46.727 | 0.000 | 24.810 | 1.012 |  | 43.480 | 44.046 | 0.000 | 28.364 | 1.027 |  | 42.571 | 43.072 | 0.000 | 26.363 | 1.027 |  | 46.321 | 46.541 | 0.000 | 18.121 | 1.023
PSPP | 46.282 | 46.703 | 0.000 | 24.788 | 1.009 |  | 43.452 | 44.019 | 0.000 | 28.360 | 1.026 |  | 42.547 | 43.049 | 0.000 | 26.356 | 1.026 |  | 46.336 | 46.552 | 0.000 | 17.919 | 1.018
LWP | 46.391 | 46.808 | 0.000 | 24.587 | 1.005 |  | 43.422 | 43.994 | 0.000 | 28.379 | 1.023 |  | 42.579 | 43.081 | 0.000 | 26.285 | 1.022 |  | 48.301 | 48.464 | 0.000 | 16.010 | 1.029
AIPW | 46.885 | 47.282 | 0.000 | 24.089 | 1.005 |  | 43.817 | 44.373 | 0.000 | 28.079 | 1.023 |  | 43.130 | 43.613 | 0.000 | 25.882 | 1.020 |  | 49.826 | 49.990 | 0.000 | 16.533 | 1.041

  * •

UW: Unweighted; FW: Fully weighted; GPPP: Gaussian Process of Propensity
Prediction; PSPP: Penalized Spline of Propensity Prediction; LWP: Linear-in-
weight prediction; AIPW: Augmented Inverse Propensity Weighting;

Table 13: Comparing the performance of the bias adjustment methods in the
simulation study for the _binary_ outcome with $(n_{A},n_{R})=(500,500)$ and
$\gamma_{1}=0.6$

| $LIN$ |  | $CUB$ |  | $EXP$ |  | $SIN$
---|---|---|---|---|---|---|---
Measure | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE |  | rBias | rMSE | crCI | lCI | rSE
Probability sample ($S_{R}$)
UW | -41.047 | 41.487 | 0.000 | 19.213 | 0.813 |  | -44.574 | 45.028 | 0.000 | 20.730 | 0.828 |  | -42.945 | 43.406 | 0.000 | 20.084 | 0.812 |  | -34.898 | 35.315 | 0.000 | 17.395 | 0.820
FW | -0.178 | 10.901 | 93.651 | 42.539 | 0.995 |  | -0.620 | 12.474 | 92.560 | 50.979 | 1.043 |  | -0.508 | 11.640 | 93.750 | 47.428 | 1.040 |  | -0.302 | 8.481 | 93.651 | 33.327 | 1.003
Non-probability sample ($S_{A}$)
UW | 86.167 | 86.338 | 0.000 | 20.986 | 0.985 |  | 92.869 | 93.119 | 0.000 | 26.171 | 0.979 |  | 86.198 | 86.428 | 0.000 | 24.101 | 0.977 |  | 63.186 | 63.318 | 0.000 | 16.359 | 1.019
FW | 0.257 | 7.843 | 94.643 | 30.712 | 0.999 |  | 0.106 | 8.183 | 96.032 | 32.740 | 1.020 |  | 0.146 | 8.318 | 93.948 | 32.044 | 0.982 |  | 0.248 | 7.226 | 95.139 | 28.741 | 1.015
Non-robust method
Model specification: QR–True
IPSW | -5.218 | 16.959 | 90.675 | 68.487 | 1.082 |  | -5.192 | 17.348 | 90.873 | 69.336 | 1.068 |  | -5.013 | 16.767 | 90.079 | 66.988 | 1.068 |  | -5.259 | 15.947 | 91.270 | 63.328 | 1.073
Model specification: QR–False
IPSW | 52.213 | 52.937 | 0.000 | 34.832 | 1.018 |  | 49.369 | 50.447 | 0.397 | 40.870 | 1.005 |  | 47.969 | 48.914 | 0.099 | 37.609 | 1.002 |  | 50.477 | 50.805 | 0.000 | 23.045 | 1.019
Doubly robust methods
Model specification: QR–True, PM–True
GPPP | -0.041 | 10.399 | 92.857 | 41.628 | 1.021 |  | -0.195 | 12.013 | 93.651 | 48.898 | 1.038 |  | 0.067 | 11.263 | 94.048 | 45.943 | 1.040 |  | -0.094 | 8.322 | 94.048 | 33.008 | 1.011
PSPP | -0.071 | 10.392 | 92.857 | 41.589 | 1.020 |  | -0.253 | 12.007 | 92.956 | 48.684 | 1.034 |  | 0.042 | 11.238 | 94.643 | 45.765 | 1.038 |  | -0.151 | 8.278 | 93.849 | 32.812 | 1.011
LWP | 0.585 | 10.393 | 92.758 | 41.847 | 1.028 |  | 0.224 | 12.129 | 93.849 | 49.125 | 1.033 |  | 0.310 | 11.319 | 94.048 | 46.165 | 1.040 |  | 1.629 | 8.595 | 93.750 | 33.723 | 1.019
AIPW | -0.141 | 10.366 | 92.659 | 41.535 | 1.022 |  | -0.401 | 12.071 | 93.254 | 48.666 | 1.029 |  | -0.318 | 11.284 | 94.345 | 45.620 | 1.031 |  | -0.274 | 8.394 | 93.452 | 33.054 | 1.005
Model specification: QR–True, PM–False
GPPP | 0.595 | 10.442 | 94.544 | 42.427 | 1.038 |  | 0.203 | 12.135 | 93.452 | 49.055 | 1.031 |  | 0.345 | 11.208 | 93.948 | 46.329 | 1.054 |  | 0.882 | 8.415 | 93.353 | 33.316 | 1.015
PSPP | 0.019 | 10.409 | 93.948 | 42.033 | 1.030 |  | -0.266 | 12.046 | 93.651 | 48.487 | 1.027 |  | -0.131 | 11.131 | 93.750 | 45.665 | 1.046 |  | -0.187 | 8.351 | 92.956 | 32.960 | 1.007
LWP | -0.122 | 10.423 | 93.750 | 41.834 | 1.023 |  | -0.303 | 12.042 | 93.353 | 48.357 | 1.024 |  | -0.183 | 11.103 | 93.849 | 45.407 | 1.043 |  | 0.162 | 8.377 | 93.155 | 33.080 | 1.007
AIPW | -0.140 | 10.431 | 93.353 | 41.598 | 1.017 |  | -0.075 | 12.003 | 93.254 | 48.215 | 1.024 |  | -0.019 | 11.115 | 93.948 | 45.235 | 1.038 |  | -0.407 | 8.372 | 92.560 | 32.762 | 0.999
Model specification: QR–False, PM–True
GPPP | 0.199 | 8.950 | 94.643 | 36.139 | 1.030 |  | 0.267 | 9.903 | 94.643 | 39.802 | 1.025 |  | 0.346 | 9.341 | 94.246 | 37.453 | 1.023 |  | -0.179 | 7.651 | 93.750 | 30.244 | 1.008
PSPP | 4.124 | 9.791 | 93.948 | 37.276 | 1.070 |  | 4.632 | 11.070 | 94.048 | 40.979 | 1.039 |  | 4.346 | 10.435 | 93.452 | 38.781 | 1.042 |  | 2.419 | 7.961 | 93.849 | 30.197 | 1.015
LWP | -0.042 | 8.924 | 94.147 | 35.868 | 1.025 |  | -0.202 | 9.907 | 94.147 | 39.346 | 1.013 |  | -0.022 | 9.262 | 93.948 | 36.989 | 1.018 |  | -0.209 | 7.591 | 93.651 | 29.763 | 1.000
AIPW | -6.490 | 21.428 | 94.643 | 87.422 | 1.092 |  | -6.913 | 23.067 | 95.933 | 93.312 | 1.081 |  | -6.310 | 21.508 | 95.536 | 87.184 | 1.081 |  | -5.406 | 16.466 | 92.262 | 66.288 | 1.087
Model specification: QR–False, PM–False
GPPP | 46.582 | 47.202 | 0.000 | 29.649 | 0.991 |  | 43.813 | 44.673 | 0.000 | 34.430 | 1.006 |  | 42.785 | 43.578 | 0.099 | 32.147 | 0.990 |  | 46.636 | 46.972 | 0.000 | 22.280 | 1.013
PSPP | 46.553 | 47.174 | 0.000 | 29.601 | 0.989 |  | 43.779 | 44.640 | 0.000 | 34.406 | 1.006 |  | 42.753 | 43.547 | 0.099 | 32.117 | 0.989 |  | 46.536 | 46.875 | 0.000 | 22.174 | 1.005
LWP | 46.613 | 47.232 | 0.000 | 29.416 | 0.984 |  | 43.758 | 44.630 | 0.000 | 34.367 | 0.998 |  | 42.752 | 43.549 | 0.099 | 32.022 | 0.985 |  | 48.424 | 48.721 | 0.000 | 21.085 | 1.002
AIPW | 47.053 | 47.652 | 0.000 | 29.122 | 0.985 |  | 44.101 | 44.957 | 0.000 | 34.142 | 0.997 |  | 43.241 | 44.019 | 0.099 | 31.741 | 0.983 |  | 49.864 | 50.171 | 0.000 | 21.994 | 1.012

  * •

UW: Unweighted; FW: Fully weighted; GPPP: Gaussian Process of Propensity
Prediction; PSPP: Penalized Spline of Propensity Prediction; LWP: Linear-in-
weight prediction; AIPW: Augmented Inverse Propensity Weighting;

###  8.2 Supplemental results on CIREN/CDS data

Table 14: Percentage of severe injury in HEAD and associated 95% CIs by
different covariates across DR adjustment methods

Covariate | n | Unweighted (95% CI) | GPPP (95% CI) | LWP (95% CI) | AIPW (95% CI)
---|---|---|---|---|---
Total | 6,271 | 25.036(23.964,26.108) | 9.552(7.33,11.774) | 10.36(4.559,16.161) | 9.658(6.398,12.918)
Gender |  |  |
Male | 3,230 | 28.359(26.805,29.914) | 11.464(7.982,14.947) | 12.526(4.69,20.361) | 10.81(6.382,15.239)
Female | 3,041 | 21.506(20.046,22.966) | 8.245(5.697,10.794) | 8.882(3.84,13.924) | 8.918(4.303,13.533)
Age group |  |  |
16-19 | 659 | 32.625(29.046,36.205) | 9.498(4.117,14.878) | 10.874(0.606,21.143) | 8.557(0,18.879)
20-39 | 2,732 | 26.354(24.702,28.006) | 10.292(7.258,13.326) | 11.027(5.256,16.799) | 10.137(4.987,15.286)
40-64 | 1,946 | 20.863(19.058,22.669) | 8.527(5.688,11.365) | 9.442(2.439,16.445) | 9.222(3.92,14.525)
65+ | 934 | 24.518(21.759,27.277) | 9.999(6.371,13.626) | 10.43(5.369,15.491) | 10.024(1.537,18.511)
Occupant role |  |  |
Driver | 1,547 | 32.515(30.18,34.849) | 9.681(4.677,14.685) | 10.958(0.535,21.382) | 9.924(0,20.727)
Passenger | 4,724 | 22.587(21.394,23.779) | 9.594(7.445,11.743) | 10.296(5.322,15.27) | 9.614(6.267,12.961)
Seating Row |  |  |
Front | 5,853 | 24.056(22.961,25.151) | 9.4(7.326,11.474) | 10.125(4.791,15.458) | 9.41(6.121,12.699)
Rear | 418 | 38.756(34.086,43.426) | 12.632(0.87,24.394) | 15.661(0,36.448) | 14.995(3.168,26.822)
Restraint use |  |  |
Restraint | 2,275 | 32.967(31.035,34.899) | 15.351(9.796,20.906) | 17.135(4.552,29.718) | 14.327(7.613,21.042)
Unrestraint | 3,996 | 20.521(19.268,21.773) | 7.01(4.926,9.094) | 7.346(4.113,10.579) | 7.34(3.457,11.222)
Air bag |  |  |
Deployed | 2,194 | 30.447(28.521,32.372) | 10.956(5.005,16.907) | 13.067(0.993,25.14) | 13.113(6.087,20.138)
Not deployed | 4,077 | 22.124(20.85,23.398) | 8.995(6.466,11.524) | 9.057(6.161,11.953) | 7.804(3.654,11.955)
Injury scale (AIS) |  |  |
3 | 1,977 | 18.412(16.703,20.12) | 13.609(9.765,17.453) | 13.61(8.5,18.719) | 12.903(8.281,17.525)
4 | 761 | 55.979(52.452,59.506) | 31.675(24.511,38.839) | 31.549(23.938,39.161) | 33.75(21.739,45.761)
5+ | 781 | 76.056(73.063,79.049) | 59.405(41.668,77.143) | 59.683(37.787,81.578) | 59.896(39.338,80.453)
Days hospitalized |  |  |
0 | 2,259 | 26.737(24.912,28.563) | 2.633(0,11.319) | 3.842(0,16.924) | 4.406(0,18.412)
1-3 | 1,757 | 17.758(15.971,19.544) | 8.564(4.978,12.15) | 8.619(4.918,12.32) | 9.408(5.25,13.566)
4-7 | 1,153 | 20.902(18.555,23.249) | 10.174(6.976,13.371) | 9.981(6.845,13.117) | 10.826(6.88,14.771)
8-14 | 640 | 28.438(24.943,31.932) | 16.411(11.916,20.907) | 16.313(11.886,20.74) | 17.117(11.688,22.547)
15+ | 462 | 50(45.441,54.559) | 27.032(21.157,32.907) | 26.964(21.18,32.747) | 23.857(17.808,29.905)
Delta-v (Km/h) |  |  |
Minor | 404 | 14.109(10.714,17.503) | 9.347(0.209,18.485) | 11.878(0,26.253) | 17.364(1.382,33.346)
Moderate | 3,304 | 19.613(18.259,20.967) | 7.748(5.154,10.343) | 8.597(2.33,14.864) | 6.326(2.517,10.135)
Severe | 2,563 | 33.75(31.919,35.58) | 15.234(11.167,19.301) | 15.395(10.571,20.219) | 15.357(8.964,21.749)
Damage distribution |  |  |
Wide | 4,657 | 23.148(21.937,24.359) | 8.304(6.187,10.421) | 9.104(3.819,14.389) | 7.276(3.906,10.647)
Narrow | 320 | 27.812(22.903,32.722) | 10.447(1.981,18.912) | 11.33(0,23.056) | 11.031(4.628,17.434)
Corner | 584 | 20.205(16.949,23.462) | 12.282(7.027,17.537) | 12.667(6.537,18.798) | 14.807(3.911,25.702)
Other | 710 | 40.141(36.535,43.746) | 15.842(6.849,24.835) | 17.071(3.194,30.949) | 21.066(6.792,35.341)
Rollover |  |  |
Yes | 4,942 | 21.833(20.681,22.985) | 8.566(6.467,10.665) | 9.295(4.417,14.173) | 7.526(4.333,10.719)
No | 1,329 | 36.945(34.35,39.54) | 12.579(6.805,18.354) | 13.867(2.222,25.512) | 17.555(8.204,26.906)
Deformation location |  |  |
Front | 3,671 | 16.78(15.571,17.989) | 7.353(4.777,9.93) | 7.905(3.188,12.621) | 6.853(2.596,11.11)
Right | 1,123 | 32.591(29.85,35.333) | 12.15(8.516,15.783) | 13.916(3.853,23.979) | 10.703(5.523,15.883)
Left | 857 | 39.44(36.168,42.712) | 13.239(1.592,24.887) | 14.049(1.539,26.559) | 16.421(2.379,30.463)
Rear | 620 | 40.323(36.461,44.184) | 15.445(7.088,23.801) | 16.007(4.144,27.869) | 17.129(2.342,31.916)
Model year |  |  |
$\leq$2003 | 2,529 | 28.035(26.284,29.785) | 13.405(8.529,18.282) | 14.961(2.984,26.938) | 17.958(10.59,25.325)
2004-2007 | 2,377 | 24.443(22.715,26.17) | 10.117(7.061,13.174) | 10.558(5.971,15.146) | 7.776(4.489,11.063)
2008-2011 | 1,019 | 20.51(18.031,22.989) | 3.33(0,8.253) | 3.656(0,9.11) | 1.094(0,7.874)
2012+ | 346 | 20.52(16.265,24.776) | 8.831(3.093,14.569) | 9.234(3.369,15.1) | 3.904(0,11.404)
Vehicle make |  |  |
American | 3,635 | 25.777(24.355,27.199) | 10.091(6.99,13.192) | 11.175(3.082,19.268) | 9.535(4.856,14.213)
Japanese | 1,927 | 24.754(22.827,26.68) | 9.997(6.843,13.15) | 10.479(5.934,15.025) | 12.601(7.211,17.991)
Korean | 387 | 21.189(17.117,25.26) | 5.661(0,12.117) | 6.576(0,16.798) | 5.023(0,12.299)
Other | 322 | 22.981(18.386,27.577) | 5.801(0,13.635) | 5.954(0,13.893) | 4.832(0,11.801)
Vehicle type |  |  |
Passenger car | 4,063 | 25.966(24.618,27.314) | 9.167(6.918,11.415) | 9.928(4.629,15.228) | 7.384(3.613,11.154)
Light truck | 1,213 | 22.341(19.997,24.685) | 9.113(5.987,12.239) | 9.52(3.705,15.335) | 13.447(6.271,20.623)
Van | 290 | 27.241(22.117,32.365) | 4.829(0,10.283) | 6.556(0,17.997) | 7.793(0,18.304)
SUV | 705 | 23.404(20.279,26.53) | 14.224(9.007,19.441) | 15.617(5.833,25.401) | 16.67(6.355,26.985)

  * •

Table 15: Percentage of severe injury in ABDOMEN and associated 95% CIs by
different covariates across DR adjustment methods

Covariate | n | Unweighted (95% CI) | GPPP (95% CI) | LWP (95% CI) | AIPW (95% CI)
---|---|---|---|---|---
Total | 6,271 | 9.919(9.179,10.658) | 6.677(4.408,8.946) | 7.621(1.93,13.313) | 6.479(2.354,10.604)
Gender |  |  |
Male | 3,230 | 10.464(9.409,11.52) | 7.694(4.134,11.253) | 8.837(1.872,15.802) | 3.552(0,11.317)
Female | 3,041 | 9.339(8.305,10.373) | 5.931(3.485,8.376) | 6.724(1.411,12.036) | 8.852(3.96,13.744)
Age group |  |  |
16-19 | 659 | 11.836(9.37,14.302) | 6.592(2.583,10.601) | 7.886(0,16.685) | 0(0,22.12)
20-39 | 2,732 | 10.505(9.355,11.655) | 6.8(4.066,9.535) | 7.782(1.873,13.691) | 7.539(1.553,13.524)
40-64 | 1,946 | 8.941(7.674,10.209) | 7.109(4.012,10.205) | 8.157(1.388,14.926) | 7.149(3.55,10.749)
65+ | 934 | 8.887(7.062,10.711) | 5.75(2.911,8.589) | 6.179(2.056,10.301) | 8.945(0.561,17.329)
Occupant role |  |  |
Driver | 1,547 | 12.864(11.195,14.532) | 8.85(4.445,13.255) | 10.308(1.336,19.28) | 13.363(2.809,23.917)
Passenger | 4,724 | 8.954(8.14,9.768) | 6.1(3.73,8.47) | 6.921(1.726,12.116) | 4.778(0,9.568)
Seating Row |  |  |
Front | 5,853 | 9.465(8.715,10.215) | 6.414(4.287,8.541) | 7.28(2.052,12.507) | 6.264(2.088,10.44)
Rear | 418 | 16.268(12.73,19.806) | 13.822(2.075,25.57) | 16.764(0,38.476) | 12.916(3.318,22.514)
Restraint use |  |  |
Restraint | 2,275 | 11.648(10.33,12.967) | 8.836(4.185,13.488) | 10.761(0,22.227) | 13.03(5.326,20.733)
Unrestraint | 3,996 | 8.934(8.05,9.818) | 5.629(3.583,7.675) | 6.103(2.64,9.565) | 2.976(0,8.312)
Air bag |  |  |
Deployed | 2,194 | 10.255(8.986,11.525) | 5.091(0,10.404) | 6.952(0,19.7) | 0.928(0,8.901)
Not deployed | 4,077 | 9.738(8.828,10.648) | 7.718(5.486,9.95) | 7.907(5.302,10.512) | 10.032(5.212,14.852)
Injury scale (AIS) |  |  |
3 | 1,977 | 7.081(5.951,8.212) | 9.233(5.979,12.487) | 9.28(5.232,13.327) | 10.554(5.247,15.861)
4 | 761 | 21.682(18.754,24.61) | 27.838(18.134,37.542) | 28.076(19.007,37.146) | 24.953(13.553,36.352)
5+ | 781 | 33.291(29.986,36.596) | 35.512(15.655,55.37) | 37.705(13.063,62.348) | 31.665(5.388,57.942)
Days hospitalized |  |  |
0 | 2,259 | 11.554(10.236,12.872) | 13.306(4.864,21.747) | 16.519(2.786,30.252) | 6.87(0,26.651)
1-3 | 1,757 | 4.098(3.171,5.025) | 3.898(0.778,7.017) | 3.158(0.132,6.183) | 3.129(0.835,5.424)
4-7 | 1,153 | 9.193(7.526,10.861) | 7.787(4.405,11.169) | 7.487(4.375,10.598) | 9.753(5.341,14.166)
8-14 | 640 | 15.156(12.378,17.934) | 12.72(8.472,16.968) | 13.127(8.583,17.671) | 13.053(8.499,17.606)
15+ | 462 | 18.615(15.066,22.164) | 17.194(11.338,23.05) | 17.839(11.819,23.858) | 16.739(9.864,23.615)
Delta-v (Km/h) |  |  |
Minor | 404 | 4.208(2.25,6.166) | 6.388(1.47,11.306) | 8.723(0,21.201) | 3.851(0,10.325)
Moderate | 3,304 | 5.72(4.928,6.512) | 4.55(2.512,6.588) | 5.446(0,11.202) | 4.565(1.801,7.329)
Severe | 2,563 | 16.231(14.803,17.659) | 11.707(8.402,15.011) | 12.236(7.964,16.508) | 11.988(2.973,21.003)
Damage distribution |  |  |
Wide | 4,657 | 10.715(9.827,11.603) | 6.978(4.739,9.217) | 7.867(2.418,13.317) | 6.987(1.455,12.519)
Narrow | 320 | 10.312(6.98,13.645) | 6.759(0.837,12.681) | 8.316(0,19.15) | 7.17(0,17.036)
Corner | 584 | 8.219(5.992,10.447) | 9.113(3.785,14.441) | 9.514(3.29,15.737) | 9.046(1.952,16.139)
Other | 710 | 5.915(4.18,7.651) | 2.464(0,6.822) | 4.08(0,13.134) | 0.848(0,3.768)
Rollover |  |  |
Yes | 4,942 | 9.996(9.16,10.832) | 7.036(4.712,9.36) | 7.864(2.674,13.054) | 9.018(5.334,12.703)
No | 1,329 | 9.631(8.045,11.217) | 5.026(0.376,9.677) | 6.532(0,15.904) | 0(0,8.629)
Deformation location |  |  |
Front | 3,671 | 8.172(7.286,9.058) | 7.344(4.903,9.785) | 8.009(3.232,12.787) | 9.683(4.673,14.693)
Right | 1,123 | 14.604(12.538,16.669) | 9.325(5.04,13.609) | 10.978(1.525,20.431) | 1.682(0,14.697)
Left | 857 | 14.002(11.679,16.326) | 4.597(0,9.713) | 5.728(0,14.156) | 5.434(0,12)
Rear | 620 | 6.129(4.241,8.017) | 2.253(0,6.802) | 3.513(0,11.383) | 1.418(0,5.151)
Model year |  |  |
$\leq$2003 | 2,529 | 10.874(9.661,12.087) | 5.716(1.128,10.303) | 6.679(0,16.721) | 1.923(0,10.724)
2004-2007 | 2,377 | 9.34(8.17,10.509) | 8.557(5.391,11.724) | 8.984(3.825,14.143) | 12.216(6.554,17.878)
2008-2011 | 1,019 | 10.01(8.167,11.853) | 5.989(1.648,10.33) | 7.077(2.546,11.607) | 6.495(0,13.18)
2012+ | 346 | 6.647(4.023,9.272) | 2.479(0,7.511) | 3.11(0,8.306) | 3.667(0,12.272)
Vehicle make |  |  |
American | 3,635 | 9.684(8.722,10.645) | 6.702(3.843,9.56) | 7.917(0.565,15.268) | 7.181(0.778,13.584)
Japanese | 1,927 | 10.171(8.822,11.521) | 7.5(4.529,10.471) | 8.118(3.518,12.719) | 6.951(2.257,11.645)
Korean | 387 | 9.561(6.631,12.49) | 5.316(2.03,8.602) | 6.271(0,13.168) | 0.991(0,7.926)
Other | 322 | 11.491(8.007,14.974) | 3.667(0.61,6.723) | 4.116(0.173,8.06) | 1.609(0,4.707)
Vehicle type |  |  |
Passenger car | 4,063 | 11.149(10.182,12.117) | 6.76(4.635,8.885) | 7.677(2.315,13.039) | 9.024(4.753,13.294)
Light truck | 1,213 | 7.997(6.47,9.523) | 7.318(3.225,11.411) | 8.158(1.289,15.028) | 0(0,13.862)
Van | 290 | 8.276(5.105,11.447) | 2.859(0,7.441) | 4.148(0,13.173) | 5.129(0,12.484)
SUV | 705 | 6.809(4.949,8.668) | 6.509(2.655,10.362) | 7.666(0,15.435) | 4.766(1.067,8.466)

  * •

Table 16: Percentage of severe injury in THORAX and associated 95% CIs by
different covariates across DR adjustment methods

Covariate | n | Unweighted (95% CI) | GPPP (95% CI) | LWP (95% CI) | AIPW (95% CI)
---|---|---|---|---|---
Total | 6,271 | 33.934(32.762,35.106) | 21.087(14.925,27.248) | 29.62(17.969,41.272) | 21.39(18.238,24.541)
Gender |  |  |
Male | 3,230 | 37.337(35.669,39.006) | 23.605(17.945,29.264) | 31.925(20.364,43.486) | 21.954(18.66,25.249)
Female | 3,041 | 30.319(28.685,31.953) | 19.353(12.307,26.399) | 28.049(15.549,40.548) | 21.074(16.628,25.52)
Age group |  |  |
16-19 | 659 | 37.329(33.636,41.022) | 17.62(6.253,28.988) | 34.815(9.195,60.436) | 21.41(13.6,29.219)
20-39 | 2,732 | 31.442(29.701,33.183) | 15.872(8.609,23.136) | 22.863(11.708,34.017) | 15.318(9.955,20.681)
40-64 | 1,946 | 32.066(29.992,34.139) | 22.877(16.442,29.312) | 31.709(18.647,44.771) | 21.864(16.993,26.734)
65+ | 934 | 42.719(39.547,45.892) | 35.715(29.256,42.175) | 41.792(31.461,52.122) | 38.108(31.117,45.098)
Occupant role |  |  |
Driver | 1,547 | 41.047(38.596,43.498) | 25.589(15.135,36.044) | 39.822(19.233,60.411) | 22.188(13.747,30.629)
Passenger | 4,724 | 31.605(30.279,32.93) | 20.007(13.585,26.429) | 27.096(16.702,37.489) | 21.249(17.329,25.17)
Seating Row |  |  |
Front | 5,853 | 33.18(31.973,34.386) | 20.399(14.202,26.596) | 28.514(17.063,39.964) | 20.94(17.786,24.095)
Rear | 418 | 44.498(39.733,49.262) | 40.118(25.011,55.225) | 59.85(33.897,85.803) | 34.6(20.286,48.914)
Restraint use |  |  |
Restraint | 2,275 | 39.253(37.246,41.259) | 25.078(15.779,34.377) | 40.585(21.1,60.069) | 28.13(21.873,34.387)
Unrestraint | 3,996 | 30.906(29.473,32.339) | 18.765(12.572,24.958) | 23.818(14.563,33.074) | 17.835(14.413,21.256)
Air bag |  |  |
Deployed | 2,194 | 36.372(34.359,38.385) | 22.703(12.088,33.318) | 38.464(17.814,59.114) | 23.947(17.058,30.836)
Not deployed | 4,077 | 32.622(31.183,34.061) | 20.517(14.113,26.92) | 24.339(14.383,34.294) | 20.319(15.73,24.908)
Injury scale (AIS) |  |  |
3 | 1,977 | 42.742(40.561,44.922) | 44.551(39.909,49.194) | 45.565(41.221,49.909) | 44.497(38.612,50.382)
4 | 761 | 72.405(69.229,75.581) | 71.412(63.902,78.923) | 71.434(63.938,78.931) | 74.925(64.879,84.971)
5+ | 781 | 70.679(67.486,73.871) | 82.191(74.038,90.344) | 83.318(73.489,93.148) | 79.427(68.421,90.433)
Days hospitalized |  |  |
0 | 2,259 | 30.102(28.21,31.993) | 16.397(3.115,29.679) | 33.637(10.187,57.087) | 20.958(15.035,26.88)
1-3 | 1,757 | 24.986(22.961,27.01) | 16.58(10.727,22.433) | 16.916(10.974,22.857) | 15.234(10.013,20.456)
4-7 | 1,153 | 35.386(32.626,38.146) | 30.08(23.956,36.203) | 30.835(24.826,36.843) | 34.479(27.631,41.326)
8-14 | 640 | 49.375(45.502,53.248) | 41.973(34.31,49.636) | 41.683(34.216,49.15) | 39.04(31.172,46.909)
15+ | 462 | 61.688(57.255,66.121) | 53.435(46.093,60.777) | 52.866(45.985,59.748) | 48.834(40.281,57.387)
Delta-v (Km/h) |  |  |
Minor | 404 | 19.059(15.229,22.889) | 11.995(1.156,22.834) | 30.193(8.357,52.029) | 8.541(0,20.813)
Moderate | 3,304 | 25.938(24.444,27.433) | 17.681(10.649,24.712) | 27.582(13.704,41.46) | 16.779(13.611,19.947)
Severe | 2,563 | 46.586(44.655,48.517) | 32.809(27.293,38.324) | 34.293(28.012,40.575) | 35.216(29.025,41.407)
Damage distribution |  |  |
Wide | 4,657 | 33.906(32.546,35.266) | 21.063(14.911,27.214) | 28.624(18.042,39.206) | 23.114(19.528,26.7)
Narrow | 320 | 36.562(31.286,41.839) | 27.796(19.029,36.564) | 37.404(23.902,50.906) | 22.562(10.103,35.022)
Corner | 584 | 26.884(23.288,30.479) | 17.923(10.176,25.67) | 24.838(10.202,39.473) | 15.681(5.905,25.458)
Other | 710 | 38.732(35.149,42.316) | 22.155(10.491,33.82) | 38.694(15.227,62.161) | 16.249(4.619,27.879)
Rollover |  |  |
Yes | 4,942 | 32.436(31.131,33.741) | 20.109(13.803,26.415) | 27.518(16.931,38.105) | 20.769(16.931,24.608)
No | 1,329 | 39.503(36.875,42.132) | 25.651(17.024,34.278) | 39.077(20.706,57.449) | 24.238(15.953,32.522)
Deformation location |  |  |
Front | 3,671 | 26.832(25.399,28.265) | 19.037(12.539,25.536) | 25.505(14.472,36.537) | 19.842(14.653,25.03)
Right | 1,123 | 45.77(42.856,48.684) | 30.62(20.887,40.352) | 42.05(25.575,58.525) | 30.289(22.563,38.016)
Left | 857 | 44.924(41.594,48.254) | 20.7(2.847,38.554) | 30.117(7.802,52.431) | 20.237(4.837,35.637)
Rear | 620 | 39.355(35.509,43.2) | 21.911(8.05,35.771) | 37.303(12.58,62.027) | 20.181(7.315,33.046)
Model year |  |  |
$\leq$2003 | 2,529 | 35.389(33.526,37.253) | 24.05(16.137,31.962) | 37.778(20.449,55.108) | 22.382(17.842,26.922)
2004-2007 | 2,377 | 34.034(32.13,35.939) | 22.589(15.129,30.049) | 29.434(17.015,41.853) | 24.151(17.576,30.727)
2008-2011 | 1,019 | 31.403(28.554,34.253) | 15.693(6.189,25.198) | 20.036(6.962,33.11) | 14.735(5.492,23.979)
2012+ | 346 | 30.058(25.227,34.889) | 18.322(7.572,29.073) | 20.336(7.789,32.883) | 23.776(12.118,35.433)
Vehicle make |  |  |
American | 3,635 | 33.92(32.381,35.459) | 25.321(18.17,32.471) | 37.287(20.562,54.012) | 24.194(19.862,28.526)
Japanese | 1,927 | 34.51(32.387,36.632) | 17.178(8.904,25.451) | 21.274(9.996,32.551) | 17.272(10.022,24.522)
Korean | 387 | 32.558(27.89,37.227) | 21.338(10.317,32.358) | 30.873(11.583,50.162) | 25.404(14.335,36.473)
Other | 322 | 32.298(27.191,37.406) | 11.894(0.98,22.807) | 13.358(0.14,26.576) | 14.575(5.943,23.206)
Vehicle type |  |  |
Passenger car | 4,063 | 35.565(34.093,37.037) | 20.78(14.442,27.117) | 28.72(17.684,39.755) | 21.834(18.109,25.559)
Light truck | 1,213 | 31.904(29.281,34.527) | 20.445(10.611,30.28) | 28.5(12.712,44.289) | 20.931(14.712,27.149)
Van | 290 | 26.897(21.793,32) | 25.071(10.311,39.832) | 39.315(14.396,64.234) | 19.598(6.469,32.727)
SUV | 705 | 30.922(27.51,34.334) | 21.916(12.779,31.053) | 32.376(15.318,49.435) | 20.32(12.643,27.996)

  * •

Table 17: Percentage of severe injury in SPINE and associated 95% CIs by
different covariates across DR adjustment methods

Covariate | n | Unweighted (95% CI) | GPPP (95% CI) | LWP (95% CI) | AIPW (95% CI)
---|---|---|---|---|---
Total | 6,271 | 3.716(3.247,4.184) | 6.735(4.696,8.774) | 6.978(2.777,11.18) | 6.205(3.15,9.261)
Gender |  |  |
Male | 3,230 | 4.18(3.489,4.87) | 6.819(4.049,9.588) | 7.154(2.499,11.809) | 8.946(5.07,12.822)
Female | 3,041 | 3.223(2.595,3.85) | 6.719(3.861,9.577) | 6.891(2.261,11.522) | 4.21(0,9.072)
Age group |  |  |
16-19 | 659 | 3.49(2.089,4.891) | 1.823(0,4.007) | 2.358(0,9.212) | 0(0,3.847)
20-39 | 2,732 | 3.807(3.089,4.524) | 5.099(2.982,7.217) | 5.406(1.363,9.448) | 3.964(0.399,7.529)
40-64 | 1,946 | 3.443(2.633,4.253) | 7.68(5.417,9.943) | 7.948(3.292,12.603) | 9.501(5.524,13.479)
65+ | 934 | 4.176(2.893,5.458) | 12.795(7.935,17.655) | 12.616(7.457,17.775) | 11.194(1.223,21.164)
Occupant role |  |  |
Driver | 1,547 | 5.624(4.476,6.772) | 7.059(2.952,11.166) | 7.549(0,16.523) | 3.584(0,10.498)
Passenger | 4,724 | 3.091(2.597,3.584) | 6.683(4.361,9.005) | 6.868(3.323,10.412) | 6.93(3.137,10.722)
Seating Row |  |  |
Front | 5,853 | 3.434(2.968,3.901) | 6.498(4.559,8.438) | 6.73(2.905,10.554) | 5.999(2.883,9.116)
Rear | 418 | 7.656(5.107,10.204) | 12.752(4.811,20.692) | 13.399(0,29.785) | 9.724(1.107,18.341)
Restraint use |  |  |
Restraint | 2,275 | 4.308(3.473,5.142) | 5.92(1.798,10.042) | 6.805(0,16.123) | 6.475(0,14.4)
Unrestraint | 3,996 | 3.378(2.818,3.939) | 6.766(4.721,8.812) | 6.797(4.24,9.353) | 6.268(3.289,9.247)
Air bag |  |  |
Deployed | 2,194 | 3.874(3.067,4.682) | 8.504(3.145,13.864) | 10.364(0.927,19.801) | 6.919(0,14.085)
Not deployed | 4,077 | 3.63(3.056,4.204) | 5.876(4.41,7.343) | 5.826(4.01,7.641) | 5.954(3.153,8.756)
Injury scale (AIS) |  |  |
3 | 1,977 | 5.513(4.507,6.52) | 17.854(14.154,21.553) | 17.101(12.953,21.249) | 18.924(12.225,25.623)
4 | 761 | 4.731(3.222,6.239) | 16.246(9.105,23.387) | 15.862(8.16,23.564) | 11.393(0.586,22.2)
5+ | 781 | 8.707(6.729,10.684) | 22.462(10.034,34.889) | 24.098(8.787,39.409) | 22.264(8.191,36.336)
Days hospitalized |  |  |
0 | 2,259 | 2.745(2.071,3.418) | 3.815(0.804,6.826) | 4.92(0,12.6) | 0(0,6.667)
1-3 | 1,757 | 2.732(1.97,3.494) | 4.476(2.538,6.415) | 4.054(2.23,5.877) | 5.118(1.926,8.31)
4-7 | 1,153 | 4.51(3.312,5.708) | 13.038(9.061,17.015) | 12.105(8.546,15.665) | 13.629(8.565,18.692)
8-14 | 640 | 5.625(3.84,7.41) | 14.223(10.23,18.215) | 13.837(10.044,17.63) | 13.278(8.82,17.737)
15+ | 462 | 7.576(5.163,9.989) | 25.109(19.802,30.416) | 24.763(19.61,29.915) | 25.392(20.03,30.754)
Delta-v (Km/h) |  |  |
Minor | 404 | 2.228(0.789,3.667) | 11.229(1.136,21.322) | 12.934(0,26.013) | 8.643(0,30.853)
Moderate | 3,304 | 2.542(2.006,3.079) | 6.269(3.382,9.156) | 6.597(1.454,11.741) | 6.322(3.002,9.642)
Severe | 2,563 | 5.462(4.583,6.342) | 8.53(5.654,11.406) | 8.535(5.507,11.562) | 7.466(3.136,11.796)
Damage distribution |  |  |
Wide | 4,657 | 3.393(2.873,3.913) | 5.28(3.515,7.045) | 5.532(1.939,9.125) | 3.803(0.55,7.057)
Narrow | 320 | 5(2.612,7.388) | 2.417(0,5.39) | 2.967(0,8.287) | 2.673(0,5.984)
Corner | 584 | 1.884(0.781,2.986) | 7.107(2.759,11.454) | 7.097(2.231,11.963) | 15.586(0.739,30.432)
Other | 710 | 6.761(4.914,8.607) | 18.668(10.843,26.494) | 19.005(6.446,31.564) | 17.857(7.203,28.512)
Rollover |  |  |
Yes | 4,942 | 3.157(2.669,3.644) | 5.129(3.248,7.01) | 5.354(1.836,8.872) | 4.668(1.216,8.119)
No | 1,329 | 5.794(4.538,7.05) | 13.905(9.303,18.508) | 14.245(5.965,22.524) | 13.444(6.794,20.094)
Deformation location |  |  |
Front | 3,671 | 3.242(2.669,3.815) | 5.676(3.614,7.738) | 5.811(2.379,9.244) | 3.488(0,7.784)
Right | 1,123 | 3.562(2.478,4.646) | 3.673(0,7.795) | 4.021(0,10.545) | 7.553(1.56,13.546)
Left | 857 | 3.851(2.562,5.139) | 7.337(0.385,14.289) | 7.933(0.269,15.598) | 7.972(0,17.665)
Rear | 620 | 6.613(4.657,8.569) | 22.12(12.372,31.869) | 22.254(9.529,34.98) | 20.896(8.037,33.755)
Model year |  |  |
$\leq$2003 | 2,529 | 3.598(2.872,4.324) | 7.792(5.022,10.561) | 8.376(0.769,15.983) | 4.647(0,10.046)
2004-2007 | 2,377 | 3.366(2.641,4.091) | 8.083(5.475,10.691) | 8.184(4.72,11.647) | 10.824(6.32,15.328)
2008-2011 | 1,019 | 4.514(3.239,5.789) | 3.349(1.139,5.558) | 3.365(1.098,5.633) | 4.816(0.267,9.366)
2012+ | 346 | 4.624(2.411,6.837) | 5.411(1.644,9.178) | 5.207(1.219,9.195) | 0(0,15.701)
Vehicle make |  |  |
American | 3,635 | 3.301(2.72,3.882) | 7.388(4.517,10.258) | 7.965(1.09,14.839) | 8.747(4.478,13.016)
Japanese | 1,927 | 4.307(3.401,5.214) | 6.099(2.908,9.29) | 6.032(2.707,9.357) | 1.562(0,7.543)
Korean | 387 | 3.359(1.564,5.154) | 8.952(2.792,15.112) | 9.172(2.504,15.841) | 8.469(0.439,16.499)
Other | 322 | 5.28(2.837,7.722) | 3.023(0,8.831) | 2.777(0,8.478) | 3.854(0,9.39)
Vehicle type |  |  |
Passenger car | 4,063 | 3.569(2.998,4.139) | 6.075(3.814,8.337) | 6.245(2.521,9.969) | 4.639(0.478,8.8)
Light truck | 1,213 | 4.122(3.003,5.241) | 8.549(3.935,13.164) | 8.846(2.517,15.175) | 9.311(2.577,16.044)
Van | 290 | 1.379(0.037,2.722) | 3.755(0,11.694) | 4.766(0,15.574) | 12.787(0,27.049)
SUV | 705 | 4.823(3.241,6.404) | 8.681(1.348,16.013) | 9.09(0.315,17.865) | 8.533(0,19.472)

  * •