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. 2020 Jun 8;10:9219. doi: 10.1038/s41598-020-65917-x

Table 1.

Simulation results comparing the ATT estimation under the alternative hypothesis.

n method selection strategy mean bias log OR
π0 π1 Δπ log OR MSE MSE* VEB (%) coverage (%) power (%)
100 GC outcome 0.000 −0.001 −0.001 0.012 0.526 0.716 −6.2 94.1 17.7
treatment 0.002 −0.001 −0.003 0.006 0.580 0.786 −5.7 94.1 14.0
common 0.002 −0.001 −0.003 0.006 0.552 0.735 −4.2 94.8 15.1
entire −0.001 −0.001 −0.001 0.013 0.558 0.768 −8.8 93.3 16.9
IPTW outcome 0.000 −0.001 −0.001 0.008 0.578 0.727 10.8 97.3 7.8
treatment −0.000 −0.001 −0.001 0.000 0.716 0.837 −1.2 95.1 9.8
common 0.002 −0.001 −0.003 0.003 0.587 0.743 6.6 96.8 8.8
entire −0.003 −0.001 0.002 0.005 0.741 0.838 −1.5 95.2 9.6
TMLE outcome −0.001 −0.001 0.000 0.002 0.694 0.794 30.0 95.7 5.8
treatment 0.000 −0.001 −0.001 −0.020 0.876 0.955 183.3 98.8 1.0
common −0.000 −0.001 −0.001 −0.001 0.702 0.794 10.4 95.3 7.3
entire −0.003 −0.001 0.001 −0.013 0.886 0.953 412.2 98.8 0.5
FM outcome −0.004 −0.001 0.003 0.022 0.665 0.787 −16.7 90.1 18.9
treatment −0.006 −0.001 0.004 0.017 0.822 0.911 −32.3 81.3 25.2
common −0.001 −0.001 −0.000 0.010 0.653 0.795 −15.3 91.0 17.5
entire −0.008 −0.001 0.006 0.022 0.842 0.921 −33.8 80.3 26.7
300 GC outcome 0.001 −0.001 −0.002 −0.021 0.283 0.555 −1.6 94.5 43.6
treatment 0.002 −0.001 −0.003 −0.024 0.319 0.606 −2.3 94.3 35.2
common 0.002 −0.001 −0.003 −0.023 0.304 0.561 −1.5 94.8 38.5
entire 0.001 −0.001 −0.002 −0.022 0.297 0.600 −2.6 94.0 39.9
IPTW outcome 0.002 −0.001 −0.003 −0.027 0.301 0.556 16.4 97.9 24.0
treatment 0.001 −0.001 −0.002 −0.026 0.372 0.628 6.6 96.2 21.4
common 0.003 −0.001 −0.004 −0.028 0.318 0.563 9.1 96.8 26.1
entire 0.001 −0.001 −0.002 −0.025 0.361 0.622 11.7 97.2 20.0
TMLE outcome 0.000 −0.001 −0.001 −0.023 0.358 0.577 −2.3 93.6 29.0
treatment 0.002 −0.001 −0.003 −0.035 0.454 0.683 51.2 99.1 6.8
common 0.001 −0.001 −0.002 −0.023 0.378 0.582 −3.5 93.0 26.5
entire 0.002 −0.001 −0.003 −0.035 0.432 0.674 81.8 99.3 4.4
FM outcome −0.000 −0.001 −0.001 −0.020 0.351 0.579 −11.7 91.9 37.2
treatment −0.001 −0.001 −0.000 −0.022 0.444 0.656 −30.2 82.7 38.9
common 0.001 −0.001 −0.002 −0.024 0.363 0.587 −14.6 90.4 36.9
entire −0.001 −0.001 0.000 −0.020 0.439 0.662 −29.3 83.2 39.1
500 GC outcome 0.001 −0.001 −0.002 −0.014 0.217 0.509 −1.1 94.7 64.5
treatment 0.001 −0.001 −0.002 −0.014 0.245 0.556 −1.5 94.4 53.6
common 0.001 −0.001 −0.002 −0.015 0.233 0.618 −0.8 94.8 57.6
entire 0.001 −0.001 −0.002 −0.014 0.228 0.552 −2.0 94.2 60.5
IPTW outcome 0.002 −0.001 −0.003 −0.019 0.230 0.509 16.5 97.9 43.3
treatment 0.000 −0.001 −0.001 −0.013 0.285 0.574 6.8 96.6 35.4
common 0.002 −0.001 −0.003 −0.018 0.244 0.514 9.2 96.8 43.7
entire 0.000 −0.001 −0.001 −0.014 0.274 0.571 12.3 97.2 33.9
TMLE outcome 0.001 −0.001 −0.002 −0.015 0.272 0.521 −4.7 93.4 48.5
treatment 0.001 −0.001 −0.002 −0.018 0.347 0.618 35.0 99.1 15.9
common 0.000 −0.001 −0.001 −0.013 0.289 0.527 −4.8 93.1 43.7
entire 0.001 −0.001 −0.002 −0.019 0.328 0.611 51.1 99.3 12.9
FM outcome 0.001 −0.001 −0.002 −0.015 0.265 0.525 −9.9 92.4 53.0
treatment −0.001 −0.001 −0.000 −0.011 0.346 0.597 −31.0 82.7 51.7
common 0.001 −0.001 −0.001 −0.014 0.283 0.530 −15.8 90.1 52.3
entire −0.002 −0.001 0.001 −0.008 0.340 0.596 −29.8 83.2 52.6
2000 GC outcome 0.000 0.000 −0.000 −0.002 0.108 0.479 −1.7 94.7 99.6
treatment 0.001 0.000 −0.000 −0.003 0.122 0.524 −1.2 94.8 98.6
common 0.001 0.000 −0.000 −0.003 0.116 0.480 −0.9 94.7 99.1
entire 0.000 0.000 −0.000 −0.002 0.113 0.523 −1.8 94.5 99.4
IPTW outcome 0.002 0.000 −0.001 −0.006 0.113 0.478 16.3 97.6 98.1
treatment 0.000 0.000 −0.000 −0.002 0.138 0.539 7.9 96.4 93.0
common 0.002 0.000 −0.001 −0.006 0.120 0.480 9.4 97.0 97.7
entire 0.000 0.000 −0.000 −0.002 0.131 0.537 13.9 97.4 93.6
2000 TMLE outcome 0.001 0.000 −0.000 −0.002 0.132 0.483 −5.9 93.3 97.5
treatment 0.000 0.000 0.000 −0.002 0.169 0.568 18.2 98.2 71.8
common −0.000 0.000 0.000 −0.000 0.142 0.486 −5.6 93.6 95.5
entire 0.001 0.000 −0.000 −0.004 0.158 0.565 23.5 98.6 75.3
FM outcome 0.000 0.000 −0.000 −0.002 0.134 0.484 −12.0 91.6 97.7
treatment 0.001 0.000 −0.000 −0.005 0.203 0.548 −41.6 74.6 89.9
common 0.001 0.000 −0.000 −0.003 0.149 0.485 −20.5 88.5 96.7
entire 0.000 0.000 0.000 −0.002 0.162 0.543 −26.9 84.5 94.8

*MSE in the presence of an unmeasured confounder. Theoretical values: π1=0.701,π0=0.589,θ=0.492.