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Table 1 Mean, standard deviation (SD), bias and mean squared error (MSE) of psi estimates using different g-estimation approaches under different data-generating mechanisms

From: Instrumental variable estimation for a time-varying treatment and a time-to-event outcome via structural nested cumulative failure time models

DAG Under the null Measure Confounding-adjusted analysis IV analysis IV analysis of nested case-control sample Unadjusted analysis
Time-fixed exposure and outcome Yes Mean 0.0013 0.0044 0.0102 0.2468
SD 0.0655 0.2001 0.2665 0.0563
Bias +0.0013 +0.0044 + 0.0102 + 0.2468
MSE 0.0043 0.0400 0.0711 0.0641
No Mean 0.4591 0.4655 0.5010 0.7016
SD 0.0579 0.1885 0.2563 0.0478
Bias 0.0000 +0.0064 +0.0419 +0.2424
MSE 0.0034 0.0355 0.0674 0.0611
Time-fixed exposure and time-varying outcome Yes Mean −0.0024 −0.0018 0.0021 0.2410
SD 0.0473 0.1446 0.1950 0.0401
Bias −0.0024 − 0.0018 +0.0021 +0.2410
MSE 0.0022 0.0209 0.0380 0.0597
No Mean 0.4523 0.4489 0.5015 0.6923
SD 0.0417 0.1365 0.1833 0.0348
Bias 0.0000 −0.0033 +0.0492 +0.2400
MSE 0.0017 0.0186 0.0360 0.0588
Time-varying exposure and outcome Yes Mean −0.0018 0.0061 0.0122 0.1717
SD 0.0539 0.1428 0.1861 0.0470
Bias −0.0018 +0.0061 +0.0122 +0.1717
MSE 0.0029 0.0204 0.0348 0.0317
No Mean 0.4600 0.4588 0.4974 0.6316
SD 0.0448 0.1293 0.1706 0.0378
Bias 0.0000 −0.0012 +0.0374 +0.1716
MSE 0.0020 0.0167 0.0305 0.0309