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Table 2 Simulation results

From: Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin

Estimator Model specification Bias (×100) at t = 3 Bias (× 100) at t = 5
Censoring Event Covariate Control Test Log of risk ratio Control Test Log of risk ratio
Scenario 1: 30% censoring in both control and test groups.
IPCW Correct 0.0 0.0 −0.2 − 0.1 0.0 − 0.4
Kaplan–Meier Incorrect    0.5 0.4 −0.2 1.9 1.5 −0.9
Parametric Correct Correct 0.0 (1.23) 0.0 (1.22) −0.2 (1.23) 0.0 (1.10) 0.0 (1.08) −0.3 (1.09)
g-formula   Correct Incorrect 0.1 0.1 0.1 1.2 0.4 3.9
   Incorrect Correct 0.5 0.1 3.4 2.0 1.7 −2.2
   Incorrect Incorrect 0.5 0.1 3.4 1.9 1.7 −2.4
Proposed Correct Correct Correct −0.1 (1.04) 0.0 (1.01) −0.3 (1.02) − 0.3 (1.00) − 0.1 (0.99) − 0.8 (1.01)
doubly robust   Correct Incorrect 0.0 0.0 − 0.1 0.2 0.0 0.8
   Incorrect Correct 0.0 0.0 −0.2 0.0 0.0 −0.4
   Incorrect Incorrect 0.0 0.0 −0.2 0.0 0.0 −0.4
  Incorrect Correct Correct −0.1 0.0 −0.2 − 0.3 −0.1 − 0.7
   Correct Incorrect 0.0 0.0 −0.1 0.2 0.0 0.9
   Incorrect Correct 0.5 0.4 −0.2 1.9 1.5 −1.0
   Incorrect Incorrect 0.5 0.4 −0.2 1.9 1.6 −0.9
Scenario 2: 20% censoring in both control and test groups.
IPCW Correct 0.0 0.0 −0.3 − 0.1 0.0 − 0.3
Kaplan–Meier Incorrect    0.3 0.2 −0.2 1.3 1.0 −0.5
Parametric Correct Correct 0.0 (1.25) 0.0 (1.24) −0.2 (1.26) 0.0 (1.06) 0.0 (1.04) −0.3 (1.04)
g-formula   Correct Incorrect 0.0 0.0 0.2 1.1 0.3 3.9
   Incorrect Correct 0.1 −0.2 4.2 1.4 1.2 −1.4
   Incorrect Incorrect 0.1 −0.2 4.2 1.3 1.2 − 1.6
Proposed Correct Correct Correct −0.1 (1.03) 0.0 (1.03) −0.3 (1.05) − 0.2 (1.00) − 0.1 (0.99) −0.6 (1.01)
doubly robust   Correct Incorrect 0.0 0.0 −0.2 0.1 0.0 0.5
   Incorrect Correct 0.0 0.0 −0.3 0.0 0.0 −0.3
   Incorrect Incorrect 0.0 0.0 −0.3 0.0 0.0 −0.3
  Incorrect Correct Correct −0.1 0.0 −0.3 − 0.2 −0.1 − 0.4
   Correct Incorrect 0.0 0.0 −0.2 0.1 0.0 0.5
   Incorrect Correct 0.3 0.2 −0.2 1.3 1.0 −0.5
   Incorrect Incorrect 0.3 0.2 −0.2 1.3 1.0 −0.5
Scenario 3: 9% censoring in control group and 12% censoring in test group
IPCW Correct 0.0 0.0 −0.3 −0.1 0.0 −0.3
Kaplan–Meier Incorrect    0.1 0.1 −0.8 0.5 0.6 −1.6
Parametric Correct Correct 0.0 (1.26) 0.0 (1.25) −0.2 (1.28) 0.0 (1.03) 0.0 (1.02) −0.3 (1.02)
g-formula   Correct Incorrect 0.0 0.0 0.1 1.0 0.2 3.8
   Incorrect Correct −0.3 −0.5 3.4 0.6 0.8 −2.2
   Incorrect Incorrect −0.3 − 0.5 3.3 0.6 0.7 −2.4
Proposed Correct Correct Correct 0.0 (1.00) 0.0 (1.00) −0.3 (1.00) −0.1 (1.00) − 0.1 (1.00) −0.4 (1.00)
doubly robust   Correct Incorrect 0.0 0.0 −0.3 0.0 0.0 0.1
   Incorrect Correct 0.0 0.0 −0.3 0.0 0.0 −0.3
   Incorrect Incorrect 0.0 0.0 −0.3 0.0 0.0 −0.3
  Incorrect Correct Correct 0.0 0.0 −0.3 −0.1 −0.1 0.0
   Correct Incorrect 0.0 0.0 −0.3 0.0 0.0 0.1
   Incorrect Correct 0.1 0.1 −0.8 0.5 0.6 −1.6
   Incorrect Incorrect 0.1 0.1 −0.8 0.5 0.6 −1.6
  1. Numbers in parentheses are the relative efficiency compared with the IPCW Kaplan–Meier estimate with a correctly specified censoring model. If the bias exceeded half of the standard error of the estimates, the printed bias is shown in bold. True values calculated from a large simulated dataset were (0.89, 0.92, 0.69) (at t = 3) and (0.81, 0.86, 0.74) (at t = 5) for control group, test group, and risk ratio, respectively. The biases (×100) from the method assuming the baseline-conditional independent censoring at t = 5 for the control and test groups were (0.5, 0.4) (scenario 1), (0.4, 0.3) (scenario 2), and (0.2, 0.2) (scenario 3)