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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)