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Table 1 Log odds ratio estimates from simulation study

From: A comparison of methods to estimate the survivor average causal effect in the presence of missing data: a simulation study

ORUY

ORUZ

Estimation method

Monotonicity

Valid

Violated

Estimatea

SE

SB

MSE

Coverageb

Estimatea

SE

SB

MSE

Coverageb

0.5

0.5

Average τ

0.92

0.09

   

0.92

0.09

   

Marginal structural model

−0.54

0.12

−29

0.01

91.6

− 0.53

0.11

−14

0.01

94.6

Sensitivity analysis

          

SP = 0.5

−0.34

0.11

164

0.04

 

−0.42

0.10

92

0.02

 

SP = 1

−0.54

0.11

−26

0.01

 

−0.52

0.10

−4

0.01

 

SP = 2

−0.84

0.11

− 305

0.12

 

−0.67

0.10

− 159

0.04

 

0.5

2.0

Average τ

1.10

0.11

   

1.10

0.11

   

Marginal structural model

−0.48

0.11

27

0.01

93.6

−0.50

0.10

11

0.01

92.4

Sensitivity analysis

          

SP = 0.5

−0.33

0.10

176

0.04

 

−0.42

0.10

95

0.02

 

SP = 1

−0.48

0.10

30

0.01

 

−0.49

0.10

20

0.01

 

SP = 2

−0.71

0.10

− 197

0.05

 

−0.61

0.10

− 106

0.02

 

2.0

0.5

Average τ

1.12

0.09

   

1.12

0.09

   

Marginal structural model

−0.46

0.10

54

0.01

90.4

−0.49

0.09

23

0.01

92.6

Sensitivity analysis

          

SP = 0.5

−0.26

0.09

266

0.07

 

−0.38

0.09

143

0.02

 

SP = 1

−0.47

0.09

46

0.01

 

−0.48

0.09

33

0.01

 

SP = 2

−0.76

0.09

− 271

0.07

 

−0.64

0.09

− 140

0.02

 

2.0

2.0

Average τ

0.90

0.08

   

0.89

0.07

   

Marginal structural model

−0.53

0.09

− 25

0.01

92.9

−0.52

0.08

−9

0.01

94.3

Sensitivity analysis

          

SP = 0.5

−0.36

0.08

183

0.03

 

−0.43

0.08

104

0.01

 

SP = 1

−0.52

0.08

−7

0.01

 

−0.50

0.08

9

0.01

 

SP = 2

−0.75

0.08

− 290

0.06

 

−0.62

0.08

− 144

0.02

 
  1. aEstimates of the log odds ratio have been averaged over 1200 simulated datasets from each scenario
  2. bCoverage indicates the percentage of datasets in each scenario where the true value of the SACE was within the bias-corrected bootstrap confidence interval of the marginal structural model
  3. MSE Mean square error, SACE Survivor average causal effect, SB Standardized bias as a percentage, SE Empirical standard error, SP Sensitivity parameter.
  4. ORUY is the odds ratio effect of U on the outcome. ORUZ is the odds ratio effect of U on survival. τ is the ratio of the odds of the outcome following high iron intake between compliant-survivors and always-survivors. True SACE log odds ratio = ln(0.6) = − 0.511.