|
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
| |
- aEstimates of the log odds ratio have been averaged over 1200 simulated datasets from each scenario
- 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
- MSE Mean square error, SACE Survivor average causal effect, SB Standardized bias as a percentage, SE Empirical standard error, SP Sensitivity parameter.
- 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.
