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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.