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Table 3 Simulated estimates with independent censoring distribution, varying censoring rate (2000 repetitions, n = 250)

From: On hazard ratio estimators by proportional hazards models in matched-pair cohort studies

Method Censoring rate MCSE MESE Log conditional-HR Log marginal-HR
Bias 95% CP (%) RMSE Bias 95% CP (%) RMSE
  Log conditional-HR = log(2) = 0.693; Log marginal-HR = 0.437         
Frailty Cox model 1 0.13 0.13 −0.03 93.50 0.14 0.23 58.80 0.27
Stratified Cox model   0.18 0.18 0.00 95.20 0.18 0.26 72.15 0.32
Unstratified Cox model without sandwich variance   0.10 0.12 −0.19 66.15 0.22 0.07 95.35 0.12
Unstratified Cox model with sandwich variance   0.10 0.10 −0.19 51.80 0.22 0.07 90.75 0.12
Frailty Cox model 2 0.15 0.15 −0.03 94.49 0.15 0.22 68.69 0.27
Stratified Cox model   0.21 0.20 0.01 95.45 0.21 0.26 76.85 0.34
Unstratified Cox model without sandwich variance   0.12 0.14 −0.16 80.70 0.20 0.09 93.25 0.15
Unstratified Cox model with sandwich variance   0.12 0.12 −0.16 70.90 0.20 0.09 88.40 0.15
Frailty Cox model 4 0.17 0.18 −0.04 95.19 0.18 0.22 78.81 0.28
Stratified Cox model   0.25 0.25 0.01 94.85 0.25 0.26 83.40 0.37
Unstratified Cox model without sandwich variance   0.15 0.17 −0.13 89.55 0.20 0.12 91.95 0.19
Unstratified Cox model with sandwich variance   0.15 0.15 −0.13 84.20 0.20 0.12 87.35 0.19
  Log conditional-HR = log(1) = 0; Log marginal-HR = 0         
Frailty Cox model 1 0.14 0.14 0.00 95.55 0.14 0.00 95.55 0.14
Stratified Cox model   0.18 0.18 0.00 95.75 0.18 0.00 95.75 0.18
Unstratified Cox model without sandwich variance   0.11 0.13 0.00 97.70 0.11 0.00 97.70 0.11
Unstratified Cox model with sandwich variance   0.11 0.11 0.00 94.55 0.11 0.00 94.55 0.11
Frailty Cox model 2 0.15 0.16 0.00 95.34 0.15 0.00 95.34 0.15
Stratified Cox model   0.21 0.21 0.00 95.30 0.21 0.00 95.30 0.21
Unstratified Cox model without sandwich variance   0.13 0.15 0.00 97.45 0.13 0.00 97.45 0.13
Unstratified Cox model with sandwich variance   0.13 0.13 0.00 94.40 0.13 0.00 94.40 0.13
Frailty Cox model 4 0.19 0.19 0.00 95.78 0.19 0.00 95.78 0.19
Stratified Cox model   0.27 0.26 0.00 95.65 0.27 0.00 95.65 0.27
Unstratified Cox model without sandwich variance   0.17 0.18 0.00 97.10 0.17 0.00 97.10 0.17
Unstratified Cox model with sandwich variance   0.17 0.17 0.00 95.05 0.17 0.00 95.05 0.17
  Log conditional-HR = log(0.5) = –0.693; Log marginal-HR = –0.438         
Frailty Cox model 1 0.15 0.15 0.04 94.19 0.15 −0.22 69.19 0.27
Stratified Cox model   0.20 0.20 0.00 95.30 0.20 −0.26 76.65 0.33
Unstratified Cox model without sandwich variance   0.12 0.14 0.17 80.55 0.21 −0.09 94.20 0.15
Unstratified Cox model with sandwich variance   0.12 0.12 0.17 70.35 0.21 −0.09 89.25 0.15
Frailty Cox model 2 0.17 0.18 0.04 94.13 0.18 −0.21 79.49 0.28
Stratified Cox model   0.25 0.25 −0.01 95.10 0.25 −0.26 83.30 0.36
Unstratified Cox model without sandwich variance   0.15 0.17 0.14 89.95 0.20 −0.12 92.25 0.19
Unstratified Cox model with sandwich variance   0.15 0.15 0.14 84.90 0.20 −0.12 88.50 0.19
Frailty Cox model 4 0.22 0.22 0.03 94.97 0.22 −0.22 84.80 0.31
Stratified Cox model   0.31 0.31 −0.01 95.45 0.31 −0.27 88.55 0.41
Unstratified Cox model without sandwich variance   0.19 0.21 0.10 93.35 0.22 −0.16 91.90 0.25
Unstratified Cox model with sandwich variance   0.19 0.20 0.10 91.05 0.22 −0.16 88.40 0.25
  1. MCSE, empirical (Monte Carlo) standard error; MESE, mean estimated standard error; 95% CP, coverage proportion of 95% confidence interval; RMS,E root mean square error