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Table 1 Performance criteria stemming from the simulation study with Scenarios A to E

From: Correcting inaccurate background mortality in excess hazard models through breakpoints

Scenario Model βa = 0.3 βx =  − 0.2
Bias Rel. bias ECR RMSE Bias Rel. bias ECR RMSE
A 1 −0.012 − 0.039 95.1 0.05 0.002 − 0.012 95.1 0.13
2 0.006 0.019 94.0 0.08 0.029 −0.146 96.4 0.21
3.1 −0.001 −0.003 91.4 0.09 0.064 −0.322 96.9 0.25
3.2 −0.003 −0.009 90.4 0.09 0.077 −0.386 96.6 0.27
4 0.000 −0.002 91.1 0.09 0.070 −0.348 96.5 0.26
B 1 −0.111 −0.370 30.1 0.12 −0.366 1.832 18.2 0.39
2 0.008 0.026 90.5 0.08 0.010 −0.050 95.6 0.23
3.1 0.001 0.003 90.6 0.08 0.040 −0.201 94.9 0.27
3.2 0.000 −0.001 91.4 0.08 0.050 −0.252 94.7 0.29
4 0.000 0.000 91.4 0.08 0.045 −0.224 94.6 0.28
C 1 0.135 0.450 14.6 0.14 0.388 −1.940 17.7 0.41
2 −0.068 −0.227 88.5 0.11 −0.181 0.904 82.0 0.27
3.1 −0.049 −0.163 90.9 0.10 −0.068 0.338 93.3 0.25
3.2 − 0.051 − 0.171 91.7 0.10 −0.051 0.256 94.1 0.25
4 −0.049 − 0.163 91.2 0.10 −0.063 0.316 93.6 0.25
D 1 −0.102 −0.340 40.1 0.11 −0.536 2.681 00.6 0.55
2 −0.052 −0.174 89.2 0.09 −0.329 1.644 57.9 0.39
3.1 −0.037 −0.122 91.7 0.09 −0.195 0.974 76.7 0.32
3.2 −0.036 −0.120 91.4 0.08 −0.172 0.860 79.2 0.32
4 −0.037 − 0.122 91.7 0.09 −0.185 0.927 77.7 0.32
E 1 −0.212 −0.707 00.7 0.22 −0.694 3.468 00.1 0.70
2 −0.006 −0.019 94.7 0.05 −0.061 0.307 92.3 0.24
3.1 −0.015 −0.051 94.6 0.06 −0.001 0.004 93.7 0.29
3.2 −0.020 −0.067 95.3 0.06 0.017 −0.087 94.3 0.30
4 −0.016 −0.052 94.7 0.06 0.003 −0.013 94.0 0.29
  1. Scenarios A to E: Proportion of subjects with x = 1 is 90%