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Table 2 Results simulation studies Ia to Id

From: No rationale for 1 variable per 10 events criterion for binary logistic regression analysis

Study Study Ia* and Ib Study Ic and Id
EPV 15 to 30 35 to 50 55 to 150 6 to10 12 to 18 20 to 30
Estimator \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\) \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\) \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\) \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\) \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\) \(\beta _{1}^{ML}\) \({\beta _{1}^{F}}\)
Bias             
Average bias 0.084 0.002 0.038 0.001 0.016 0.000 0.069 0.002 0.033 0.000 0.020 0.000
max 0.261 0.016 0.091 0.005 0.056 0.006 0.217 0.021 0.075 0.011 0.046 0.005
min 0.025 -0.004 0.013 -0.002 0.004 -0.005 0.023 -0.005 0.016 -0.003 0.009 -0.003
Average relative bias (%) 7.8 0.1 3.6 0.1 1.5 0.0 8.4 0.4 4.8 0 2.9 0
max 18.8 1.2 6.6 0.5 4.0 0.5 31.2 3.0 10.8 1.6 6.5 0.7
min 3.5 -0.5 1.9 -0.3 0.5 -0.7 3.3 -0.7 2.3 -0.5 1.3 -0.0
>+10% relative bias (%) 18.8 0 0 0 0 0 37.5 0 3 0 0 0
Coverage 90% CI             
Average coverage (%) 90.4 90.1 90.2 90.2 90.1 90.0 90.4 90.3 90.2 90.2 90.1 90.2
max 92.9 90.8 91.1 90.7 91.0 90.7 92.1 91.2 90.8 90.6 90.9 90.8
min 89.1 89.4 89.3 89.6 89.4 89.2 89.6 89.6 89.7 89.6 89.3 89.6
> ± 1% nominal (%) 15.6 0 3.1 0 0.6 0 10 2.5 0 0 0 0
Average width 1.102 1.059 0.752 0.738 0.487 0.483 1.183 1.133 0.828 0.811 0.653 0.646
Mean Square Error             
Average MSE 0.160 0.118 0.063 0.055 0.025 0.024 0.169 0.125 0.070 0.062 0.042 0.039
Separated data sets             
Total (%) 0.006 0 0 0.001 0 0
  1. *only for β1log(1)