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 |