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Table 2 Performance of the estimated regression coefficients of models fitted using different methods under study

From: Performance of Firth-and logF-type penalized methods in risk prediction for small or sparse binary data

   Estimates Relative bias (%) MSE
Coefficient Prev.(%) MLE FIRTH logF(1,1) logF(2,2) RIDGE MLE FIRTH logF(1,1) logF(2,2) RIDGE MLE FIRTH logF(1,1) logF(2,2) RIDGE
  5.5 0.33 0.29 0.30 0.28 0.26 10.84 -3.56 -1.29 -6.82 -14.72 0.25 0.19 0.20 0.18 0.10
  11.5 0.33 0.31 0.32 0.31 0.26 8.71 2.68 5.46 2.44 -12.23 0.10 0.09 0.10 0.09 0.07
β 1 20.4 0.30 0.29 0.29 0.29 0.24 0.14 -4.54 -1.81 -3.62 -19.50 0.07 0.06 0.06 0.06 0.05
  39.6 0.31 0.30 0.31 0.30 0.25 4.13 -0.14 2.62 1.19 -16.32 0.04 0.04 0.04 0.04 0.03
  59.9 0.31 0.29 0.30 0.30 0.25 1.68 -2.48 0.20 -1.19 -16.87 0.05 0.04 0.04 0.04 0.04
  5.5 0.80 0.87 0.86 0.71 0.58 -11.19 -3.41 -4.19 -21.26 -35.13 0.66 0.76 0.75 0.50 0.36
  11.5 0.98 0.91 0.91 0.82 0.78 8.92 1.50 0.67 -8.85 -13.36 0.48 0.42 0.42 0.33 0.29
β 2 20.4 0.95 0.90 0.89 0.84 0.76 5.34 0.02 -0.74 -6.12 -15.61 0.27 0.23 0.23 0.21 0.23
  39.6 0.92 0.89 0.89 0.86 0.75 2.19 -0.74 -1.50 -4.94 -16.14 0.18 0.16 0.16 0.15 0.18
  59.9 0.92 0.89 0.89 0.86 0.75 2.36 -0.56 -1.33 -4.77 -16.36 0.15 0.14 0.14 0.13 0.17
  1. Relative bias and MSE were calculated over number of simulations for which the convergence is achieved. The maximum failure rate of convergence, out of 1000 simulations, for MLE was 13% for lowest prevalence, and for RIDGE it is 51%. Max MCE=0.0251