Skip to main content

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