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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)