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Table 1 Variable selection results from 100 simulation runs: median number of true positives | false positives and calculated upper bound for the per-family-error rate (PFER, in brackets) for different values of q and π thr

From: Boosting the discriminatory power of sparse survival models via optimization of the concordance index and stability selection

     

C-index boosting

  

Cox

p

p inf

n

PH-viol

q

Ï€ thr = 0.5

Ï€ thr = 0.6

Ï€ thr = 0.7

Ï€ thr = 0.8

Ï€ thr = 0.9

without π thr

lasso

1000

4

200

false

100

4 |8 (24.8)

4 |3 (11.4)

4 |1 (4.27)

4 |0 (1.92)

4 |0 (0.75)

4 |180

4 |36

    

50

4 |1 (5.20)

4 |0 (2.61)

4 |0 (0.97)

4 |0 (0.43)

4 |0 (0.17)

  
    

20

4 |0 (0.61)

4 |0 (0.33)

3 |0 (0.14)

3 |0 (0.06)

2 |0 (0.02)

  
    

15

4 |0 (0.32)

3 |0 (0.17)

3 |0 (0.08)

3 |0 (0.04)

2 |0 (0.01)

  
    

10

3 |0 (0.13)

3 |0 (0.07)

3 |0 (0.04)

2 |0 (0.02)

2 |0 (0.01)

  
    

5

2 |0 (0.03)

2 |0 (0.02)

2 |0 (0.01)

2 |0 (0.00)

1 |0 (0.00)

  

500

4

200

false

100

4 |14 (51.9)

4 |5 (27.9)

4 |2 (10.4)

4 |0 (4.73)

4 |0 (1.87)

4 |166

4 |31

    

50

4 |3 (12.4)

4 |1 (5.71)

4 |0 (2.13)

4 |0 (0.96)

4 |0 (0.38)

  
    

20

4 |0 (1.55)

4 |0 (0.82)

4 |0 (0.30)

3 |0 (0.14)

3 |0 (0.05)

  
    

15

4 |0 (0.79)

4 |0 (0.44)

3 |0 (0.17)

3 |0 (0.07)

3 |0 (0.03)

  
    

10

4 |0 (0.31)

3 |0 (0.16)

3 |0 (0.07)

3 |0 (0.03)

2 |0 (0.01)

  
    

5

3 |0 (0.07)

3 |0 (0.03)

2 |0 (0.02)

2 |0 (0.01)

1 |0 (0.00)

  

500

4

200

true

100

4|13 (51.9)

4|5 (27.9)

4|2 (10.4)

4|0 (4.73)

4|0 (1.87)

4 |171

4 |36

    

50

4|2 (12.4)

4|1 (5.71)

4|0 (2.13)

4|0 (0.96)

4|0 (0.38)

  
    

20

4|0 (1.55)

4|0 (0.82)

4|0 (0.30)

4|0 (0.14)

3|0 (0.05)

  
    

15

4|0 (0.79)

4|0 (0.44)

4|0 (0.17)

3|0 (0.07)

3|0 (0.03)

  
    

10

4|0 (0.31)

4|0 (0.16)

3|0 (0.07)

3|0 (0.03)

2|0 (0.01)

  
    

5

3|0 (0.07)

3|0 (0.03)

2|0 (0.02)

2|0 (0.01)

1|0 (0.00)

  

50

4

200

false

20

4 |7 (50.0)

4 |4 (50.0)

4 |2 (6.33)

4 |1 (3.06)

4 |0 (1.25)

4 |43

4 |14

    

15

4 |3 (50.0)

4 |2 (8.12)

4 |1 (2.88)

4 |0 (1.34)

4 |0 (0.54)

  
    

10

4 |1 (5.19)

4 |0 (2.79)

4 |0 (1.04)

4 |0 (0.47)

4 |0 (0.19)

  
    

5

4 |0 (1.24)

4 |0 (0.57)

4 |0 (0.21)

4 |0 (0.10)

3 |0 (0.04)

  

500

12

200

false

100

12|12 (51.9)

12|4 (27.9)

12|1 (10.4)

11|0 (4.73)

9|0 (1.87)

12 |150

12 |78

    

50

9|2 (12.4)

8|0 (5.71)

7|0 (2.13)

6|0 (0.96)

3|0 (0.38)

  
    

20

5|0 (1.55)

4|0 (0.82)

3|0 (0.30)

2|0 (0.14)

1|0 (0.05)

  
    

15

4|0 (0.79)

3|0 (0.44)

2|0 (0.17)

1|0 (0.07)

0|0 (0.03)

  
    

10

3|0 (0.31)

2|0 (0.16)

1|0 (0.07)

0|0 (0.03)

0|0 (0.01)

  

500

40

200

false

200

17|13 (500)

12|5 (500)

8|2 (63.3)

4|0 (30.6)

1|0 (12.5)

35 |139

9 |12

    

100

16|12 (51.9)

11|4 (27.9)

7|2 (10.4)

4|0 (4.73)

1|0 (1.87)

  
    

50

6|2 (12.4)

4|1 (5.71)

2|0 (2.13)

1|0 (0.96)

0|0 (0.38)

  
    

25

2|0 (2.6)

1|0 (1.3)

0|0 (0.48)

0|0 (0.21)

0|0 (0.08)

  
  1. In every setting p inf predictors were truly informative, p−p inf were non-informative; PH-viol: settings were the proportional hazards assumption was violated. C-index boosting without stability selection (without π thr) was fitted on all p predictors with a fixed large m stop; in case of the Cox lasso the shrinkage parameter was optimized via 10-fold cross-validation
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