1’s 20 0’s

20 1’s20 0’s

30 1’s20 0’s

10 1’s50 0’s

40 1’s10 0’s

40 1’s

10 0’s

30 1’s

20 0’s

20 1’s10 1’s

50 0’s

More 1’s ------------------------------------------------ Less 1’s

Why is C statistic the same as area under ROC curve?

Example: 4 leaf tree, 100 1’s 100 0’s

Areas: (Number of 1’s)x(Number of 0’s)

40 1’s

10 0’s

30 1’s

20 0’s

20 1’s10 1’s

50 0’s

More 1’s ------------------------------------------------ Less 1’s

40x90 Concordant Pairs

IF cut is after 1st leaf

20+20+50 = 90 0’s

CUT

40 1’s

10 0’s

30 1’s

20 0’s

20 1’s10 1’s

50 0’s

More 1’s ------------------------------------------------ Less 1’s

90x40 Concordant Pairs

IF cut is after 1st leaf

30x70 more Concordant PairsIF cut is after 2nd

20+50 = 70 0’s

40 1’s

10 0’s

30 1’s

20 0’s

20 1’s10 1’s

50 0’s

More 1’s ------------------------------------------------ Less 1’s

30x70 more Concordant PairsIF cut is after 2nd

CUT

0.36 proportion concordant

0.21 proportionconcordant

0.10 prop.concordant

Blue boxes are ties, proportions .4x.1=.04, .3x.2=.06, .2x.2=.04, .1x.5=.05Proportion ties = .04+.06+.04+.05. Half of that = sum of blue triangles belowdiagonals = .02+.03+.02+.025 = .095. Area under ROC curve (black diagonal lines) is 0.36+0.21+0.10+0.095 = C = 0.765

Left of cut point => decide 1

Diagonal line coordinates at ends are (proportion 0’s declared 1’s, proportion 1’s declared 1’s) =

(sensitivity , 1-specificity) !!!

0.10 1’s

0.20 1’s

0.30 1’s

0.40 1’s

In terms of PROPORTIONS:

0.10 0.20 0.20 0.50 proportions of 0’s = blue box widths

ROCcurve