1. Why is C statistic the same as area under ROC curve?
Example:
4 leaf tree, 100 1’s ’s
1’s
20 0’s
1’s
20 0’s
1’s
50 0’s
1’s
10 0’s
Areas: (Number of 1’s)x(Number of 0’s)
40 1’s
30 1’s
20 1’s
10 1’s
10 0’s
20 0’s
50 0’s
More 1’s   Less 1’s

2. 40x90 Concordant
Pairs
IF cut is after 1st leaf
= 90 0’s
CUT
40 1’s
30 1’s
20 1’s
10 1’s
10 0’s
20 0’s
50 0’s
More 1’s   Less 1’s

3. 30x70 more Concordant Pairs
IF cut is after 2nd
90x40 Concordant
Pairs
IF cut is after 1st leaf
20+50 = ’s
40 1’s
30 1’s
20 1’s
10 1’s
10 0’s
20 0’s
50 0’s
More 1’s   Less 1’s

4. 30x70 more Concordant Pairs
IF cut is after 2nd
CUT
40 1’s
30 1’s
20 1’s
10 1’s
10 0’s
20 0’s
50 0’s
More 1’s   Less 1’s

5. 0.36 proportion concordant
In terms of PROPORTIONS:
ROC
curve ’s
0.10 prop.
concordant
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) !!! ’s
0.21 proportion
concordant ’s
0.36 proportion concordant ’s
proportions of 0’s = blue
box widths
Blue boxes are ties, proportions .4x.1=.04, .3x.2=.06, .2x.2=.04, .1x.5=.05
Proportion ties = Half of that = sum of blue triangles below
diagonals = = Area under ROC curve (black diagonal
lines) is = C = 0.765