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Why is C statistic the same as area under ROC curve? Example: 4 leaf tree, 100 1’s 100 0’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. - PowerPoint PPT Presentation
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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