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Understanding ROC Curve Analysis: A Practical Example of AUC Calculation

This demonstration explores the concepts of Receiver Operating Characteristic (ROC) curves and Area Under the Curve (AUC) calculations in binary classification. Using a specific dataset, we calculate sensitivity and specificity while constructing the ROC curve. The analysis showcases how to derive concordant pairs and account for ties in predictions. With examples illustrating the conditions for Say 1 and Say 0, this guide breaks down the methodology to help understand performance indicators for classification models.

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Understanding ROC Curve Analysis: A Practical Example of AUC Calculation

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Presentation Transcript

  1. ROC Curve Demo

  2. Say 1 Say 0 %1s 1 0 | | %0s |<-logits of the 1s->| | |<-logits of the 0s->|

  3. Say 1 Say 0

  4. Say 1 Say 0

  5. Say 1 Say 0

  6. Say 1 Say 0

  7. Say 1 Say 0

  8. Say 1 Say 0

  9. Say 1 Say 0

  10. Example 2 0 1 Say 1 Say 0 X=10 X=13 X=16 1 - specificity

  11. Example 2 0 1 X=10 X=13 X=16 Say 1 Say 0 (2/25, 18/35) 1 - specificity

  12. Example 2 0 1 X=10 X=13 X=16 (10/25, 30/35) (2/25, 18/35) Say 1 Say 0 1 - specificity

  13. Example 2 0 1 X=10 X=13 X=16 (10/25, 30/35) (1, 1) (2/25, 18/35) Say 1 Say 0 1 - specificity

  14. Example 2 0 1 X=10 X=13 X=16 Tie Tie Say 1 Say 0 18 x 23 1 - specificity

  15. Example 2 0 1 X=10 X=13 X=16 Tie Tie 15 x 12 Tie Tie Tie Say 1 Say 0 18 x 23 Tie 1 - specificity

  16. Example 2 0 1 X=10 X=13 X=16 15x5/2 Tie Tie 8x12/2 Tie 15 x 12 Tie Tie Tie 2x18/2 18 x 23 Tie Tie Say 1 Tie Say 0 1 - specificity AUC Area Under Curve = concordant pair plus ½ ties (proportions) Pairs: 25x35=875 with 0 paired with 1. Proportion Concordant: (18x23+12x15)/(25x35)=(18/25)x(23/35)+(12/25)x(15/35) ½ Proportion Ties ½(2x18 + 8x12 + 15x5)/(25x35) AUC = 697.5/875 = 0.7971.

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