Plotting and Intrepretating an ROC Curve
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This section continues the hypothyroidism example started in the the previous
section. We showed that the table at left can be summarized by the operating
characteristics at right:
| T4 value |
Hypothyroid |
Euthyroid |
| 5 or less |
18 |
1 |
| 5.1 - 7 |
7 |
17 |
| 7.1 - 9 |
4 |
36 |
| 9 or more |
3 |
39 |
| Totals: |
32 |
93 |
| Cutpoint |
Sensitivity |
Specificity |
| 5 |
0.56 |
0.99 |
| 7 |
0.78 |
0.81 |
| 9 |
0.91 |
0.42 |
The operating characteristics (above right) can be reformulated slightly
and then presented graphically as shown below to the right:
| Cutpoint |
True Positives |
False Positives |
| 5 |
0.56 |
0.01 |
| 7 |
0.78 |
0.19 |
| 9 |
0.91 |
0.58 |
This type of graph is called a Receiver Operating Characteristic curve (or ROC curve.)
It is a plot of the true positive rate against the false positive rate for the different possible
cutpoints of a diagnostic test.
An ROC curve demonstrates several things:
- It shows the tradeoff between sensitivity and specificity
(any increase in sensitivity will be accompanied by a decrease in specificity).
- The closer the curve follows the left-hand border and then the top border of the ROC space,
the more accurate the test.
- The closer the curve comes to the 45-degree diagonal of the ROC space, the less accurate the test.
- The slope of the tangent line at a cutpoint gives the likelihood ratio (LR) for that value of the
test. You can check this out on the graph above. Recall that the LR for T4 < 5 is 52. This
corresponds to the far left, steep portion of the curve. The LR for T4 > 9 is 0.2. This corresponds
to the far right, nearly horizontal portion of the curve.
- The area under the curve is a measure of text accuracy. This is discussed further in the
next section.
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