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:

  1. It shows the tradeoff between sensitivity and specificity (any increase in sensitivity will be accompanied by a decrease in specificity).
  2. The closer the curve follows the left-hand border and then the top border of the ROC space, the more accurate the test.
  3. The closer the curve comes to the 45-degree diagonal of the ROC space, the less accurate the test.
  4. 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.
  5. The area under the curve is a measure of text accuracy. This is discussed further in the next section.

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