9.4.8 Receiver Operating Characteristic Curves


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Interprets Receiver Operating Characteristic Curves

Receiver operating characteristic (ROC) curves are used to evaluate the diagnostic accuracy of a test by plotting the true positive rate (sensitivity) against the false positive rate (1-specificity) at various threshold values. A ROC curve shows how well a test can discriminate between individuals with and without disease or condition. The area under the ROC curve (AUC) is a measure of the overall performance of the test, with an AUC of 0.5 indicating no better discrimination than chance, and an AUC of 1 indicates perfect discrimination.

Interpreting a ROC curve involves looking at the shape and location of the curve. A curve that is closer to the upper left corner indicates better performance of the test, with high sensitivity and specificity. A curve that is closer to the diagonal line indicates poor discrimination, with the test having little ability to differentiate between individuals with and without the disease or condition. The optimal cut-off point for a test is the point closest to the upper left corner of the curve, which balances sensitivity and specificity.

It is important to note that ROC curves are not designed to determine the best cut-off point for a test, but rather to evaluate the overall diagnostic accuracy of a test. The selection of a cut-off point will depend on various factors, such as the prevalence of the disease, the potential harm of false positives and false negatives, and the cost and availability of confirmatory tests.

How an ROC curve is drawn:

The ROC curve is a visual representation of model performance across all thresholds. The long version of the name, receiver operating characteristic, is a holdover from WWII radar detection.

The ROC curve is drawn by calculating the true positive rate (TPR) and false positive rate (FPR) at every possible threshold (in practice, at selected intervals), then graphing TPR over FPR. A perfect model, which at some threshold has a TPR of 1.0 and a FPR of 0.0, can be represented by either a point at (0, 1) if all other thresholds are ignored.

Area under the curve:

The area under the ROC curve (AUC) represents the probability that the model, if given a randomly chosen positive and negative example, will rank the positive higher than the negative.

The perfect model above, containing a square with sides of length 1, has an area under the curve (AUC) of 1.0. This means there is a 100% probability that the model will correctly rank a randomly chosen positive example higher than a randomly chosen negative example. 

AUC is a useful measure for comparing the performance of two different models, as long as the dataset is roughly balanced. The model with greater area under the curve is generally the better one.

Interpreting AUC values:

  • AUC = 1.0: This indicates a perfect model, which distinguishes perfectly between the two classes with 100% sensitivity and 100% specificity. The model correctly classifies all positive and negative instances without any errors.
  • AUC = 0.5: This reflects a model with no discriminative power, equivalent to random guessing. The model is as likely to classify an instance correctly as it is to classify it incorrectly.
  • AUC < 0.5: This suggests that the model is performing worse than random guessing. In practice, such a model would likely have its predictions inverted, which could improve its performance.

Higher AUC Values:

  • Closer to 1: A higher AUC value indicates that the model has a strong ability to distinguish between the two classes. It means the model has a high true positive rate and a low false positive rate, showing good performance.

Lower AUC Values:

  • Closer to 0.5: A lower AUC value suggests that the model struggles to differentiate between the positive and negative classes, leading to poorer performance.

In summary, a higher AUC value is generally desirable, indicating better model performance, while a lower AUC value signals that the model may need improvement.

References:

  1. Fawcett, Tom (2006). “An Introduction to ROC Analysis” (PDF). Pattern Recognition Letters. 27 (8): 861–874. doi:10.1016/j.patrec.2005.10.010.
  2. Zweig, M.H. and Campbell, G., 1993. Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical chemistry, 39(4), pp.561-577.
  3. https://developers.google.com/machine-learning/crash-course/classification/roc-and-auc#:~:text=Receiver%2Doperating%20characteristic%20curve%20(ROC),-The%20ROC%20curve&text=The%20ROC%20curve%20is%20drawn,then%20graphing%20TPR%20over%20FPR.