1. Calculate and graph the nonparametric ROC curve (refer to the graph showing how you would interpret the ROC)
2. Calculate the nonparametric area under the ROC curve (refer to the graph showing how you would interpret the ROC)
3. Calculate the nonparametric statistical significance of the ROC curve
ROC Curve:
The area under a ROC curve (AUC) is a standard measure of the performance of diagnostic tests. The greater the AUC, the better the performance. For most applications, you will accept a test that is excellent for detecting disease when the ROC curve area is above 0.90, and you will reject a test with a value below 0.80. In fact, most professional organizations recommend that you use ROC analysis when evaluating the performance of a diagnostic test.
Figure 1: ROC Curve
The x-axis is your true positive rate (sensitivity) and the y-axis is your false positive rate (1-specificity). The blue line is the ROC curve. Note that the ROC curve is always above and to the right of the point (0,1). The red dot shows your operating point.
ROC Area:
The area under the ROC curve is the nonparametric estimate of the proportion of patients correctly classified as having the disease with a positive test result and the proportion correctly classified as not having the disease with a negative test result. If you have a positive test and the disease is present, the test is 100% sensitive and you will be classified as having the disease. If you have a positive test and the disease is not present, the test is 100% specific and you will be classified as not having the disease. You can always assume that if a test is positive, the disease is present and if the test is negative, the disease is not present. However, when both the sensitivity and specificity are high, the ROC area will approach 1.0.
ROC Significance:
The area under the ROC curve is a statistical measure. There are several methods of calculating a significance level of the ROC curve, such as the Z score and Wald-Wolfowitz runs test. But these methods are valid only when the ROC curve area is greater than 0.50. When the area is lower than 0.50, you can get negative statistical significance when the test is better than random guessing.
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