The Logistic platform contains an option to fit a receiver operating characteristic (ROC) curve for the logistic regression model. The ROC Curve option in the Logistic platform uses the Target Level from the platform launch window as the positive response level in the ROC curve. See Example of ROC Curves.
Suppose you have a value of the X variable that is a diagnostic measurement and you want to determine a threshold value of the X variable that indicates the following:
• A condition exists if the value of the X variable is greater than the threshold.
• A condition does not exist if the value of the X variable is less than the threshold.
For example, you could measure a blood component level as a diagnostic test to predict a type of cancer. Consider the diagnostic test as you vary the threshold and thus cause more or fewer false positives and false negatives. You then plot those rates. The ideal is to have a very narrow range of values of the X variable that best divides true negatives and true positives. The Receiver Operating Characteristic (ROC) curve shows how rapidly this transition happens. The goal of the ROC curve is to have diagnostics that maximize the area under the curve.
Two standard definitions are used in medicine:
• Sensitivity is the probability that a given value of the X variable correctly predicts an existing condition. For a given x, the probability of incorrectly predicting the existence of a condition is 1 – sensitivity.
• Specificity is the probability that a test correctly predicts that a condition does not exist.
A ROC curve is a plot of sensitivity by (1 – specificity) for each value of the X variable. The area under the ROC curve is a common index used to summarize the information contained in the curve.
If a test predicted perfectly, it would have a value above which the entire abnormal population would fall and below which all normal values would fall. It would be perfectly sensitive and then pass through the point (0, 1) on the grid. The closer the ROC curve comes to this ideal point, the better its discriminating ability. A test with no predictive ability produces a curve that follows the diagonal of the grid (DeLong et al. 1988).
The ROC curve is a graphical representation of the relationship between the false-positive and true-positive rates. A standard way to evaluate the relationship is using the area under the curve, which appears below the plot in the report. In the plot, a yellow 45-degree angle line is drawn at a tangent to the ROC Curve. This marks the cutoff point that maximizes the sum of sensitivity and specificity.