Basic Analysis and Graphing - SAS

Chapter 7 Performing Simple Logistic Regression 225
Logistic Platform Options
Lift Curve
Save Probability Formula
Script
Produces a lift curve for the model. A lift curve shows the same
information as a ROC curve, but in a way to dramatize the richness
of the ordering at the beginning. The Y-axis shows the ratio of how
rich that portion of the population is in the chosen response level
compared to the rate of that response level as a whole. See the
Modeling and Multivariate Methods book for details about lift curves.
Creates new data table columns that contain formulas. See “Save
Probability Formula” on page 226.
This menu contains options that are available to all platforms. They
enable you to redo the analysis or save the JSL commands for the
analysis to a window or a file. For more information, see Using JMP.
ROC Curves
Suppose you have an x value that is a diagnostic measurement and you want to determine a threshold value
of x that indicates the following:
• A condition exists if the x value is greater than the threshold.
• A condition does not exist if the x value is less than the threshold.
For example, you could measure a blood component level as a diagnostic test to predict a type of cancer.
Now 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 x criterion values that
best divides true negatives and true positives. The Receiver Operating Characteristic (ROC) curve shows
how rapidly this transition happens, with the goal being to have diagnostics that maximize the area under
the curve.
Two standard definitions used in medicine are as follows:
• Sensitivity, the probability that a given x value (a test or measure) correctly predicts an existing condition.
For a given x, the probability of incorrectly predicting the existence of a condition is 1 – sensitivity.
• Specificity, 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 x. The area under the ROC curve is
a common index used to summarize the information contained in the curve.
When you do a simple logistic regression with a binary outcome, there is a platform option to request a
ROC curve for that analysis. After selecting the ROC Curve option, a window asks you to specify which
level to use as positive.
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).