ROC Analysis

Receiver Operating Characteristic or ROC Curves are useful visualization tools that allow a quick assessment of the quality of a model. They are usually plotted in reference to a Baseline or Random Model, with the Area Under the ROC Curve (or AUC for short) as a popular indicator of the quality of a model.

So, for the Random Model, the area under the ROC curve is equal to 0.5, which means that the further up (or down, for inverted models) a model is from 0.5 the better it is. Indeed, for perfect models on both sides of the random line, what is called ROC heaven takes place when AUC = 1 (for normal models) or AUC = 0 (for inverted models). Below is shown a typical ROC curve obtained for a risk assessment model using a training dataset with 18,253 cases. This model has an R-square of 0.245889 (R-square values might seem unusually low, but in risk assessment applications R-square values around 0.23 are considered excellent and indicative of a good model) and an AUC of 0.800028.

And below is shown a Gallery of ROC Curves typical of intermediate models generated during a GeneXproTools run. These specifically were created for a risk assessment problem with a training dataset with 18,253 cases and using a small population of just 30 programs. The R-square of each model, as well as the generation at which they were discovered, are also shown as illustration. From left to right and top to bottom, they are as follow (see also the twin Gallery of Logistic Fit Charts in the Logistic Fit section):

Generation 0


Generation 3


Generation 8


Generation 12


Generation 14


Generation 344

where SE_(t) and SP_(t) are, respectively, the sensitivity and specificity over all possible threshold values t of the model. Thus, the Optimal Model Threshold corresponds to the model output at the Optimal Cutoff Point.

In the ROC Table, GeneXproTools also shows all “SE + SP -1” values and highlights in light green the row with the Optimal Cutoff Point and corresponding Optimal Model Threshold. These parameters are also shown in the Quantiles Statistics Report.

 

The Optimal Model Threshold can be obviously used to infer a Confusion Matrix (in GeneXproTools it is called ROC Confusion Matrix) and, in the Cutoff Points Table, you have access to the Predicted Class, the Match, and Type values used to build this ROC Confusion Matrix (you can see the graphical representation of the ROC Confusion Matrix in the Confusion Matrix section).

The visualization of the ROC Confusion Matrix is a valuable tool and can in fact be used to determine the right number of buckets to achieve a good fit with the Logistic Regression Model. But GeneXproTools allows you to do more with the ROC Confusion Matrix and associated Optimal Model Threshold. By allowing the conversion of Logistic Regression runs to the Classification Framework, you can use this model, with its finely adapted Optimal Model Threshold, straightaway to make categorical classifications using the Classification Scoring Engine of GeneXproTools.

The Youden index is also used to evaluate a wide set of useful statistics at the Optimal Cutoff Point (OCP statistics for short). They include:

• TP (True Positives)
• TN (True Negatives)
• FP (False Positives)
• FN (False Negatives)
• TPR (True Positives Rate or Sensitivity)
• TNR (True Negatives Rate or Specificity)
• FPR (False Positives Rate, also known as 1-Specificity)
• FNR (False Negatives Rate)
• PPV (Positive Predictive Value)
• NPV (Negative Predictive Value)
• Classification Accuracy (Correct Classifications)
• Classification Error (Wrong Classifications)

How they are calculated is shown in the table below ("TC" represents the number of Total Cases):

It is worth pointing out that OCP statistics are quantile-independent and therefore are a good indicator of what could be achieved with a model in terms of logistic fit and accuracy.