264 PART 5 Looking for Relationships with Correlation and Regression

consequences of the two types of false predictions. A false-positive screening

result from a mammogram may mean the patient is worried until the negative

diagnosis is confirmed by ultrasound, and a false-negative screening results from

a prostate cancer screening may result in a delay in identifying the prostate tumor.

To find this optimal cut value, you need to know precisely how sensitivity and

specificity play against each other — that is, how they simultaneously vary with

different cut values. There’s a neat way to do that which we explain in the follow-

ing section.

Rocking with ROC curves

The graph used to display the sensitivity/specificity tradeoff for any fitted logistic

model is called the Receiver Operator Characteristics (ROC) graph. The name comes

from its original use during World War II to analyze the performance characteris-

tics of people who operated RADAR receivers, but the name has stuck, and now it

is also referred to as an ROC curve.

An ROC graph has a curve that shows you the complete range of sensitivity and

specificity that can be achieved for any fitted logistic model based on the selected

cut value. The software generates an ROC curve by effectively trying all possible

cut values of predicted probability between 0 and 1, calculating the predicted out-

comes, cross-tabbing them against the observed outcomes, calculating sensitivity

and specificity, and then graphing sensitivity versus specificity. Figure 18-7 shows

the ROC curve from the logistic model developed from the data in Figure  18-1

(using R software; see Chapter 4).

FIGURE 18-7:

ROC curve from

dose mortality

data.

© John Wiley & Sons, Inc.