Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

The proportion of true positives among all cases is calledsensitivity(Se), and the propor- tion of true negatives among all nonc ...

Why does the area under the ROC measure discriminatory performance(DP)? We discuss this question and other characteristics of RO ...

In our overview, we pointed out that the sensitiv- ity and specificity values that result from a given cut-point may vary with t ...

EXAMPLE Table 10.2 Classification Tables for Two Models by Varying Classification Cut-Point (cp) MODEL 1 Se = 0.00, Se = 0.10, P ...

EXAMPLE (continued) Table 10.3 Summary of Classification Information For Models 1 and 2 (incl. 1Specificity) MODEL 1: cp 1.00 0 ...

Study Subjects Randomly select Case Control P(Xcase) > P(Xnoncase)? EXAMPLE Table 10.3: Collectively compare Se with 1Sp ove ...

III. Receiver Operating Characteristic (ROC) Curves Denotes cut-point for classification 1.0 ROC Example 1.0 1 – Sp (= FPR) Se ( ...

Moreover, we will see that the answer to this question can be quantified by obtaining the area under an ROC curve (AUC): the lar ...

Observing the above ROCs, we see that, for Model 1, TPR (i.e., Se) is consistently higher than its corresponding FPR (i.e., 1Sp ...

Note, however, that it is typically unusual to obtain an AUC as high as 0.90, and if so, almost all exposed subjects are cases a ...

We then fit a logistic model P(X) to this data set, and we compute the predicted probability of being a case, i.e.,P^ðXiÞ, for e ...

We now illustrate how this numerical formula translates into the geometrical area under the curve. The method we illustrate is o ...

The resulting ROC curve is shown at the left. The AUC for this curve is 0.7095. We now show the calculation of this area using t ...

Finally, the 20 cases that did not have either risk factorX 1 ¼0 andX 2 ¼0 are discordant with 2þ 48 þ 50 ¼100 noncases and tied ...

Within the above rectangle, the concordant pairs are represented by the areaunder the ROC curve while thediscordant pairsare rep ...

EXAMPLE (continued) Alternative calculation of sub-area: Rewrite np¼ 100  200 as (10 + 50 + 20 + 20) (2 + 48 + 50 + 100) Classi ...

The combined area under the rescaled ROC curve is then 7,095, which represents a propor- tion of 0.7095 of the total rectangular ...

The logistic model used in the analysis is shown at the left, and includes all five predictor variables. Although some of these ...

Notice that at cut-point 0.100, 36 of 45 true events were correctly classified as events, and 9 of 45 were incorrectly classifie ...

Using the notation just described, the formulae for these discrimination measures are shown at the left, with the first of these ...