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

VI. SUMMARY

DP¼discriminatory performance of a

binary logistic model

Good DP:model discriminates

casesðY¼ 1 Þfrom

noncasesðY¼ 0 Þ

One approach:

Classification/Diagnostic Table
True (Observed) Outcome
cp Y¼ 1 Y¼ 0
Predicted Y¼ 1 nTP nFP
Outcome Y¼ 0 nFN nTN
n 1 n 0

cp¼cut-point for classifying cases
vs. noncases
Se¼Pr(trueþ| true C)¼nTP/n 1
Sp¼Pr(true| true NC)¼nTN/n 0

Another approach:
Plotand/orsummary mea-
surebased on a range of cut-
points

1.0

1.0

cut-points for
Se (=TPR) classification

1 – Sp (= FPR)

ROC curve

́

́

́

́

́

AUC¼area under ROC curve

AUC¼ 1 : 0 )perfectDP

ðSe¼ 1 SpÞ

AUC¼ 0 : 5 )noDP

This presentation is now complete. We have

described how to assessdiscriminatory perfor-

mance (DP)of a binary logistic model.

A model providesgood DPif the covariates in

the model help to predict (i.e., discriminate)

which subjects will develop the outcome

(Y¼1, or the cases) and which will not

develop the outcome (Y¼0, or thenoncases).

One way to measureDPis to consider the

sensitivity(Se)and specificity(Sp)from a clas-

sification tablethat combines observed and

predicted outcomes over all subjects. The

closer both the sensitivity and specificity are

to 1, the better is the discrimination.

An alternative way to measureDPinvolves a

plot and/or summary measure based on a

range of cut-points chosen for a given model.

A widely used plot is theROC curve, which

graphs the sensitivity by 1 minus the specific-

ity for a range of cut-points. Equivalently, the

ROC is a plot of thetrue positive rate(TPR¼

Se)bythefalse positive rate(FPR¼ 1 Sp).

A popular summary measure based on the

ROC plot is the area under the ROC curve,

orAUC. The larger the AUC, the better is the

DP. An AUC of 1 indicates perfect DP and an

AUC of 0.5 indicates no DP.

Presentation: VI. Summary 371