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

EXAMPLE (continued)

Table 10.3

Summary of Classification

Information For Models 1 and 2

(incl. 1Specificity)

MODEL 1:

cp 1.00 0.75 0.50 0.25 0.10 0.00

Se 0.00 0.10 0.60 1.00 1.00 1.00

Sp 1.00 1.00 1.00 1.00 0.40 0.00

1–Sp 0.00 0.00 0.00 0.00 0.60 1.00

MODEL 2:

cp 1.00 0.75 0.50 0.25 0.10 0.00

Se 0.00 0.10 0.60 0.80 0.90 1.00

Sp 1.00 0.90 0.40 0.20 0.10 0.00

1–Sp 0.00 0.10 0.60 0.80 0.90 1.00

Model 1: Se increases at faster rate

than 1Sp

Model 2: Se and 1Sp increase at

same rate

1 Sp more appealing than Sp

because

Se and 1Sp both focus on

predicted cases

Se¼Prop:True PositivesðTPÞ

¼nTP=n 1

wherenTP¼correctly predicted

cases

12 Sp¼Prop:FalsePositiveðFPÞ

¼nFP=n 0

wherenFP¼falsely predicted

cases

Good discrimination

+ðexpectÞ

Se¼nTP=n 1 > 1 Sp¼nFP=n 0

Correctly predicted

cases

falsely predicted

noncases

An alternative way to evaluate the discrimina-

tion performance exhibited in a classification

table is to consider “1specificity” (1–Sp)

instead of “specificity” in addition to the

sensitivity.

The tables at the left summarize the results of

the previous misclassification tables, and they

include1–Spvalues as additional summary

information.

For Model 1, when wecompare Se to 1 – Sp

values as the cut-point decreases, we see that

the Se values increase at a faster rate than the

values of 1Sp.

For Model 2, however, we find that both Se and

1 Sp values increase at the exact same rate.

Using 1Sp instead of Sp is descriptively

appealing for the following reason: both Se

and 1Sp focus, respectively, on the proba-

bility of being either correctly or falsely pre-

dicted to be a case.

Among the observed (i.e., true) cases, Se con-

siders the proportion of subjects who are “true

positives” (TP), that is, correctly predicted as

cases. Among the observed (i.e., true) noncases,

1 Sp considers the proportion of subjects

who are “false positives” (FP), that is, are falsely

predicted as cases.

One would expect for a model that has good

discrimination that the proportion of true

cases that are (correctly) predicted as cases

(i.e., Se) would be higher than the proportion

of true noncases that are (falsely) diagnosed as

cases (i.e., 1Sp). Thus, to evaluate discrimi-

nation performance, it makes sense to com-

pare Se (i.e., involving correctly diagnosed

cases) with 1Sp (i.e., involving falsely pre-

dicted noncases).

Presentation: II. Assessing Discriminatory Performance Using Sensitivity 353