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

In our overview, we pointed out that the sensitiv-

ity and specificity values that result from a given

cut-point may vary with the cut-point chosen.

As a simple illustration, suppose the following

two extreme cut-points are used:cp¼1 and

cp¼0. The corresponding classification tables

for each of these cut-points are shown below at

the left.

If the cut point iscp¼1, then assuming that

P^ðXÞ¼ 1 is not attained for any subject, there

will beno predicted casesamong either then 1

true cases or then 0 true noncases. For this

situation, then, the sensitivity is 0 and the

specificity is 1.

On the other hand, if the cut-point iscp¼0,

then assuming thatP^ðXÞ¼ 0 is not attained for

any subject, there will beno predicted noncases

among either then 1 true cases or then 0 true

noncases. For this situation, then, the sensitiv-

ity is 1 and the specificity is 0.

Let us now consider what would happen ifcp

decreases from 1 to 0. As we will show by

example, ascpdecreases from 1 to 0, the sensi-

tivity will increase from 0 to 1 whereas the

specifity will decrease from 1 to 0.

Sp and Se values vary with cp

Two differentcps:cp¼ 1 andcp¼ 0

cp 51 :Se 5 0, Sp 51

OBSY

Y¼ 1 Y¼ 0

PRED Y¼10 0

Y Y¼ 0 nFN nTN

n 1 n 0

cp 5 0: Se 5 1, Sp 50

OBSY

Y¼ 1 Y¼ 0

PRED Y¼ 1 nTP nFP

Y Y¼00 0

n 1 n 0

Question: cpdecreases from 1 to 0?

Answer: Se increases from 0 to 1
Sp decreases from 1 to 0

Presentation: II. Assessing Discriminatory Performance Using Sensitivity 351