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

EXAMPLE

Table 10.2

Classification Tables for Two

Models by Varying Classification

Cut-Point (cp)

MODEL 1

Se = 0.00,

Se = 0.10,

PRED

Y

Y = 1 Y = 0

Y = 0

Y = 1 00

100 100

Y = 1

Y = 0

Y = 1 0

100

Y = 0

0

100

Y = 1 Y = 0

Y = 0

Y = 1 10 0

90 90

Y = 1 Y = 0

Y = 0

Y = 1 60 60

40 40

Y = 1 Y = 0

Y = 0

Y = 1 80 80

20 20

Y = 1 Y = 0

Y = 0

Y = 1 90 90

10 10

Y = 1 Y = 0

Y = 0

Y = 1 60 0

40 100

Y = 1 Y = 0

Y = 0

Y = 1 100 0

0 100

Y = 1 Y = 0

Y = 0

Y = 1 100 60

040

Y = 1 Y = 0

Y = 0

Y = 1 100 100

0 0

Y = 1

Y = 0

Y = 1 100 100

0

Y = 0

0

Y = 1 Y = 0

Y = 0

Y = 1 10 0

90 100

PREDY

PRED

Y

PREDY

PRED

Y

PREDY

Se = 0.00,

Se = 0.10,

Sp = 1.00

Sp = 1.00

Sp = 1.00

Sp = 0.90

OBS Y

OBS Y

OBS Y

OBS Y

Se = 0.60,Sp = 1.00 Se = 0.60,Sp = 0.40

OBS Y OBS Y

Se = 1.00,Sp = 1.00 Se = 0.80,Sp = 0.20

OBS Y OBS Y

Se = 1.00,Sp = 0.40 Se = 0.90,Sp = 0.10

OBS Y OBS Y

Se = 1.00,Sp = 0.00 Se = 1.00,Sp = 0.00

OBS Y OBS Y

MODEL 2

cP = 1.00

cP = 0.75

cP = 0.50

cP = 0.25

cP = 0.10

cP = 0.00

Spmay change at a different rate than

Se

We illustrate on the left the classification tables

and corresponding sensitivity and specificity

values obtained from varying the cut-points

for two hypothetical logistic regression models.

Based on this information, what can you con-

cludefor each modelseparately as to how the

sensitivity changes as the cut-pointcpdecreases

from 1.00 to 0.75 to 0.50 to 0.25 to 0.10 to 0.00?

Similarly, what can you conclude for each

model as to how the specificity changes as the

cut-point decreases from 1.00 to 0.00?

The answers to the above two questions are

thatfor both models, as the cut-put cpdecreases

from 1.00 to 0.00,the sensitivity increasesfrom

0.00 to 1.00 andthe specificity decreasesfrom

1.00 to zero. Note that this result will always be

the case foranybinary logistic model.

Next question: For each model separately, as

the cut-point decreases, does the sensitivity

increase at a faster rate than the specificity

decreases?

The answer to the latter question depends on

which model we consider. For Model 1, the

answer is yes, since the sensitivity starts to

change immediately as the cut-point changes,

whereas the specificity remains at 1 until the

cut-point changes to 0.10.

For Model 2, however, the answer is no,

because the sensitivity increases at the same

rate that the specificity decreases. In particu-

lar, the sensitivity increases by 0.10 (from 0.00

to 0.10) while the sensitivity decreases by 0.10

(from 1.00 to 0.90), followed by correspond-

ingly equal changes of 0.50, 0.20, 0.10 and

0.10 as the cut-point decreases to 0.

So, even though the sensitivity increases and

the specificity decreases as the cut-point

decreases,the specificity may change at a differ-

ent rate than the sensitivitydepending on the

model being considered.

352 10. Assessing Discriminatory Performance of a Binary Logistic Model