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

Recall that AGEGP is coded as 0 for aged 50–64

or 1 for aged 65–79. Both estrogen use and

smoking status are also coded as dichotomous

variables. ESTROGEN is coded as 1 for ever

user and 0 for never user. SMOKING is coded

as 1 for current smoker and 0 for former or

never smoker.

The log odds comparing Adenosquamous

(D¼1) to Adenocarcinoma (D¼0) is equal

toa 1 plusb 11 timesX 1 plusb 12 timesX 2 plus

b 13 timesX 3.

Similarly, the log odds comparing Other type

(D¼2) to Adenocarcinoma (D¼0) is equal to

a 2 plusb 21 timesX 1 plusb 22 timesX 2 plusb 23

timesX 3.

The output for the analysis is shown on the left.

There are two beta estimates for each of the

three predictor variables in the model. Thus,

there are a total of eight parameters in the

model, including the intercepts.

EXAMPLE (continued)

X 1 ¼AGEGP^0 if50--64

1 if65--79



X 2 ¼ESTROGEN^0 if never user

1 if ever user



X 3 ¼SMOKING

0 if former or never

smoker

1 if current smoker

8

<

:

Adenosquamous vs. Adenocarcinoma:

ln

PðD¼ 1 jXÞ

PðD¼ 0 jXÞ



¼a 1 þb 11 X 1 þb 12 X 2

þb 13 X 3

Other vs. Adenocarcinoma:

ln

PðD¼ 2 jXÞ

PðD¼ 0 jXÞ



¼a 2 þb 21 X 1 þb 22 X 2

þb 23 X 3

Variable Estimate S.E. Symbol

Intercept 1 1.2032 0.3190 ^a 2
Intercept 2 1.8822 0.4025 ^a 1

AGEGP 0.2823 0.3280 ^b 21
AGEGP 0.9871 0.4118 ^b 11

ESTROGEN0.1071 0.3067 ^b 22
ESTROGEN0.6439 0.3436 ^b 12

SMOKING 1.7913 1.0460 ^b 23
SMOKING 0.8895 0.5254 ^b 13

Presentation: V. Extending the Polytomous Model toGOutcomes 445