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

General case for one predictor

ORg¼expbg 1 X** 1 X* 1

hi

;where

g¼ 1 ; 2

Computer output for polytomous
model:
Is output listed in ascending or
descending order?

The special case of a dichotomous predictor

can be generalized to include categorical or

continuous predictors. To compare any two

levels (X 1 ¼X** 1 vs.X 1 ¼X* 1 ) of a predictor, the

odds ratio formula is e to the bg 1 times

(X** 1 X* 1 ), wheregdefines the category of the

disease variable (1 or 2) being compared with

the reference category (0).

The output generated by a computer package

for polytomous logistic regression includes

alphas and betas for the log odds terms being

modeled. Packages vary in the presentation of

output, and the coding of the variables must be

considered to correctly read and interpret the

computer output for a given package. For

example, in SAS, ifD¼0 is designated as the

reference category, the output is listed in des-

cending order (see Appendix). This means that

the listing of parameters pertaining to the

comparison with categoryD¼2 precedes the

listing of parameters pertaining to the com-

parison with categoryD¼1, as shown on the

left.

The results for the polytomous model examin-

ing histological subtype and age are presented

on the left. The results were obtained from

running PROC LOGISTIC in SAS. See the

Computer Appendix for computer coding.

There are two sets of parameter estimates. The

output is listed in descending order, with

a 2 labeled as Intercept 1 anda 1 labeled as inter-

cept 2. IfD¼2 had been designated as the

reference category, the output would have

been in ascending order.

EXAMPLE

SAS

Reference category:D¼ 0

Parameters forD¼2 comparison

precedeD¼1 comparison.

Variable Estimate symbol

Intercept 1 ^a 2

Intercept 2 ^a 1

X 1 ^b 21

X 1 ^b 11

EXAMPLE

Variable Estimate S.E. Symbol

Intercept 1 1.4534 0.2618 ^a 2

Intercept 2 1.9459 0.3223 ^a 1

AGEGP 0.4256 0.3215 ^b 21

AGEGP 0.7809 0.3775 ^b 11

Presentation: III. Odds Ratio with Three Categories 439