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

II. Polytomous Logistic
Regression: An
Example with Three
Categories

?

E D

When modeling a multilevel outcome variable,

the epidemiological question remains the

same: What is the relationship of one or more

exposure or study variables (E) to a disease or

illness outcome (D)?

In this section, we present an example of a

polytomous logistic regression model with

one dichotomous exposure variable and an

outcome (D) that has three categories. This is

the simplest case of a polytomous model. Later

in the presentation, we discuss extending the

polytomous model to more than one predictor

variable and then to outcomes with more than

three categories.

The example uses data from the National Can-

cer Institute’s Black/White Cancer Survival

Study (Hill et al., 1995). Suppose we are inter-

ested in assessing the effect of age group on

histological subtype among women with pri-

mary endometrial cancer. AGEGP, the expo-

sure variable, is coded as 0 for aged 50–64 or

1 for aged 65–79. The disease variable, histo-

logical subtype, is coded 0 for adenocarci-

noma, 1 for adenosquamous, and 2 for other.

There is no inherent order in the outcome vari-

able. The 0, 1, and 2 coding of the disease

categories is arbitrary.

The 32 table of the data is presented on the

left.

EXAMPLE

Simplest case of polytomous model:

 Outcome with three categories

 One dichotomous exposure

variable

Data source:

Black/White Cancer Survival Study

E¼AGEGP^0 if50--64

1 if65--79



D¼SUBTYPE

0 if Adenocarcinoma

1 if Adenosquamous

2 if Other

8

<

:

SUBTYPE (0, 1, 2) uses arbitrary

coding.

AGEGP

50–64 65–79

E¼ 0 E¼ 1

Adenocarcinoma

D¼ 0

77 109

Adenosquamous

D¼ 1

11 34

Other

D¼ 2

18 39

434 12. Polytomous Logistic Regression