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

Presentation

I. Overview

Modeling

outcomes with

more than two

ordered levels

FOCUS

Ordinal: levels have natural ordering

Ordinal outcome ) Polytomous
model or
ordinal
model

Ordinal model takes into account
order of outcome levels

II. Ordinal Logistic
Regression: The
Proportional Odds
Model

Proportional Odds Model/
Cumulative Logit Model

This presentation and the presentation in Chap.

12 describe approaches for extending the stan-

dard logistic regression model to accommodate

a disease, or outcome, variable that has more

than two categories. The focus of this presenta-

tion is on modeling outcomes with more than

twoorderedcategories. We describe theform

and keycharacteristicsof one model for such

outcome variables: ordinal logistic regression

using the proportional odds model.

Ordinal variables have a natural ordering among

the levels. An example is cancer tumor grade,

ranging from well differentiated to moderately

differentiated to poorly differentiated tumors.

An ordinal outcome variable with three or more

categories can be modeled with a polytomous

model, as discussed in Chap. 12, but can also be

modeled using ordinal logistic regression,

provided that certain assumptions are met.

Ordinal logistic regression, unlike polytomous

regression, takes into account any inherent

ordering of the levels in the disease or outcome

variable, thus making fuller use of the ordinal

information.

The ordinal logistic model that we shall

develop is called the proportional odds or

cumulative logit model.

EXAMPLE

Tumor grade:

 Well differentiated

 Moderately differentiated

 Poorly differentiated

466 13. Ordinal Logistic Regression