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

IV. The Model and Odds
Ratio for a Nominal
Exposure Variable
(No Interaction Case)

Several exposures:E 1 ,E 2 ,...,Eq

 Model

 Odds ratio

Nominal variable:>2 categories

e.g., ü occupational status in

four groups

SSU (0 – 5) ordinal

k categories ) k1 dummy
variables
E 1 ,E 2 ,...,Ek 1

For instance, suppose the medians of each

quintile are 120, 140, 160, 180, and 200. Then

odds ratios can be computed comparing SBP*

equal to 200 with SBP**equal to 120, followed

by comparing SBP*equal to 200 with SBP**

equal to 140, and so on until all possible pairs

of odds ratios are computed. We would then

have a table of odds ratios to consider for asses-

sing the relationship of SBP to the disease out-

come variable. The check marks in the table

shown here indicate pairs of odds ratios that

compare values of SBP*and SBP**.

The final special case of the logistic model that

we will consider expands theE, V, Wmodel to

allow for several exposure variables. That is,

instead of having a singleEin the model, we

will allow severalEs, which we denote byE 1 ,

E 2 , and so on up throughEq. In describing

such a model, we consider some examples

and then give a general model formula and a

general expression for the odds ratio.

First, suppose we have a single nominal ex-

posure variable of interest; that is, instead of

being dichotomous, the exposure contains

more than two categories that are not order-

able. An example is a variable such as occupa-

tional status, which is denoted in general as

OCC, but divided into four groupings or occu-

pational types. In contrast, a variable like

social support, which we previously denoted

as SSU and takes on discrete values ordered

from 0 to 5, is an ordinal variable.

When considering nominal variables in a logis-

tic model, we use dummy variables to distin-

guish the different categories of the variable. If

the model contains an intercept terma, then

we use k1 dummy variables E 1 ,E 2 , and

so on up to Ek 1 to distinguish among k

categories.

EXAMPLE (continued)

SBP* SBP** OR

200 120 ü

200 140 ü

200 160 ü

200 180 ü

180 120 ü

180 140 ü

180 160 ü

160 140 ü

160 120 ü

140 120 ü

82 3. Computing the Odds Ratio in Logistic Regression