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

EXAMPLE

Our example assumes:

 AGE and GENDER risk factors

 AGE and GENDER potential

effect modifiers of interest

 Interaction of PREVHOSP and

PAMU also of interest

No interaction model:

Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þ

þðg 1 V 1 þg 2 V 2 Þ

Distinction between oneEand sev-
eralEs:

SingleE: Only one type of
interaction,EWs

SeveralEs:

Two types of interaction,EiWjs

andEiEks

Potentially omitEs from final

model

General form: EVW model for
severalEs

Logit PðXÞ¼aþ~

q

i¼ 1

biEiþ~

p 1

j¼ 1

gjVj

þ~

q

i¼ 1

~

p 2

k¼ 1

dikEiWk

þ~

q

i¼ 1

~

q

i^0 ¼ 1

i 6 ¼i^0

d*ii 0 EiEi^0

For our example, therefore, we have assumed

that AGE and GENDER are well-known risk

factors for MRSA, and that there is also interest

to assess whether each of these variables are

effect modifiers of either or both of the expo-

sure variables. We also assume that the inter-

action of the exposures with each other is of

interest.

If, on the other hand, we decided that interac-

tion of any kind was either not of interest or not

practically interpretable, our initial model

would omit such interaction terms. In such a

case, the initial model would still involve the

twoEs, but it would be a no interaction model,

as shown at the left.

The primary distinction between the modeling

strategy for a singleEvariable vs. severalEsis

that, in the latter situation, there are two types

of interactions to consider: interactions ofEs

withWs and interactions ofEs with otherEs.

Also, when there are severalEs, we may con-

sider omitting someEs (as nonsignificant) in

the final (“best”) model.

Although we will return to this example

shortly, we show here at the left the general

form of the EVW model when there are several

exposures. This model is written rather suc-

cinctly using summation signs, including dou-

ble summation signs when considering

interactions. Notice that in this general form,

there areqexposure variables,p 1 potential con-

founders, andp 2 potential effect modifiers.

246 8. Additional Modeling Strategy Issues