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

VI. Assessing Interaction
Involving Matching
Variables

The previous section considered a study of the

relationship between smoking (SMK) and myr-

ocardial infarction (MI) in which cases and

controls were matched on four variables:

AGE, RACE, SEX, and Hospital. Two addi-

tional control variables, SBP and ECG, were

not involved in the matching.

In the above example, interaction was evalu-

ated by including SBP and ECG in the logistic

regression model as product terms with the

exposure variable SMK. A test for interaction

was then carried out using a likelihood ratio

test to determine whether these two product

terms could be dropped from the model.

Suppose the investigator is also interested in

considering possible interaction between expo-

sure (SMK) and one or more of the matching

variables. The proper approach to take in such

a situation is not as clear-cut as for the previ-

ous interaction assessment. We now discuss

two options for addressing this problem.

The first option involves adding product terms of

the formEV 1 ito the model for each dummy

variableV 1 iindicatingamatchingstratum.

The general form of the logistic model that

accommodates interaction defined using this

option is shown on the left. The expression to

the right of the equals sign includes terms for

the intercept, the main exposure (i.e., SMK),

the matching strata, other control variables not

matched on, product terms between the expo-

sure and the matching strata, and product

terms between the exposure and other control

variables not matched on.

EXAMPLE

D¼MI

E¼SMK

AGE, RACE, SEX, HOSPITAL:

matched

SBP, ECG: not matched

Interaction terms:

SMKSBP, SMKECG

tested using LR test

Interaction between

SMK and matching variables?

Two options.

Option 1:

Add product terms of the form

EV 1 i

logit PðXÞ¼aþbEþ~

i

g 1 iV 1 iþ~

i

g 2 jV 2 j

þE~

i

d 1 iV 1 iþE~

k

dkWk;

where

V 1 i¼dummy variables for

matching strata

V 2 j¼other covariates (not

matched)

Wk¼effect modifiers defined from

other covariates

404 11. Analysis of Matched Data Using Logistic Regression