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

Using the above (option 1) interaction model,

we can assess interaction of exposure with the

matching variables by testing the null hypoth-

esis that all the coefficients of theEV 1 iterms

(i.e., all thed 1 i) are equal to zero.

If this “chunk” test is not significant, we could

conclude that there is no interaction involving

the matching variables. If the test is significant,

we might then carry out backward elimination

to determine which of theEV 1 iterms need to

stay in the model. (We could also carry out

backward elimination even if the “chunk” test

is nonsignificant.)

A criticism of this (option 1) approach is that if

significant interaction is found, then it will be

difficult to determine which of possibly several

matching variables are effect modifiers. This is

because the dummy variables (V 1 i) in the

model represent matching strata rather than

specific effect modifier variables.

Another problem with option 1 is that there

may not be enough data in each stratum (e.g.,

when pair-matching) to assess interaction. In

fact, if there are more parameters in the model

than there are observations in the study, the

model will not execute.

A second option for assessing interaction

involving matching variables is to consider

product terms of the formEW1m, where

W1mis an actual matching variable.

The corresponding logistic model is shown at

the left. This model contains the exposure vari-

ableE, dummy variablesV 1 ifor the matching

strata, nonmatched covariates V 2 j, product

termsEW1minvolving the matching vari-

ables, andEWkterms, where theWkare

effect modifiers defined from the unmatched

covariates.

EXAMPLE (continued)

Option 1:

TestH 0 : Alld 1 i¼0.
(Chunk test)
Not significant)No interaction
involving matching
variables
Significant)Interaction involving
matching variables
)Carry out backward
elimination of
EV 1 iterms

Criticisms of option 1:
 Difficult to determine which of
several matching variables are
effect modifiers. (TheV 1 i
represent matching strata, not
matching variables.)

 Not enough data to assess

interaction (number of

parameters may exceedn).

Option 2:
Add product terms of the form
EW 1 m;

whereW1mis amatching variable

logitPðXÞ¼aþbE¼~

i

g 1 iV 1 iþ~

j

g 2 jV 2 j

þE~

m

d 1 mW 1 m

þE~

k

dkWk;

where
W1m¼matching variables in original
form
W 2 k¼effect modifiers defined from
other covariates (not matched)

Presentation: VI. Assessing Interaction Involving Matching Variables 405