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

Using the above (option 2) interaction model,

we can assess interaction of exposure with the

matching variables by testing the null hypoth-

esis that all of the coefficients of theEW 1 m

terms (i.e., all of thed1m) equal zero.

As with option 1, if the “chunk” test for interac-

tion involving the matching variables is not

significant, we could conclude that there is no

interaction involving the matching variables.

If, however, the chunk test is significant, we

might then carry out backward elimination to

determine which of theEW1mterms should

remain in the model. We could also carry out

backward elimination even if the chunk test is

not significant.

A problem with the second option is that the

model for this option is not hierarchically well-

formulated (HWF), since components (W1m)of

product terms (EW1m) involving the match-

ing variables are not in the model as main

effects. (See Chap. 6 for a discussion of the

HWF criterion.)

Although both options for assessing interaction

involving matching variables have problems,

the second option, though not HWF, allows

for a more interpretable decision about which

of the matching variables might be effect modi-

fiers. Also, even though the model for option

2 is technically not HWF, the matching vari-

ables are at least in some sense in the model

as both effect modifiers and confounders.

One way to avoid having to choose between

these two options is to decide not to match on

any variable that you wish to assess as an effect

modifier. Another alternative is to avoid asses-

sing interaction involving any of the matching

variables,whichisoftenwhatisdoneinpractice.

EXAMPLE (continued)

Option 2:

TestH 0 : Alld1m¼0.

(Chunk test)

Not significant)No interaction

involving matching

variables

Significant)Interaction involving

matching variables

)Carry out Backwards

Elimination of

EW 1 mterms

Criticism of option 2:

The model is technically not HWF.

EW1min model but notW1m

Option 1 Option 2

Interpretable? No Yes

HWF? Yes No (but

almost

yes)

Alternatives to options 1 and 2:

 Do not match on any variable that

you consider a possible effect

modifier.

 Do not assess interaction for any

variable that you have matched

on.

406 11. Analysis of Matched Data Using Logistic Regression