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

IV. Confounding
Assessment with
Interaction

Interaction

stage completed –

Begin confounding

Start with model containing

E, all Vi, all ViVj

and

remaining EVi and EViVj

Gold standard model

Returning to our example involving fiveVvari-

ables, suppose that the point estimates and

confidence intervals for various subsets ofVs

are given as shown here. Then there are only

two eligible subsets other than the gold stan-

dard – namelyV 3 alone, andV 4 andV 5 together

because these two subsets give the same odds

ratio as the gold standard.

Considering precision, we then conclude that

we should control for all fiveVs, that is, the

gold standard, because no meaningful gain in

precision is obtained from controlling for

either of the two eligible subsets ofVs. Note

that when V 3 alone is controlled, the CI is

wider than that for the gold standard. When

V 4 andV 5 are controlled together, the CI is the

same as the gold standard.

We now consider how to assess confounding

when the model contains interaction terms.

A flow diagram that describes our recom-

mended strategy for this situation is shown

here. This diagram starts from the point in the

strategy where interaction has already been

assessed. Thus, we assume that decisions have

been made about which interaction terms are

significant and are to be retained in all further

models considered.

In the first step of the flow diagram, we start

with a model containingEand all potential

confounders initially specified asViandViVj

terms plus remaining interaction terms deter-

mined from interaction assessment. This

includes thoseEViandEViVjterms found to

be significant plus thoseEViterms that are

components of significantEViVjterms. Such

EViterms must remain in all further models

considered because of the hierarchy principle.

This model is thegold standard modelto which

all further models considered must be com-

pared. By gold standard, we mean that the

odds ratio for this model controls for all poten-

tial confounders in our initial model, that is, all

theVis andViVjs.

EXAMPLE

logit PðXÞ¼aþbEþg 1 V 1 þþg 5 V 5

Vs in model

*e b^ meaningfully different from 2.5

95% CI

V 1 , V 2 , V 3 , V 4 , V 5

V 3 only

V 4 , V 5 only

other subsets

2.5

2.7

2.3

*

(1.4, 3.5)

(1.1, 4.2)

(1.3, 3.4)

—

same

width wider

e b

Presentation: IV. Confounding Assessment with Interaction 215