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

Apply hierarchy principle to identify

Vi, and ViVj terms

to remain in all further models

Focus on Vi, and ViVj terms

not identified above:

Candidates for elimination

Assess confounding/precision for

these variables

Interaction terms in model

+

FinalðconfoundingÞstep

difficultsubjective

Safest approach:
Keep all potential confounders in
model: controls confounding
but may lose precision

Confounding – general procedure:

dOR change?

Gold
standard
model

vs. Model without

one or more

ViandViVj

(1) Identify subsets so that

(2) Control for largest gain
in precision.
Difficult when there is interaction

OR (^) GS ≈ OR (^) subset.
In the second step of the flow diagram, we
apply the hierarchy principle to identify those
ViandViVjterms that are lower order compo-
nents of those interaction terms found signifi-
cant. Such lower order components must
remain in all further models considered.
In the final step of the flow diagram, we focus
on only thoseViandViVjterms not identified
by the hierarchy principle. These terms are
candidatesto be dropped from the model as
nonconfounders. For those variables identified
as candidates for elimination, we thenassess
confounding followed by consideration of
precision.
If the model contains interaction terms, the
final (confounding) step is difficult to carry
out and requires subjectivity in deciding
which variables can be eliminated as noncon-
founders. We will illustrate such difficulties by
the example below.
To avoid making subjective decisions, the saf-
est approach is to keep all potential confoun-
ders in the model, whether or not they are
eligible to be dropped. This will ensure the
proper control of confounding but has the
potential drawback of not giving as precise an
odds ratio estimate as possible from some
smaller subset of confounders.
In assessing confounding when there are inter-
action terms, the general procedure is analo-
gous to when there is no interaction. We assess
whether the estimated odds ratio changes from
the gold standard model when compared to a
model without one or more of the eligibleVis
andViVjs.
More specifically, we carry out the following
two steps:
(1) Identify those subsets ofVis andViVjs
giving approximately the same odds ratio
estimate as the gold standard (GS).
(2) Control for that subset which gives the
largest gain in precision.
216 7. Modeling Strategy for Assessing Interaction and Confounding