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

To assess (data-based) confounding here, we

must determine whether there is a meaningful

difference between the gold standard and

asterisked odds ratio expressions. There are

two alternative ways to do this. (The assess-

ment of confounding involves criteria beyond

what may exist in the data.)

One way is to compare corresponding esti-

mated coefficients in the odds ratio expression,

and then to make a decision whether there is a

meaningful difference in one or more of these

coefficients.

If we decideyes, that there is a difference, we

then conclude that there is confounding due to

V 3 , so that we cannot eliminateV 3 from the

model. If, on the other hand, we decideno,

that corresponding coefficients are not differ-

ent, we then conclude that we do not need to

control for the confounding effects ofV 3 .In

this case, we may consider droppingV 3 from

the model if we can gain precision by doing so.

Unfortunately, this approach for assessing

confounding is difficult in practice. In particu-

lar, in this example, the odds ratio expression

involves four coefficients, and it is likely that at

least one or more of these will change some-

what when one or more potential confounders

are dropped from the model.

To evaluate whether there is a meaningful

change in the odds ratio therefore requires an

overall decision as to whether the collection of

four coefficients,b^and three^d, in the odds

ratio expression meaningfully change. This is

a more subjective decision than for the no

interaction situation whenb^is the only coeffi-

cient to be monitored.

EXAMPLE (continued)

Meaningful difference?

Gold standard model:

dOR¼exp^bþ^d 1 V 1 þ^d 2 V 2 þ^d 4 V 4



Model withoutV 3 :

dOR*¼exp^b*þ^d* 1 V 1 þ^d* 2 V 2 þ^d* 4 V 4



b, d 1 , d 2 , d 4 vs. b, d 1 , d 2 , d 4

∗∗ ∗ ∗

Difference?

Yes ) V 3 confounder;

cannot eliminateV 3

No ) V 3 not confounder;

dropV 3 if precision gain

Difficult approach:

 Four coefficients to compare

 Coefficients likely to change

Overall decision required about

change in

^b;^d 1 ;^d 2 ;^d 4

More subjective than when no

interaction (only^b)

220 7. Modeling Strategy for Assessing Interaction and Confounding