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

In general, when no interaction,
assess confounding by:

 Monitoring changes in effect
measure for subsets ofVs, i.e.,
monitor changes in
dOR¼e^b

 Identify subsets of Vs giving
approximately samedOR as
gold standard

If dOR (subset ofVs)¼dOR (gold
standard), then
 which subset to use?

 why not use gold standard?

Answer: precision

less precise more precise

less narrow more narrow

CIs:( ) ( )

CI for GS may be either less precise
or more precise than CI for subset

In general, regardless of the number ofVsin

one’s model, the method for assessing con-

founding when there is no interaction is to

monitor changes in the effect measure cor-

responding to different subsets of potential

confounders in the model. That is, we must

see to what extent the estimated odds ratio

given by e to the^bfor a given subset is different

from the gold standard odds ratio.

More specifically, to assess confounding, we

need to identify subsets of theVs that give

approximately the same odds ratio as the gold

standard. Each of these subsets controls for

confounding.

If we find one or more subsets of theVs, which

give us the same point estimate as the gold

standard, how then do we decide which subset

to use? Moreover, why do not we just use the

gold standard?

The answer to both these questions involves

consideration of precision. By precision, we

refer to how narrow a confidence interval

around the point estimate is. The narrower

the confidence interval, the more precise the

point estimate.

For example, suppose the 95% confidence

interval around the gold standarddOR of 2.5

that controls for all fiveVs has limits of 1.4

and 3.5, whereas the 95% confidence interval

around thedOR of 2.7 that controls forV 3 only

has limits of 1.1 and 4.2.

Then the gold standard OR estimate is more

precise than the OR estimate that controls for

V 3 only because the gold standard has the nar-

rower confidence interval. Specifically, the

narrower width is 3.5 minus 1.4, or 2.1,

whereas the wider width is 4.2 minus 1.1, or

3.1.

Note that it is possible that the gold standard

estimate actually may be less precise than an

estimate resulting from control of a subset of

Vs. This will depend on the particular data set

being analyzed.

EXAMPLE

95% confidence interval (CI)

dOR¼ 2 : 5 ORd¼ 2 : 7

Gold standard

all fiveVs

Reduced model

V 3 only

3.5 – 1.4 = 2.1 4.2 – 1.1 = 3.1

()( )

1.4 narrower 3.5

more precise

1.1 wider 4.2

less precise

Presentation: III. Confounding and Precision Assessment When No Interaction 213