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

Why do not we use gold standard?

Answer. Might find subset of Vs
that will

 gain precision (narrower CI)

 without sacrificing validity
(same point estimate)

Which subset to control?

Answer. subset with most meaning-
ful gain in precision

Eligible subset. same point estimate
as gold standard

Recommended procedure:

(1) Identify eligible subsets ofVs

(2) Control for that subset with
largest gain in precision

However, if no subset givesbetter
precision, use gold standard

Scientific: Gold standard usesall
relevant variables for control

The answer to the question why do not we just

use the gold standard is that we might gain a

meaningful amount of precision controlling

for a subset ofVs without sacrificing validity.

That is, we might find a subset ofVs to give

essentially the same estimate as the gold stan-

dard but which also has a much narrower con-

fidence interval.

For instance, controlling forV 4 andV 5 may

obtain the same point estimate as the gold

standard but a narrower confidence interval,

as illustrated here. If so, we would prefer the

estimate that usesV 4 andV 5 in our model to

the gold standard estimate.

We also asked the question, “How do we decide

which subset to use for control?” The answer to

this is to choose that subset which gives the

most meaningful gain in precision among all

eligible subsets, including the gold standard.

Byeligible subset, we mean any collection ofVs

that gives essentially the same point estimate

as the gold standard.

Thus, we recommend the following general

procedure for the confounding and precision

assessment stage of our strategy:

(1) Identify eligible subsetsofVs giving

approximately the same odds ratio as the

gold standard.

(2) Control for that subset which gives the

largest gain in precision. However, if no

subset gives meaningfully better precision

than the gold standard, it isscientifically

better to control for allVs using the gold

standard.

The gold standard is scientifically better

because persons who critically appraise the

results of the study can see that when using

the gold standard, all the relevant variables

have been controlled for in the analysis.

EXAMPLE

Model dOR CI

3 V 4 andV 5 same

(2.3)

narrower

(1.9, 3.1)

Gold

standard

same

(2.5)

wider

(1.4, 3.5)

214 7. Modeling Strategy for Assessing Interaction and Confounding