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

III. Confounding and
Precision Assessment
When No Interaction

Confounding:

No statistical testing

(validity issue)

Confounding before precision

##

Gives correct Gives narrow

answer confidence

interval

No interaction model:

logit PðXÞ¼aþbEþ~giVi

(no terms of formEW)

Interaction
present?

Confounding

assessment?

No Straightforward

Yes Difficult

The final stage of our strategy concerns the

assessment of confounding followed by consid-

eration of precision. We have previously

pointed out that this stage, in contrast to the

interaction assessment stage, is carried out

without the use of statistical testing. This is

because confounding is a validity issue and,

consequently, does not concern random error

issues that characterize statistical testing.

We have also pointed out that controlling for

confounding takes precedence over achieving

precision because the primary goal of the anal-

ysis is to obtain the correct estimate rather

than a narrow confidence interval around the

wrong estimate.

In this section, we focus on the assessment of

confounding when the model contains no

interaction terms. The model in this case con-

tains onlyEandVterms but does not contain

product terms of the formEtimesW.

The assessment of confounding is relatively

straight-forward when no interaction terms

are present in one’s model. In contrast, as we

shall describe in the next section, it becomes

difficult to assess confounding when interac-

tion is present.

In considering the no interaction situation, we

first consider an example involving a logistic

model with a dichotomousEvariable and five

Vvariables, namely,V 1 throughV 5.

For this model, the estimated odds ratio that

describes the exposure–disease relationship is

given by the expression e to the^b, whereb^is the

estimated coefficient of theEvariable. Because

the model contains no interaction terms, this

odds ratio estimate is a single number that

represents an adjusted estimate that controls

for all fiveVvariables.

EXAMPLE

Initial model

logit PðXÞ¼aþbEþg 1 V 1 þþg 5 V 5

dOR¼eb^

(a single number)

adjusts forV 1 ,...,V 5

Presentation: III. Confounding and Precision Assessment When No Interaction 211