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

If interaction present:

 Do not assess confounding for
effect modifiers

 Assessing confounding for
other variables difficult and
subjective

Confounding followed by precision:

( ) ( )

Valid

imprecise

biased

precise

VALIDITY BEFORE PRECISION

right answer precise answer

On the other hand, if interaction assessment is

considered worthwhile, and, moreover, if signif-

icant interaction is found, then this precludes

assessing confounding for those variables iden-

tified as effect modifiers. Also, as we will describe

in more detail later, assessing confounding for

variables other than effect modifiers can be quite

difficult and, in particular, extremely subjective,

when interaction is present.

The final stage of our strategy calls for the

assessment of confounding followed by consid-

eration ofprecision. This means that it is more

important to get a valid point estimate of the

E–Drelationship that controls for confounding

than to get a narrow confidence interval

around a biased estimate that does not control

for confounding.

For example, suppose controlling for AGE,

RACE,andSEX simultaneously gave an

adjusted odds ratio estimate of 2.4 with a 95%

confidence interval ranging between 1.2 and

3.7, whereas controlling forAGE alonegave an

odds ratio of 6.2 with a 95% confidence interval

ranging between 5.9 and 6.4.

Then, assuming thatAGE,RACE, andSEXare

considered important risk factorsfor the disease

of interest, we would prefer to use the odds

ratio of 2.4 over the odds ratio of 6.2. This is

because the 2.4 value results from controlling

for all the relevant variables and, thus, gives us

a more valid answer than the value of 6.2,

which controls for only one of the variables.

Thus, even though there is a much narrower

confidence interval around the 6.2 estimate

than around the 2.4, the gain in precision from

using 6.2 does not offset the bias in this estimate

when compared to the more valid 2.4 value.

In essence, then,validity takes precedence over

precision, so that it is more important to get the

right answer than a precise answer. Thus, in the

third stage of our strategy, we seek an estimate

that controls for confounding and is, over and

above this, as precise as possible.

EXAMPLE

Control

Variables aOR

AGE, RACE, SEX

AGE

2.4 (1.2, 3.7)

6.2 (5.9, 6.4)

VALID

BIASED narrow

wide

95% CI

6.2

3.7 5.9 6.4

2.4

1.2

0

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Presentation: III. Overview of Recommended Strategy 171