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

EXAMPLE (continued)

Option C(continued)

Estimated Regression Coefficients
and ORs
Model: I(GS) II III IV
Vsin
model

AGE,

GEN AGE GEN Neither

^b 1 1.0503 1.1224 1.2851 1.2981

^b 2 0.9772 1.0021 0.8002 0.8251

^d* 1.0894 0.8557 0.9374 0.8398

dOR 22.5762 19.6918 20.5467 19.3560

Confounding (Option C):
Which models have “same”dOR asGS
model?

dOR forGSis highest

+

OnlyGSmodel controls confounding

Change of Estimate Results:
10% Rule
Model: I (GS) II III IV
Vsin
model

AGE,

GEN AGE GEN Neither

dOR 22.576219.691820.546719.3560

Within

10% of

GS?

–NoYes No

Note:10% of 22.5762: (20.3186,
24.8338)

Two alternative conclusions:
(a) OnlyGSmodel controls
confounding
(b) GSmodel (I) and model III
both control confounding

At the left, we show for each model, the values

of these three estimated regression coefficients

together with their corresponding OR esti-

mates.

From this information, we must decide

whether any one or more of models II*, III*,

and IV* yields the “same”OR as obtained ford

theGSmodel (I*).

Notice, first, that the OR estimate for theGS

model (22.5762) is somewhat higher than the

estimates for the other three models, suggest-

ing that only theGSmodel controls for con-

founding.

However, using a “change-of-estimate” rule

of 10%, we find that the dOR (20.5467) for

model III*, which drops AGE but retains GEN-

DER, is within 10% of theOR (22.5762) for thed

GSmodel. This result suggests that there are

two candidate models (I* and III*) that control

for confounding.

From the above results, we must decide at this

point which of two conclusions to draw about

confounding: (a) the only model that controls

for confounding is theGSmodel; or (b) both

theGSmodel (I*) and model III* control for

confounding.

Presentation: II. Modeling Strategy for Several Exposure Variables 255