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

EXAMPLE (continued)

Options A and B(continued)

However:^b 1 and^b 2 likely differ for
each model

Estimate Regression Coefficients
andORs^

OR

b 1

b 2

Vs in model

Model:

AGE,GEN

I (GS)

AGE

II

GEN

III

Neither

IV

Assessing confounding (OptionB):
Which models have “same”dOR as GS
model?

Quick glance: OR for GS highest

• Only GS model controls
  confounding

Change of Estimate Results:

10% Rule

Vs in model AGE,GEN AGE GEN Neither

Model: I (GS) II III IV

OR

Only GS model controls confounding

Model A Output –2 1n L=279.317

Note: ±10% of 26.2430: (23.6187, 28.8673)

Within 10%

of GS?

Model at this point contains
E 1 , E 2 , V 1 , and V 2
can’t drop
haven’t yet
addressed

Param

Intercept

PREVHOSP

PAMU

AGE

GENDER

DF Estimate Std Err ChiSq Pr > ChiSq

Es

Vs

Wald for
E 1 (PREVHOSP):P¼0.0002
E 2 (PAMU):P<0.0001

However, since the models do not all have the

same predictors, the estimates of the regres-

sion coefficients are likely to differ somewhat.

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

of these two estimated regression coefficients

together with their corresponding OR esti-

mates.From this information, we must decide

which one or more of the four models controls

for confounding. Certainly, the GS model con-

trols for confounding, but do any of the other

models do so also?

An equivalent question is: which of the other

three models yields the “same”OR as obtainedd

for the GS model? A quick glance at the table

indicates that theOR estimate for the GS modeld

is somewhat higher than the estimates for the

other three models,suggesting that only the GS

model controls for confounding.

Moreover, if we use a “change-of-estimate” rule

of 10%, we find that none of models II, III, or

IV have andOR within 10% of thedOR of 26.2430

for the GS model (I), although model III comes

very close.

This result indicates that the only model that

controls for confounding is the GS model.That

is, we cannot drop either AGE or GENDER from

the model.

We therefore have decided that bothVs need

to stay in the model, but we have not yet

addressed theEs in the model.

The only other variable that we might consider

dropping at this point isE 1 orE 2 , provided we

decide that one of these is nonsignificant,

controlling for the other. However, on inspec-

tion of the output for this model, shown again

at the left, we find that the Wald statistic forE 1

is significant (P¼0.0002), as is the Wald sta-

tistic forE 2 (P<0.0001).

Presentation: II. Modeling Strategy for Several Exposure Variables 251