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

EXAMPLE (continued)

Option C(continued)

⇓

Suppose decide only GS(B)

control confounding

Model at this point contains

E 1 , E 2 , V 1 , V 2 and E 1 E2,

can’t drop

have not yet

addressed

Next step: testE 1 E 2 :

Waldw^2 ðreduced modelBÞ

¼ 1 : 5562 ;P¼ 0 : 2122 ðn:s:Þ

LR¼ 2 ln LmodelA 2 ln LmodelBÞ

¼ 279 : 317  277 : 667 ¼ 1 : 650 w^21 df

ðP¼ 0 : 1989 Þ

No-interaction ModelA:

Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þþðg 1 V 1

þg 2 V 2 Þ;

whereV 1 ¼C 1 ¼AGE,

V 2 ¼C 2 ¼GENDER

E 1 ¼PREVHOSP,

E 2 ¼PAMU

Recall:Options A and B)

ModelAis best

Option C:onlyGSmodel controls

confounding

+

ModelAis best

Alternative decision about

confounding forOption C

+

2 candidate models control

confounding:

Model I*:GS(B)

Model III*: (AGE dropped)

How to decide between models?

Answer:Precision

Suppose we decide that only theGSmodel

controls for confounding. Then, 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.

For the next step, we would test whether the

E 1 E 2 product term is significant.

From our output for reduced modelBgiven

previously, we find that the Wald test for the

PRHPAM term (i.e.,E 1 E 2 ) is not significant

(P¼0.2122). The corresponding LR test is

obtained by comparing2lnL statistics for

reduced modelsAandB, yielding a LR statistic

of 1.650, also nonsignificant.

We can now reduce our model further by

dropping theE 1 E 2 term, which yields the no-

interaction modelA, shown at the left.

Recall that ModelAwas chosen as the best

model usingOptionsAandB. Consequently,

using Option C, if we decide that the only

model that controls confounding is theGS(B)

model (I* above), then our best model for

OptionCis also ModelA.

The above conclusion (i.e., ModelAis best),

nevertheless, resulted from the decision that

only theGS(B)model controlled for confound-

ing. However, we alternatively allowed for two

candidate models, theGS(B)model (I*) and

model III*, which dropped AGE from the

model, to control for confounding.

If we decide to consider model III* in addition

to theGS(B)model, how do we decide between

these two models? The answer, according to

the modeling strategy described in Chap. 7, is

to considerprecision.

256 8. Additional Modeling Strategy Issues