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

According to our strategy, it is necessary that

our initial model, or any subsequently deter-

mined reduced model, be hierarchically well

formulated. To check this, we assess whether

all lower order components of any variable in

the model are also in the model.

For example, the lower order components of a

product variable like CATAGE are CAT and

AGE, and both these terms are in the model as

main effects. If we identify the lower order

components of any other variable, we can see

that the model we are considering is truly hier-

archically well formulated.

Note that if we add to the above model the

three-way product term CATECGSMK,

the resulting model is not hierarchically well

formulated. This is because the term ECG

SMK has not been specified as one of theV

variables in the model.

At this point in our model strategy, we are ready

to consider simplifying our model by eliminat-

ing unnecessary interaction and/or confound-

ing terms. We do this using a hierarchical

backward elimination procedure, which consid-

ers eliminating the highest-order terms first,

then the next highest-order terms, and so on.

Because the highest-order terms in our initial

model are two-way products of the formEW,we

first consider eliminating some of these interac-

tion terms. We then consider eliminating theV

terms, which are the potential confounders.

Here, we summarize the results of the interac-

tion assessment and confounding assessment

stages and then return to provide more details

of this example in Chap. 7.

The results of the interaction stage allow us to

eliminate three interaction terms, leaving in

the model the two product terms CATCHL

and CATHPT.

Thus, at the end of interaction assessment, our

remaining model contains our exposure vari-

able CAT, the fiveVs namely, AGE, CHL, SMK,

ECG, and HPT plus two product terms CAT

CHL and CATHPT.

EXAMPLE (continued)

HWF model?

i.e., given variable, are lower order

components in model?

e:g:;CATAGE

+

CAT and AGE both in model as main

effects

HWF model?YES

If CATECGSMK in model, then

notHWF model

because

ECGSMK not in model

Next

Hierarchical backward elimination

procedure

First, eliminateEWterms

Then, eliminateVterms

Interaction assessment

and

confounding assessments (details in

Chap. 7)

Results of Interaction Stage:

CATCHL and CATHPT

are the only two interaction terms to

remain in the model

Model contains

CAT|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl};AGE;CHL;SMK;ECG;HPT;

Vs

CATCHL and CATHPT

190 6. Modeling Strategy Guidelines