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

Because CAT is the exposure variable, we must

leave CAT in all further models regardless of

the hierarchy principle. In addition, CHL and

HPT are the twoVs that must remain in all

further models.

This leaves theVvariables AGE, SMK, and

ECG as still being candidates for elimination

as possible nonconfounders.

As described earlier, one approach to assessing

whether AGE, SMK, and ECG are nonconfoun-

ders is to determine whether the coefficients in

the odds ratio expression for the CAT, CHD

relationship change meaningfully as we drop

one or more of the candidate terms AGE, SMK,

and ECG.

The odds ratio expression for the CAT, CHD

relationship is shown here. This expression

containsb^, the coefficient of the CAT variable,

plus two terms of the form^dtimesW, where the

Ws are the effect modifiers CHL and HPT that

remain as a result of interaction assessment.

The gold standard odds ratio expression is

derived from the model remaining after inter-

action assessment. This model controls for all

potential confounders, that is, theVs, in the

initial model. For the Evans County data, the

coefficients in this odds ratio, which are

obtained from the printout above, areb^equals

12.6894, ^d 1 equals 0.0692, and ^d 2 equals

2.3318.

The table shown here provides the odds ratio

coefficients^b;^d 1 , and^d 2 for different subsets of

AGE, SMK, and ECG in the model. The first

row of coefficients is for the gold standard

model, which contains all fiveVs. The next

row shows the coefficients obtained when

SMK is dropped from the model, and so on

down to the last row which shows the coeffi-

cients obtained when AGE, SMK, and ECG are

simultaneously removed from the model so

that only CHL and HPT are controlled.

EXAMPLE (continued)

Thus, retain CAT, CHL, and HPT in all

further models

Candidates for elimination:

AGE, SMK, ECG

Assessing confounding:

Do coefficients inOR expressiond

change?

ORd¼expð^bþ^d 1 CHLþ^d 2 HPTÞ;

where

^b¼coefficient of CAT

^d 1 ¼coefficient of CC¼CATCHL

^d 2 ¼coefficient of CH¼CATHPT

Gold standardOR (alld Vs):

ORd¼expð^bþ^d 1 CHLþ^d 2 HPTÞ;

where

^b¼ 12 : 6894 ;^d 1 ¼ 0 : 0692 ;^d 2

¼ 2 : 3318

Viin model ^b ^d 1 ^d 2

All fiveV

variables

12.6894 0.0692 2.3318

CHL, HPT,

AGE, ECG

12.7285 0.0697 2.3836

CHL, HPT,

AGE, SMK

12.8447 0.0707 2.3334

CHL, HPT,

ECG, SMK

12.5684 0.0697 2.2081

CHL, HPT, AGE 12.7879 0.0707 2.3796

CHL, HPT, ECG 12.6850 0.0703 2.2590

CHL, HPT, SMK 12.7198 0.0712 2.2210

CHL, HPT 12.7411 0.0713 2.2613

226 7. Modeling Strategy for Assessing Interaction and Confounding