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

In scanning the above table, it is seen for each

coefficient separately (that is, by looking at the

values in a given column) that the estimated

values change somewhat as different subsets of

AGE, SMK, and ECG are dropped. However,

there does not appear to be a radical change in

any coefficient.

Nevertheless, it is not clear whether there is

sufficient change in any coefficient to indicate

meaningful differences in odds ratio values.

Assessing the effect of a change in coefficients

on odds ratio values is difficult because the

coefficients are on the log odds ratio scale. It

is more appropriate to make our assessment of

confounding using odds ratio values rather

than log odds ratio values.

To obtain numerical values for the odds ratio for

a given model, we must specify values of the

effect modifiers in the odds ratio expression. Dif-

ferent specifications will lead to different odds

ratios.Thus,foragivenmodel,wemustconsider

a summary table or graph that describes the

different odds ratio values that are calculated.

To compare the odds ratios for two different

models, say the gold standard model with the

model that deletes one or more eligibleVvari-

ables, we must compare corresponding odds

ratio tables or graphs.

As an illustration using the Evans County data,

we compare odds ratio values computed from

the gold standard model with values computed

from the model that deletes the three eligible

variables AGE, SMK, and ECG.

The table shown here gives odds ratio values

for the gold standard model, which contains all

fiveVvariables, the exposure variable CAT, and

the two interaction terms CATCHL and CAT

HPT. In this table, we have specified three

different row values for CHL, namely, 200, 220,

and 240, and two column values for HPT,

namely, 0 and 1. For each combination of

CHL and HPT values, we thus get a different

odds ratio.

EXAMPLE (continued)

Coefficients change somewhat. No
radical change

Meaningful differences inOR?d
 Coefficients on log odds ratio scale
 More appropriate: odds ratio scale

OR = exp(b + d 1 CHL + d 2 HPT)

Specify values of effect modifiers
Obtain summary table of ORs

Compare
gold standard vs. other models
using (withoutVs)
odds ratio tables or graphs

Evans County example:
Gold standard
vs.
Model without AGE, SMK, and ECG

Gold standardOR:d
dOR¼expð 12 : 6894 þ 0 : 0692 CHL
 2 : 3318 HPTÞ

HTP = 0

CHL = 200

CHL = 220

CHL = 240

CHL = 200, HPT = 0 ⇒ OR = 3.16

HTP = 1

OR = 3.16 OR = 0.31

OR = 1.22

OR = 4.89

OR = 12.61

OR = 50.33

CHL = 220, HPT = 1 ⇒ OR = 1.22

Presentation: V. The Evans County Example Continued 227