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

For example, if CHL equals 200 and HPT

equals 0, the computed odds ratio is 3.16,

whereas if CHL equals 220 and HPT equals 1,

the computed odds ratio is 1.22.

The table shown here gives odds ratio values,

indicated by “asterisked”dOR, for a model that

deletes the three eligible V variables, AGE,

SMK, and ECG. As with the gold standard

model, the odds ratio expression involves the

same two effect modifiers CHL and HPT, and

the table shown here considers the same com-

bination of CHL and HPT values.

If we compare corresponding odds ratios in the

two tables, we can see sufficient discrepancies.

For example, when CHL equals 200 and HPT

equals 0, the odds ratio is 3.16 in the gold

standard model, but is 4.57 when AGE, SMK,

and ECG are deleted. Also, when CHL equals

220 and HPT equals 1, the corresponding odds

ratios are 1.22 and 1.98.

Thus, because the two tables of odds ratios

differ appreciably, we cannot simultaneously

drop AGE, SMK, and ECG from the model.

Similar comparisons can be made by compar-

ing the gold standard odds ratio with odds

ratios obtained by deleting other subsets, for

example, AGE and SMK together, or AGE and

ECG together, and so on. All such comparisons

show sufficient discrepancies in corresponding

odds ratios. Thus, we cannot drop any of the

three eligible variables from the model.

We conclude that all fiveVvariables need to be

controlled, so that the final model contains the

exposure variable CAT, the fiveVvariables, and

the interaction variables involving CHL and

HPT.

EXAMPLE (continued)

CHL¼ 200 ;HPT¼ 0 ¼)ORd¼ 3 : 16

CHL¼ 220 ;HPT¼ 1 ¼)ORd¼ 1 : 22

dOR with AGE, SMK, ECG deleted:

dOR*¼expð 12 : 7411 þ 0 : 0713 CHL

 2 : 2613 HPTÞ

HPT¼0 HPT¼ 1

CHL¼ 200 dOR*¼ 4 : 57 dOR*¼ 0 : 48

CHL¼ 220 dOR*¼ 19 : 01 dOR*¼ 1 : 98

CHL¼ 240 dOR*¼ 79 : 11 dOR*¼ 8 : 34

Gold standarddOR:dOR*

w/o AGE, SMK, ECG

HPT= 0 HPT=1HPT= 0 HPT=^1

CHL = 200

CHL = 220

CHL = 240

3.16 4.57

19.01

79.11

0.48

1.98

8.34

12.61

50.33

0.31

1.22

4.89

Cannot simultaneously drop AGE,

SMK, and ECG from model

gold standard other models

vs.

Other models: delete AGE and SMK or

delete AGE and ECG, etc.

Result: cannot drop AGE, SMK, or

ECG

Final model:

E: CAT

FiveVs: CHL, HPT, AGE, SMK, ECG

Two interactions: CATCHL,

CATHPT

228 7. Modeling Strategy for Assessing Interaction and Confounding