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

Most situations

useonly EVi

product terms

+

interaction assessment

less complicated

+

do not needViVjterms

for HWF model:

To evaluate whetherEV 3 is significant, we can

perform a likelihood ratio (LR) chi-square test

with one degree of freedom. For this test, the

two models being compared are the full model

consisting ofEV 1 V 2 , all threeEViterms and all

Viterms, including those of the formViVj, and

the reduced model that omits theEV 3 term

being tested. Alternatively, a Wald test can be

performed using theZstatistic equal to the

coefficient of theEV 3 term divided by its stan-

dard error.

Suppose that both the above likelihood ratio

and Wald tests are nonsignificant. Then we

can drop the variableEV 3 from the model.

Thus, at the end of the interaction assessment

stage for this example, the following terms

remain in the model:EV 1 V 2 ,EV 1 ,EV 2 ,V 1 ,V 2 ,

V 3 ,V 1 V 2 , andV 1 V 3.

All of theVterms, includingV 1 V 2 andV 1 V 3 ,

in the initial model are still in the model at

this point. This is because we have been asses-

sing interaction only, whereas theV 1 V 2 and

V 1 V 3 terms concern confounding. Note that

although theViVjterms are products, they are

potential confounders in this model because

they do not involve the exposure variableE.

Before discussing confounding, we point out

that for most situations, the highest-order

interaction terms to be considered are two-fac-

tor product terms of the formEVi. In this case,

interaction assessment begins with such two-

factor terms and is often much less compli-

cated to assess than when there are terms of

the formEViVj.

In particular, when only two-factor interaction

terms are allowed in the model, then it isnot

necessary to have two-factor confounding

terms of the formViVjin order for the model

to be hierarchically well formulated. This

makes the assessment of confounding a less

complicated task than when three-factor inter-

actions are allowed.

EXAMPLE (continued)

LR statisticw^21

Full model: EV 1 V 2 , EV 1 , EV 2 , EV 3 ,

V 1 , V 2 , V 3 , V 1 V 2 , V 1 V 3

Reduced model:EV 1 V 2 ,EV 1 ,EV 2 ,

V 1 ,V 2 ,V 3 ,V 1 V 2 ,V 1 V 3

Wald test:Z¼

^dEV 3

S^dEV 3

Suppose both LR and Wald tests are

nonsignificant:

then dropEV 3 from model

Interaction stage results:

EV 1 V 2 ;EV 1 ;EV 2

V 1 ;V 2 ;V 3

V 1 V 2 ;V 1 V 3

)

confounders

AllVi(andViVj) remain in model after

interaction assessment

210 7. Modeling Strategy for Assessing Interaction and Confounding