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

EXAMPLE (continued)

Option A: Overall (chunk) interaction,
then, in order.EWs,EEs,
Vs, andEs

Option B: AssessEWs first, then, in
orderEEs,Vs, andEs

Option C: AssessEWs first, then,
in order,Vs, EEs,and
Es

Reduced Model B(w/oEWterms):

Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þ

þðg 1 V 1 þg 2 V 2 Þ

þd*E 1 E 2

Note: Reduced modelBpreferred to
full interaction model

Model B Output: –21n L =277.667

Param

Intercept

PREVHOSP

PAMU

AGE

GENDER

DF Estimate Std Err ChiSq Pr > ChiSq

Es

Vs
EE PRHPAM

Confounding:
DoesOR meaningfully changed
when AGE and/or GENDER are
dropped?

GS model: reduced modelBabove

ORGSðBÞ¼exp½b 1 ðE 1 *E 1 Þ

þb 2 ðE 2 *E 2 Þ

þd*ðE 1 *E 2 *E 1 E 2 ފ;

whereX¼(E 1 ,E 2 *) andX¼(E 1 ,E 2 )
are two specifications of the twoEs

Recall that both OptionsA and Bassessed

interaction ofEWs andEEs before considering

confounding and precision, where OptionA

used an overall (chunk) test for interaction

andOptionBdid not. We are now ready to

considerOptionC, which assesses interactions

involvingEWs first, then confounding and pre-

cision (i.e., theVs), after whichEEs and finally

Es are evaluated.

Since all three Options, includingOptionC,

assessEWs beforeEEs,Vs, andEs, we have

already determined the results for theEWs.

That is, we can drop all theEWs, which yields

reduced modelB, as shown again at the left.

The corresponding (edited) output for modelB

is shown again here. This model retains theEE

product term PRHPAM (¼E 1 E 2 ), which using

OptionC, will not be considered for exclusion

until we address confounding for AGE and

GENDER (i.e., theVs).

To assess confounding, we need to determine

whether the estimated OR meaningfully changes

(e.g., by more than 10%) when either AGE or

GENDER or both are dropped from the model.

Here, the gold standard (GS) model is the

reduced modelB, which contains theE 1 E 2 term.

The formula for the odds ratio for the GS

model is shown at the left, where (E 1 *,E 2 *)

and (E 1 ,E 2 ) denote two specifications of the

two exposures PREVHOSP (i.e.,E 1 ) and PAMU

(i.e., E 2 ). This formula contains three para-

meters:b 1 ,b 2 , andd*.

Presentation: II. Modeling Strategy for Several Exposure Variables 253