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

General Model: OnlyEs andEEs

Logit PðXÞ¼aþ~

q

i¼ 1

biEiþ~

q

i¼ 1

~

i^0 ¼ 1

i 6 ¼i^0

q

d*ii 0 EiEi 0

Modeling Strategy: All Es, no Cs

Step 1: Define initial model (above formula)

Step 2: Assess interaction involving Es

Option A*: Overall chunk test for EEs,

followed by backward elimination of EEs

Step 4: Test for nonsignif Es if not components

of significant EEs

EXAMPLE

MRSA example Initial Model, Special

case (b)

Logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þd*E 1 E 2

Final model: AllEs, noCs:

Logit PðXÞ¼aþb 1 E 1 þb 2 E 2 ;

whereE 1 ¼PREVHOSP and

E 2 ¼PAMU

One other issue: specifying the
initial model
(MRSA example)

EXAMPLE

Possible Causal Diagrams for MRSA

Study

Diagram 1

Diagram 2

V 1

V 1 V 2

V 2

E 2

E 2

D

D

E 1

E 1

D = MRSA (0,1)

V 1 = AGE

V 2 = GENDER

E 1 = PREVHOSP

E 2 = PAMU

Diagram 1)PAMU intervening

variable;

AGE and GENDER

confounders

In this case (b), our general model takes the

simplified form shown at the left.

For this model, we recommend a correspond-

ingly simplified strategy as shown at the left

that involves statistical testing only, first for

EEterms, and then forEs that are not compo-

nents of significant EEs. In terms of the

options we previously described, we only need

to consider a modified version of Option A, and

that Step 3, once again, can be omitted.

Applying this situation to our MRSA data, the

initial model (w/o theCs) is shown at the left.

TestingH 0 :d*¼0 in this model yields a nonsig-

nificant result (data not shown), and the final

model (since individualEs cannot be dropped)

is the no-interaction model shown here.

We now address one other issue, which con-

cerns how to specify the initial model. We

describe this issue in the context of the MRSA

example.

At the left, we consider two possiblecausal

diagramsfor the MRSA data.

Diagram 1 indicates that PAMU (i.e.,E 2 )isan

intervening variable in the causal pathway

between PREVHOSP (i.e.,E 1 ) and MRSA out-

come, and that AGE and GENDER (i.e.,V 1

and V 2 ) are confounders of the relationship

between PREVHOSP and MRSA.

Presentation: II. Modeling Strategy for Several Exposure Variables 261