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

EXAMPLE (continued)

Outcome:D¼MRSA status

(0¼no, 1¼yes)

Predictors:

PREVHOSP (0¼no, 1¼yes)

PAMU (0¼no, 1¼yes)

AGE (continuous)

GENDER (0¼F, 1¼M)

Question:

PREVHOSP, PAMU

controlling for AGE, GENDER

MRSA

TwoEs:E 1 ¼PREVHOSP

E 2 ¼PAMU

TwoCs:C 1 ¼AGE

C 2 ¼GENDER

Initial model:

Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þ

þðg 1 V 1 þg 2 V 2 Þ

þðd 11 E 1 W 1 þd 12 E 1 W 2

þd 21 E 2 W 1 þd 22 E 2 W 2 Þ

þd*E 1 E 2 ;

whereV 1 ¼C 1 ¼W 1 and

V 2 ¼C 2 ¼W 2.

V 1 andV 2 : potential confounders

W 1 andW 2 : potential effect

modifiers

E 1 E 2 : interaction of exposures

Modeling Strategy with Several
Exposures

Step 1: Variable Specification
(Initial Model)
Considers the following:

 Study question
 Literature review
 Biological/medical
conceptualization

(previously recommended with
only oneE)

The outcome variable is MRSA status (1¼yes,

0 ¼no), and covariates of interest included the

following variables: PREVHOSP (1¼previous

hospitalization, 0¼no previous hospitaliza-

tion), PAMU (1¼antimicrobial drug use in

the previous 3 months, 0¼no previous anti-

microbial drug use), AGE (continuous), and

GENDER (1¼male, 0¼female).

For these data, we consider the following ques-

tion: Are the variables PREVHOSP and PAMU

associated with MRSA outcome controlling for

AGE and GENDER?

For this question, our predictors include two

Es (PREVHOSP and PAMU) and twoCs (AGE

and GENDER).

We now consider an initial EVW model (shown

at the left) that includes bothEs and bothCsas

main effects plus product terms involving each

Ewith eachCand the product of the twoEs.

This initial model considers the control vari-

ables AGE and GENDER as both potential con-

founders (i.e.,V 1 andV 2 ) and as potential effect

modifiers (i.e.,W 1 andW 2 ) of bothE 1 andE 2.

The model also contains an interaction term

involving the twoEs.

As recommended in the previous chapters

when only one exposure variable was being

considered, we continue to emphasize that

the first step in one’s modeling strategy, even

with two or moreEs, is to specify the initial

model. This step requires consideration of the

literature about the study question and/or out-

come and/or variables needing to be controlled

based on one’s biological/medical conceptuali-

zation of the study question.

Presentation: II. Modeling Strategy for Several Exposure Variables 245