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

III. Example 2:
Aspirin–Heart Bypass
Study

Data source: Gavaghan et al., 1991

Subjects: 214 patients received up
to 6 coronary bypass grafts.

Randomly assigned to treatment
group:

ASPIRIN¼

1 if daily aspirin

0 if daily placebo



Response (D): Occlusion of a bypass
graft 1 year later

D¼

1 if blocked

0 if unblocked



Additional covariates:
AGE (in years)
GENDER (1¼male, 2¼female)
WEIGHT (in kilograms)
HEIGHT (in centimeters)

Correlation structures to consider:

 Exchangeable

 Independent

Model 1:interaction model

Interaction terms between ASPIRIN
and the other four covariates
included.

logit PðD¼ 1 jXÞ

¼b 0 þb 1 ASPIRINþb 2 AGE

þb 3 GENDERþb 4 WEIGHT

þb 5 HEIGHTþb 6 ASPIRINAGE

þb 7 ASPIRINGENDER

þb 8 ASPIRINWEIGHT

þb 9 ASPIRINHEIGHT

The next example uses data from a study in

Sydney, Australia, which examined the efficacy

of aspirin for prevention of thrombotic graft

occlusion after coronary bypass grafting

(Gavaghan et al., 1991). Patients (K¼214)

were given a variable number of artery

bypasses (up to six) in a single operation, and

randomly assigned to take either aspirin (ASPI-

RIN¼1) or a placebo (ASPIRIN¼0) every

day. One year later, angiograms were per-

formed to check each bypass for occlusion

(the outcome), which was classified as blocked

(D¼1) or unblocked (D¼0). Additional cov-

ariates include AGE (in years), GENDER (1¼

male, 2¼female), WEIGHT (in kilograms),

and HEIGHT (in centimeters).

In this study, there is no meaningful distinc-

tion between artery bypass 1, artery bypass 2,

or artery bypass 3 in the same subject. Since

the order of responses within a cluster is arbi-

trary, we may consider using either the exchan-

geable or independent correlation structure.

Other correlation structures make use of an

inherent order for the within-cluster responses

(e.g., monthly measurements), so they are not

appropriate here.

The first model considered (Model 1) allows for

interaction between ASPIRIN and each of the

other four covariates. The model can be stated

as shown on the left.

Presentation: III. Example 2: Aspirin–Heart Bypass Study 551