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

Comparison of model results for
ASPIRIN

Correlation

structure

Odds

ratio 95% CI

Exchangeable
(GEE)

0.26 (0.20, 0.35)

Independent
(SLR)

0.26 (0.19, 0.36)

In this example, predictor values
did not vary within a cluster.

IV. Example 3: Heartburn
Relief Study

Data source: Fictitious crossover
study on heartburn relief.

Subjects: 40 patients; 2 symptom-
provoking meals each; 1 of 2
treatments in random order

TreatmentðRXÞ¼^1 if active RX
0 if standard RX



Response (D): Relief from
symptoms after 2 hours

D¼^1 if yes
0 if no



Each subject has two observations

RX¼ 1

RX¼ 0

RX is time dependent: values
change for each subject (cluster)

A comparison of the odds ratio estimates with

95% confidence intervals for the no-interaction

models of both the GEE model and SLR is

shown on the left. The odds ratio estimates

and 95% confidence intervals are very similar.

This is not surprising, since only a modest

amount of correlation is detected in the work-

ing correlation matrixð^r¼ 0 : 0954 Þ.

In this example, none of the predictor variables

(ASPIRIN, AGE, GENDER, WEIGHT, or

HEIGHT) had values that varied within a clus-

ter. This contrasts with the data used for the

next example in which the exposure variable of

interest is a time-dependent variable.

The final dataset discussed is a fictitious cross-

over study on heartburn relief in which 40 sub-

jects are given two symptom-provoking meals

spaced a week apart. Each subject is adminis-

tered an active treatment for heartburn

(RX¼1) following one of the meals and a stan-

dard treatment (RX¼0) following the other

meal in random order. The dichotomous out-

come is relief from heartburn, determined

from a questionnaire completed 2 hours after

each meal.

There are two observations recorded for each

subject: one for the active treatment and the

other for the standard treatment. The variable

indicating treatment status (RX) is a time-

dependent variable since it can change values

within a cluster (subject). In fact, due to the

design of the study, RX changes values in every

cluster.

Presentation: IV. Example 3: Heartburn Relief Study 555