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

Only onerestimated

Order of observations within a
cluster is arbitrary.

Can exchange positions of observa-
tions.

K¼14 schools

ni¼# students from schooli

~

K

i¼ 1

ni¼ 237

Schooli:exchangeorder# 2 $# 9

• Will not affect analysis

Number of responses (ni) can vary
byi

Autoregressive

Assumption: correlation depends
on interval of time between
responses

12 20

r1,2 > r1,20

Time

(in months)

As in all correlation structures used for GEE

analyses, the same set of correlation para-

meters are assumed for modeling each cluster.

For the exchangeable correlation structure,

this means that there is only one correlation

parameter to be estimated.

A feature of the exchangeable correlation

structure is that the order of observations

within a cluster is arbitrary. For example, con-

sider a study in which there is a response from

each of 237 students representing 14 different

high schools. It may be reasonable to assume

that responses from students who go to the

same school are correlated. However, for a

given school, we would not expect the correla-

tion between the response of student #1 and

student #2 to be different from the correlation

between the response of student #1 and stu-

dent #9. We could therefore exchange the

order (the position) of student #2 and student

#9 and not affect the analysis.

It is not required that there be the same num-

ber of responses in each cluster. We may have

10 students from one school and 15 students

from a different school.

Autoregressive correlation structure:

An autoregressive correlation structure is gen-

erally applicable for analyses in which there

are repeated responses over time within a

given cluster. The assumption behind an auto-

regressive correlation structure is that the cor-

relation between responses depends on the

interval of time between responses. For exam-

ple, the correlation is assumed to be greater for

responses that occur 1 month apart rather than

20 months apart.

512 14. Logistic Regression for Correlated Data: GEE