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

GEE vs. MLM

GEE model: logit m = b 0 + b 1 RX

No subject-specific

random effects (b 0 i)

Within-subject correlation specified
in R matrix

MLM model: logit mi = b 0 + b 1 RX +

Subject-specific

random effects

b 0 i

Marginal model ) E(Y|X)not
conditioned on cluster-specific
information
(e.g.,notallowed asX

 Earlier values ofY

 Subject-specific effects)

Marginal models (examples):

GEE

ALR

SLR

Heartburn Relief Study

b 1 ¼parameter of interest

BUT

interpretation of exp (b 1 )depends

on type of model

A GEE model can also be expressed in terms of

theith subject’s mean response (mi), as shown

at left using the heartburn example. The GEE

model contrasts with the MLM, and the condi-

tional logistic regression, since the GEE model

does not contain subject-specific effects (fixed

or random). With the GEE approach, the

within-subject correlation is handled by

the specification of a correlation structure for

theRmatrix. However, the mean response is

not directly modeled as a function of the indi-

vidual subjects.

A GEE model represents a type of model called a

marginal model. With a marginal model, the

mean response E(Y|X) is not directly

conditioned on any variables containing infor-

mation on the within-cluster correlation. For

example, the predictors (X)inamarginal

model cannot be earlier values of the response

from the same subject or subject-specific effects.

Other examples of marginal models include the

ALR model, described earlier in the chapter,

and the standard logistic regression with one

observation for each subject. In fact, any model

using data in which there is one observation

per subject is a marginal model because in that

situation, there is no information available

about within-subject correlation.

Returning to the Heartburn Relief Study exam-

ple, the parameter of interest is the coefficient

of the RX variable,b 1 , not the subject-specific

effect,b 0 i. The research question for this study

is whether the active treatment provides

greater relief for heartburn than the standard

treatment. The interpretation of the odds ratio

exp(b 1 ) depends, in part, on the type of model

that is run.

Presentation: IV. The Generalized Linear Mixed Model Approach 585