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

Key difference:GEE vs. ALR

GEE:rjkare typically nuisance
parameters

ALR: ORjkare parameters of
interest

ALR: allows inferences about both
^aandb^s

III. Conditional Logistic
Regression

This points out a key difference in the GEE and

ALR approaches. With the GEE approach, the

correlation parameters are typically consid-

ered to be nuisance parameters, with the para-

meters of interest being the regression

coefficients (e.g., ASPIRIN). In contrast, with

the ALR approach, the association between

different responses is also considered to be of

interest. Thus, the ALR approach allows statis-

tical inferences to be assessed from both the

alpha parameter and the beta parameters

(regression coefficients).

Another approach that is applicable for certain

types of correlated data is a matched analysis.

This method can be applied to the Heartburn

Relief Study example, with “subject” used as

the matching factor. This example was pre-

sented in detail in Chap. 15. Recall that the

dataset contained 40 subjects, each receiving

an active or standard treatment for the relief of

heartburn. In this framework, within each

matched stratum (i.e., subject), there is an

exposed observation (the active treatment)

and an unexposed observation (the standard

treatment). A conditional logistic regression

(CLR) model, as discussed in Chap. 11, can

then be formulated to perform a matched anal-

ysis. The model is shown on the left.

This model differs from the GEE model for the

same data, also shown on the left, in that the

conditional model contains 39 dummy variables

besides RX. Each of the parameters (gi)forthe

39 dummy variables represents the (fixed)

effects for each of 39 subjects on the outcome.

The 40th subject acts as the reference group

since all of the dummy variables have a value

of zero for the 40th subject (see Chap. 11).

EXAMPLE

Heartburn Relief Study

(“subject” as matching factor)

40 subjects received:

 Active treatment (“exposed”)

 Standard treatment

(“unexposed”)

CLR model

logit PðXÞ¼b 0 þb 1 RXþ~

39

i¼ 1

giVi;

where

Vi¼

1 for subjecti

0 otherwise

(

GEE model

logit PðXÞ¼b 0 þb 1 RX

CLR vs. GEE

##

39 Vi

(dummy

variables)

noVi

Presentation: III. Conditional Logistic Regression 575