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

Heartburn Relief Model:

(Subject modeled asfixed effect)

logit PðXÞ¼b 0 þb 1 RX

þ~

39

i¼ 1

giVi;

where

Vi¼

1 for subject i

0 otherwise

(

Alternative approach:
Subject modeled asrandom effect

What if study is replicated?

Different sample

) different subjects

b 1 unchanged (fixed effect)

gdifferent

Parameters themselves may be
random (not just their estimates)

With the conditional logistic regression

approach,subjectis modeled as afixedeffect

with the gamma parameters (g), as shown on

the left for the Heartburn Relief example.

An alternative approach is to model subject as

arandomeffect.

To illustrate this concept, suppose we attempted

to replicate the heartburn relief study using a

different sample of 40 subjects.We might expect

the estimate forb 1 , the coefficient for RX, to

change due to sampling variability. However,

the true value ofb 1 would remain unchanged

(i.e.,b 1 is a fixed effect). In contrast, because

there are different subjects in the replicated

study, the parameters representing subject

(i.e., the gammas) would therefore also be dif-

ferent. This leads to an additional source of

variability that is not considered in the CLR, in

that some of the parameters themselves (and

not just their estimates) are random.

In the next section, we present an approach for

modeling subjectas a random effect, which

takes into account that the subjects represent

a random sample from a larger population.

Presentation: III. Conditional Logistic Regression 579