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

Estimation of

predictors

Analysis

Within-

subject

variability

Between-

subject

variability

Matched (CLR)
p

Correlated (GEE)
pp

No within-subject variability for an
independent variable

• parameter will not be estimated
  using CLR

The estimated odds ratios and the standard

errors for the parameter estimate for RX are

shown at left for the conditional logistic regres-

sion (CLR) model, as well as for the GEE and

standard logistic regression (SLR) discussed in

Chap. 15. The odds ratio estimate for the CLR

model is somewhat larger than the estimate

obtained at 1.35 using the GEE approach. The

standard error for the RX coefficient estimate

in the CLR model is also larger than what was

obtained in either the GEE model using empir-

ical standard errors or in the standard logistic

regression, which uses model-based standard

errors.

An important distinction between the CLR and

GEE analytic approaches concerns the treat-

ment of the predictor (independent) variables

in the analysis. A matched analysis (CLR) relies

on within-subject variability (i.e., variability

within the matched strata) for the estimation

of its parameters. A correlated (GEE) analysis

takes into account both within-subject varia-

bility and between-subject variability. In fact,

if there is no within-subject variability for an

independent variable (e.g., a time-independent

variable), then its coefficient cannot be esti-

mated using a conditional logistic regression.

In that situation, the parameter cancels out in

the expression for the conditional likelihood.

This is what occurs to the intercept as well as

to the coefficients of the matching factor

dummy variables when CLR is used.

To illustrate the consequences of only includ-

ing independent variables with no within-

cluster variability in a CLR, we return to the

Aspirin–Heart Bypass Study discussed in the

previous section. Recall that patients were

given a variable number of artery bypasses in

a single operation and randomly assigned to

either aspirin or placebo therapy. One year

later, angiograms were performed to check

each bypass for reocclusion.

EXAMPLE

CLR with time-independent

predictors (Aspirin–Heart Bypass

Study)

Subjects: 214 patients received up to 6

coronary bypass grafts.

Treatment:

ASPIRIN¼

1 if daily aspirin

0 if daily placebo

8

><

>:

D¼

1 if graft blocked

0 if graft unblocked

8

><

>:

EXAMPLE (continued)

Model comparison

Model OR s^b

CLR 1.50 0.5271

GEE 1.35 0.3868

SLR 1.35 0.4486

Presentation: III. Conditional Logistic Regression 577