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

In general, with longitudinal data,
independent variables may be
either

1. Time-dependent
   or


2. Time-independent

Outcome variable generally varies
within a cluster

Goal of analysis: to account for out-
come variation within and between
clusters

Model for Infant Care Study:

logit PðD¼ 1 jXÞ¼b 0 þb 1 BIRTHWGT

þb 2 GENDER

þb 3 DIARRHEA

GEE Model(GENMOD output)

Variable Coefficient

Empirical

Std Err

Wald

p-value

INTERCEPT 1.3978 1.1960 0.2425
BIRTHWGT 0.0005 0.0003 0.1080
GENDER 0.0024 0.5546 0.9965
DIARRHEA 0.2214 0.8558 0.7958

Interpretation of GEE model simi-
lar to SLR

OR estimates

Confidence intervals

Wald test statistics

9

=

;

Use same

formulas

Underlying assumptions

Method of parameter

estimation

9

=

;

Differ

Odds ratio

ORdðDIARRHEA¼ 1 vs:DIARRHEA¼ 0 Þ

¼expð 0 : 2214 Þ¼ 1 : 25

In general, with longitudinal data, independent

variables may or may not vary within a cluster.

A time-dependent variable can vary in value,

whereas a time-independent variable does

not. The values of theoutcome variable, in

general, will vary within a cluster.

A correlated analysis attempts to account for

the variation of the outcome from both within

and between clusters.

We state the model for the Infant Care Study

example in logit form as shown on the left.

In this chapter, we use the notation b 0 to

represent the intercept rather thana,asais

commonly used to represent the correlation

parameters in a GEE model.

Next, the output obtained from running a GEE

model using the GENMOD procedure in SAS is

presented. This model accounts for the corre-

lations among the monthly outcome within

each of the 136 infant clusters. Odds ratio esti-

mates, confidence intervals, and Wald test

statistics are obtained using the GEE model

output in the same manner (i.e., with the

same formulas) as we have shown previously

using output generated from running a stan-

dard logistic regression. The interpretation of

these measures is also the same. What differs

between the GEE and standard logistic regres-

sion models are the underlying assumptions

and how the parameters and their variances

are estimated.

The odds ratio comparing symptoms of diar-

rhea vs. no diarrhea is calculated using the

usual e to the^bformula, yielding an estimated

odds ratio of 1.25.

Presentation: II. An Example (Infant Care Study) 495