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

Wald test

H 0 :b 3 ¼ 0

Z¼

0 : 7764

0 : 4538

¼ 1 : 711 ;P¼ 0 : 0871

Comparison of analysis
approaches:

1. dOR and 95% CI for DIARRHEA

GEE model SLR model
dOR 1.25 2.17

95% CI 0.23, 6.68 0.89, 5.29

2. P-Value of Wald test for
   BIRTHWGT

GEE model SLR model

P-Value 0.1080 0.0051

Why these differences?

GEE model: 136 independent

clusters (infants)

Naive model: 1,203 independent

outcome measures

Effects of ignoring correlation
structure:

 Not usually so striking

 Standard error estimates more
often affected than parameter
estimates

 Example shows effects onboth
standard error and parameter
estimates

The Wald test statistic for DIARRHEA in the

SLR model is calculated to be 1.711. The

correspondingP-value is 0.0871.

This example demonstrates that the choice

of analytic approach can affect inferences

made from the data. The estimates for the

odds ratio and the 95% confidence interval for

DIARRHEA are greatly affected by the choice

of model.

In addition, the statistical significance of the

variable BIRTHWGT at the 0.05 level depends

on which model is used, as theP-value for the

Wald test of the GEE model is 0.1080, whereas

theP-value for the Wald test of the standard

logistic regression model is 0.0051.

The key reason for these differences is the

way the outcome is modeled. For the GEE

approach, there are 136 independent clusters

(infants) in the data, whereas the assumption

for the standard logistic regression is that there

are 1,203 independent outcome measures.

For many datasets, the effect of ignoring

the correlation structure in the analysis is not

nearly so striking. If there are differences in

the resulting output from using these two

approaches, it is more often the estimated stan-

dard errors of the parameter estimates rather

than the parameter estimates themselves that

show the greatest difference. In this example

however, there are strong differences in both

the parameter estimates and their standard

errors.

Presentation: II. An Example (Infant Care Study) 497