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

Empirical (robust) variance esti-
mators:

 An adjustment of model-based
estimators

 Uses observedrjkbetween
responses

 Consistent even ifCi
misspecified

“
Advantageof empirical estimator

Estimation ofbvs. estimation of
var(b^)

 bis estimated by^b

 varð^bÞis estimated bydvarð^bÞ

The true value ofbdoes not depend
on the study

The true value of var(b^)does depend
on the study design and the type of
analysis

Choice of working correlation
structure

)affectstruevariance of^b

Empirical (robust) variance estimatorsare an

adjustment of model-based estimators (see

Liang and Zeger, 1986). Both the model-based

approach and the empirical approach make

use of the working correlation matrix. How-

ever, the empirical approach also makes use

of the observed correlations between responses

in the data. The advantage of using the empiri-

cal variance estimator is that itprovides a con-

sistent estimate of the variance even if the

working correlation is not correctly specified.

There is a conceptual difference between the

estimation of a regression coefficient and the

estimation of its variance [dvarð^bÞ]. The regres-

sion coefficient,b, is assumed to exist whether

a study is implemented or not. The distribution

of^b, on the other hand, depends on character-

istics of the study design and the type of analy-

sis performed. For a GEE analysis, the

distribution ofb^depends on such factors as

the true value ofb, the number of clusters, the

number of responses within the clusters,

the true correlations between responses, and

the working correlation structure specified

by the user. Therefore, thetruevariance of^b

(and not just its estimate) depends, in part, on

the choice of a working correlation structure.

518 14. Logistic Regression for Correlated Data: GEE