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

To correctly specify a GEE model:

 Specify correctg(m)

 Specify correctCi

^bh consistent even ifCimisspeci-

fied
but

^bhmore efficient ifCicorrect

To construct CIs, needdvarðb^Þ

Two types of variance estimators:

 Model-based

 Empirical

No effect on^b

Effect ondvarðb^Þ

Model-based variance estimators:

 Similar in form to variance
estimators in GLM

 Consistent only ifCicorrectly
specified

To correctly specify a GLM or GEE model,

one must correctly model the mean response

[i.e., specify the correct link function g(m)

and use the correct covariates]. Otherwise,

the parameter estimates will not be consistent.

An additional issue for GEE models is whether

the correlation structure is correctly specified

by the working correlation structure (Ci).

A key property of GEE models is that parame-

ter estimates for the regression coefficients are

consistent even if the correlation structure is

misspecified. However, it is still preferable for

the correlation structure to be correctly speci-

fied. There is less propensity for error in the

parameter estimates (i.e., smaller variance) if

the correlation structure is correctly specified.

Estimators are said to be moreefficientif the

variance is smaller.

For the construction of confidence intervals

(CIs), it is not enough to know that the param-

eter estimates are asymptotically normal. In

addition, we need to estimate the variance of

the parameter estimates (not to be confused

with the variance of the outcome). For GEE

models, there are two types of variance estima-

tor, calledmodel-basedandempirical, that can

be obtained for the fitted regression coeffi-

cients. The choice of which estimator is used

has no effect on the parameter estimate (^b), but

rather the effect is on the estimate of its vari-

ance½dvarð^bފ.

Model-based variance estimators are of a

similar form as the variance estimators in

a GLM, which are based on maximum like-

lihood theory. Although the likelihood is

never formulated for GEE models, model-

based variance estimators are consistent esti-

mators, but only if the correlation structure is

correctly specified.

Presentation: IX. Empirical and Model-Based Variance Estimators 517