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

Impact of misspecification

(usually)

OR

Sb

For Models 1–5:

dOR range¼ 1 : 25  3 : 39

dOR range suggests model

instability.

Instability likely due to small num-
ber (nine) of exposed cases.

Which models to eliminate?

Models 4 and 5 (independent):

Evidence of correlated

observations

Model 2 (exchangeable):
If autocorrelation suspected

Remaining models: similar results:

Model 1 (AR1)

dORð 95 %CIÞ¼ 1 : 25 ð 0 : 23 ; 6 : 68 Þ

Model 3 (fixed)

dORð 95 %CIÞ¼ 1 : 29 ð 0 : 26 ; 6 : 46 Þ

Typically, a misspecification of the correlation

structure has a stronger impact on the stan-

dard errors than on the odds ratio estimates.

In this example, however, there is quite a bit of

variation in the odds ratio estimates across the

five models (from 1.25 for Model 1 to 2.17 for

Model 4 and Model 5).

This variation in odds ratio estimates suggests

a degree of model instability and a need for

cautious interpretation of results. Such evi-

dence of instability may not have been appar-

ent if only a single correlation structure had

been examined. The reason the odds ratio var-

ies as it does in this example is probably due to

the relatively few infants who are exposed

cases (n¼9) for any of their nine monthly

measurements.

It is easier to eliminate prospective models

than to choose a definitive model. The working

correlation matrices of the first two models

presented (AR1 autoregressive and exchange-

able) suggest that there is a positive correlation

between responses for the outcome variable.

Therefore, an independent correlation struc-

ture is probably not justified. This would elim-

inate Model 4 and Model 5 from consideration.

The exchangeable assumption for Model 2 may

be less satisfactory in a longitudinal study if it

is felt that there is autocorrelation in the

responses. If so, that leaves Model 1 and

Model 3 as the models of choice.

Model 1 and Model 3 yield similar results, with

an odds ratio and 95% confidence interval of

1.25 (0.23, 6.68) for Model 1 and 1.29 (0.26,

6.46) for Model 3. Recall that our choice of

correlation values used in Model 3 was influ-

enced by the working correlation matrices of

Model 1 and Model 2.

550 15. GEE Examples