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

The regression parameter estimates are very

similar for the two models. The odds ratio for

aspirin use on artery reocclusion is estimated

as exp(1.3302)¼0.264 using the GEE model

and exp(1.3253)¼0.266 using the ALR

model. The standard errors for the aspirin

parameter estimates are the same in both mod-

els (0.1444), although the standard errors for

some of the other parameters are slightly larger

in the ALR model.

The corresponding measure of association

(the odds ratio) estimate from the ALR model

can be found by exponentiating the coeffi-

cient of ALPHA1. This odds ratio estimate is

exp(0.4716)¼0.62. As with the estimated

exchangeable correlationð^rÞfrom the GEE

approach, the exchangeable OR estimate,

whichislessthan1,alsoindicatesanegative

association between any pair of outcomes

(i.e., reocclusions on the same bypass patient).

A 95% confidence interval for the OR can be

calculated as exp[0.4716  1.96(0.1217)],

which yields the confidence interval (0.49,

0.79). TheP-value for the Wald test is also given

in the output at 0.0001, indicating the statistical

significance of the ALPHA1 parameter.

For the GEE model output, an estimated stan-

dard error (SE) or statistical test is not given

for the correlation estimate. This is in contrast

to the ALR output, which provides a standard

error and statistical test for ALPHA1.

EXAMPLE (continued)

Odds ratios

dORASPIRIN¼1vs:ASPIRIN¼ 0 :

GEE!expð 1 : 3302 Þ¼ 0 : 264

ALR!expð 1 : 3253 Þ¼ 0 : 266

S.E. (Aspirin)¼0.1444 (GEE and

ALR)

Measure of associationðdORjkÞ

dORjk¼expðALPHA 1 Þ

¼expð 0 : 4716 Þ¼ 0 : 62

(Negative association:

similar to^r¼ 0 : 0954

95% CI for ALPHA1

¼exp½ð 0 : 4716  1 : 96 ð 0 : 1217 ފ

¼ð 0 : 49 ; 0 : 79 Þ

P-value¼0.0001

)ALPHA1 significant

GEE (r) ALR (ALPHA1)

SE? No Yes

Test? No Yes

574 16. Other Approaches for Analysis of Correlated Data