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

Output from using the GEE approach is pre-

sented on the left. An exchangeable correlation

structure is assumed. (This GEE output has

previously been presented in Chap. 15)

The correlation parameter estimate obtained

from the working correlation matrix of the

GEE model is0.0954, which suggests a nega-

tive association between reocclusions on the

same bypass patient.

Output obtained from SAS PROC GENMOD

using the ALR approach is shown on the left

for comparison. An exchangeable odds ratio

structure is assumed. The assumption underly-

ing the exchangeable odds ratio structure is

that the odds ratio between theith subject’s

jth andkth responses is the same (for alljand

k, j 6 ¼k). The estimated exchangeable odds

ratio is obtained by exponentiating the coeffi-

cient labeled ALPHA1.

EXAMPLE (continued)

GEE Approach (Exchangeabler)

Variable Coefficient

Empirical

Std Err

zWald

p-value

INTERCEPT0.4713 1.6169 0.7707
ASPIRIN 1.3302 0.1444 0.0001
AGE 0.0086 0.0087 0.3231
GENDER 0.5503 0.2559 0.0315
WEIGHT 0.0007 0.0066 0.9200
HEIGHT 0.0080 0.0105 0.4448
Scale 1.0076

Exchangeable Ci (GEE: r= –0.0954)

ALR approach (Exchangeable OR)

Variable Coefficient

Empirical

Std Err

zwald

p-value

INTERCEPT 0.4806 1.6738 0.7740
ASPIRIN 1.3253 0.1444 0.0001
AGE 0.0086 0.0088 0.3311
GENDER 0.5741 0.2572 0.0256
WEIGHT 0.0003 0.0066 0.9665
HEIGHT 0.0077 0.0108 0.4761
ALPHA1 0.4716 0.1217 0.0001
“

expðALPHA1Þ¼cORjkðexchangeableÞ

Presentation: II. The Alternating Logistic Regressions Algorithm 573