Same as before!

Marginal Models/GEE: Accounting for
Correlation
–
Model 1
•
This model does NOT assume the observations are independent! We can show this using a
correlation matrix
for the J = 9 observations for subject i = 1.
•
Note 1: “
corrw
” option printed this matrix for us.
•
Note 2: “
type
= exch
” forced all off
-diagonal correlations to be the same
(“exchangeable”)
Correlation Matrix for Subject 1
Observation
1
2
3
4
5
6
7
8
9
1
1
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
2
1
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
3
1
0.4381
0.4381
0.4381
0.4381
0.4381
0.4381
4
1
0.4381
0.4381
0.4381
0.4381
0.4381
5
1
0.4381
0.4381
0.4381
0.4381
6
1
0.4381
0.4381
0.4381
7
1
0.4381
0.4381
8
1
0.4381
9
1
Does this appropriately
describe the correlation
in our data?

Marginal Models/GEE: Accounting for
Correlation
–
Model 2
•
Now let’s
try a more appropriate correlation structure with our GEEs
:
•
Logistic regression:
𝑙?𝑔𝑖?(𝑃(𝑌
??
= 1|𝑿)) = 𝛽
0
+ 𝛽
1
???????? + 𝛽
2
?????? + 𝛽
3
????????
proc genmod
data
=infant
descending
;
model
outcome = birthwgt gender diarrhea /
dist
=bin
link
=logit;
repeated subject
= idno /
within
= month
type
= ar(1)
corrw
;
run
;
OR for diarrhea?
e
0.22
= 1.25
95% CI (0.23, 6.68)
Same calculation as in
regular logistic regression!

Marginal Models/GEE: Accounting for
Correlation
–
Model 2
•
This model does NOT assume the observations are independent! We can show this using a
correlation matrix
for the J = 9 observations for subject i = 1.
•
Note: “
type
= ar(1)
” created an “autoregressive” correlation structure –
what do you
notice about the correlations?
Correlation Matrix for Subject 1
Observation
1
2
3
4
5
6
7
8
9
1
1
0.5254
0.2760
0.1450
0.0762
0.0400
0.0210
0.0110
0.0058
2
1
0.5254
0.2760
0.1450
0.0762
0.0400
0.0210
0.0110
3
1
0.5254
0.2760
0.1450
0.0762
0.0400
0.0210
4
1
0.5254
0.2760
0.1450
0.0762
0.0400
5
1
0.5254
0.2760
0.1450
0.0762
6
1
0.5254
0.2760
0.1450
7
1
0.5254
0.2760
8
1
0.5254
9
1
Does this appropriately
describe the correlation
in our data?