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

GLIMMIX can be used for GEE models. The model is restated below:

logit PðOUTCOME¼ 1 jXÞ¼b 0 þb 1 BIRTHWGTþb 2 GENDERþb 3 DIARRHEA

To illustrate how a GEE model is run using PROC GLIMMIX, we compare the code
used to run PROC GENMOD for the same model described in the previous section on
GEE. This model only contains fixed effects. The code is shown first for PROC
GENMOD and then for PROC GLIMMIX. An AR1 structure is chosen as the working
correlation matrix in PROC GENMOD and as the working covariance matrix in
PROC GLIMMIX. The code follows:

PROC GENMOD DATA¼REF.INFANT DESCENDING;

CLASS IDNO MONTH;

MODEL OUTCOME¼BIRTHWGT GENDER DIARRHEA /DIST¼BIN LINK¼LOGIT;

REPEATED SUBJECT¼IDNO / TYPE¼AR(1) WITHIN¼MONTH CORRW;

ESTIMATE‘log odds ratio (DIARRHEA 1 vs 0)’DIARRHEA 1/EXP;

RUN;

PROC GLIMMIX DATA¼REF.INFANT EMPIRICAL;

CLASS IDNO MONTH;

MODEL OUTCOME¼BIRTHWGT GENDER DIARRHEA /DIST¼BIN LINK¼LOGIT SOLUTION

CHISQ;

RANDOM _RESIDUAL_ / SUBJECT¼IDNO TYPE¼AR(1) VCORR;

ESTIMATE‘log odds ratio (DIARRHEA 1 vs 0)’DIARRHEA 1/EXP;

RUN;

The DESCENDING option is not used in PROC GLIMMIX as it recognizes the value
OUTCOME¼1 as an event and OUTCOME¼0 as a nonevent. The EMPIRICAL
option in the PROC GLIMMIX statement requests empirical standard errors for the
parameter estimates. The options shown in the MODEL statement of PROC GLIM-
MIX were described in the previous example. The RANDOM statement with the key
word RESIDUAL following it plays the same role in PROC GLIMMIX as the
REPEATED statement does in PROC GENMOD. The cluster variable in the infant
dataset, IDNO, is defined with the SUBJECT¼option. The TYPE¼option defines the
correlation structure for the residuals (the R matrix). The VCORR option requests
that the correlation matrix for the random error be printed in the output. The output
from PROC GLIMMIX follows:

The GLIMMIX Procedure

Model Information

Data Set REF.INFANT

Response Variable OUTCOME

Response Distribution Binomial

Link Function Logit

Variance Function Default

Variance Matrix Blocked By IDNO

Estimation Technique Residual PL

Degrees of Freedom Method Between-Within

Fixed Effects SE Adjustment Sandwich–Classical

628 Appendix: Computer Programs for Logistic Regression