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

starting point for building more complicated models. The model is the same as used
earlier in this appendix and is repeated below:

logit PðCHD¼ 1 jXÞ¼b 0 þb 1 CATþb 2 AGEþb 3 CHLþb 4 ECGþb 5 SMK

þb 6 HPTþb 7 CHþb 8 CC

For comparison, we show how to run this model using PROC GENMOD and then
using PROC GLIMMIX. Two ESTIMATE statements are used to request odds ratio
estimates derived from a linear combination of parameters and a CONTRAST state-
ment is used to request a chunk test for the two interaction terms using the
generalized Wald test. The default test with the CONTRAST statement in PROC
GENMOD is the likelihood ratio test (shown earlier), but because the CONTRAST
statement in PROC GLIMMIX does not produce a likelihood ratio test statistic, the
WALD option was used in PROC GENMOD for comparability. The CHISQ option in
the CONTRAST statement of PROC GLIMMIX requests a Wald chi-square test
statistic to be given in addition to the default F test. The code is shown below:

PROC GENMOD DATA¼REF.EVANS DESCENDING;

MODEL CHD¼CAT AGE CHL ECG SMK HPT CH CC/LINK¼LOGIT DIST¼BINOMIAL;

ESTIMATE‘OR (CHL¼220, HPT¼1)’CAT 1 CC 220 CH 1/EXP;

ESTIMATE‘OR (CHL¼220, HPT¼0)’CAT 1 CC 220 CH 0/EXP;

CONTRAST‘WALD test for interaction terms’CH 1, CC 1/WALD;

RUN;

PROC GLIMMIX DATA¼REF.EVANS;

MODEL CHD¼CAT AGE CHL ECG SMK HPT CH CC/DIST¼BIN LINK¼LOGIT SOLUTION

NOSCALE DDFM¼NONE;

ESTIMATE‘OR (CHL¼220, HPT¼1)’CAT 1 CC 220 CH 1/EXP;

ESTIMATE‘OR (CHL¼220, HPT¼0)’CAT 1 CC 220 CH 0/EXP;

CONTRAST‘Wald test for interaction terms’CH 1, CC 1/CHISQ;

RUN;

Notice that PROC GLIMMIX does not use the DESCENDING option (as does PROC
GENMOD) to indicate that CHD¼1 is the value for an event rather than CHD¼0.
Both procedures use the DIST¼BIN and LINK¼LOGIT in the MODEL statement to
indicate that the outcome follows a binomial distribution with a logit link function.
The SOLUTION option in PROC GLIMMIX requests that the parameter estimates for
the fixed effects appear in the output. Parameter estimates are given with PROC
GENMOD by default. The NOSCALE and DDFM¼NONE options in PROC GLIMMIX
allow the test of significance (using a T test in PROC GLIMMIX) to be equivalent to
that given by PROC GENMOD (using a chi-square test). The ESTIMATE statements
do not differ in the two procedures.

The output is essentially the same as that given earlier in this appendix when PROC
GENMOD was first described and is omitted here.

PROC GLIMMIX can be used to run GEE models that allow random effects as well as
fixed effects. In the previous section, a GEE model was run using PROC GENMOD on
the infant dataset. We now consider the same model and demonstrate how PROC

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