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

Parameter DF Estimate Standard Error Chi-Square Pr>ChiSq

(continued)

RACE 1 0.4270 0.2720 2.4637 0.1165

ESTROGEN 1 0.7763 0.2493 9.6954 0.0018

Odds Ratio Estimates

Effect

Point

Estimate

95% Wald

Confidence Limits

RACE 1.533 0.899 2.612

ESTROGEN 0.460 0.282 0.750

The Score test for the proportional odds assumption yields a chi-square value of
0.9051 and ap-value of 0.6360. Notice that there are two intercepts, but only one
parameter estimate for each independent variable.

B. PROC GENMOD

PROC GENMOD can also be used to perform an ordinal regression; however, it does
not provide a test of the proportional odds assumption. The code is as follows:

PROC GENMOD DATA¼REF.CANCER DESCENDING;

MODEL GRADE¼RACE ESTROGEN/ LINK¼CUMLOGIT DIST¼MULTINOMIAL;

RUN;

Recall that with PROC GENMOD, the link function (LINK¼) and the distribution of
the response variable (DIST¼) must be specified. The proportional odds model uses
the cumulative logit link function, while the response variable follows the multino-
mial distribution. The LINK¼CUMLOGIT option could also be used with PROC
LOGISTIC but it is unnecessary since that is the default when the response variable
has three or more levels. The output is omitted.

C. Analyst Application

The Analyst Application can also be used to run an ordinal regression model. Once
thecancer.sas7bdatdataset is opened in the spreadsheet, select Statistics!Regres-
sion!Logistic. In the dialog box, select GRADE as the Dependent variable. Next,
specify which value of the outcome should be modeled using the Model Pr{} button.
In this case, we wish to model the “Upper (decreasing) levels” (i.e., 2 and 1) against
the lowest level. Select and add the covariates (RACE and ESTROGEN) to the
Quantitative box. Various analysis and output options can be selected under the
Model and Statistics buttons. For example, under Statistics, the covariance matrix
for the parameter estimates can be requested as part of the output.

Click on OK in the main dialog box to run the program. The output generated is from
PROC LOGISTIC and is identical to the output presented previously. A check of the
Log window in SAS shows the code that was used to run the analysis.

SAS 621