Since the respiratory data in Example 42.5 are binary, you can use the ALR algorithm to model the log odds ratios instead of using working correlations to model associations. In this example, a “fully parameterized cluster” model for the log odds ratio is fit. That is, there is a log odds ratio parameter for each unique pair of responses within clusters, and all clusters are parameterized identically. The following statements fit the same regression model for the mean as in Example 42.5 but use a regression model for the log odds ratios instead of a working correlation. The LOGOR=FULLCLUST option specifies a fully parameterized log odds ratio model.
proc genmod data=resp descend; class id treatment(ref="P") center(ref="1") sex(ref="M") baseline(ref="0") / param=ref; model outcome=treatment center sex age baseline / dist=bin; repeated subject=id(center) / logor=fullclust; run;
The results of fitting the model are displayed in Output 42.6.1 along with a table that shows the correspondence between the log odds ratio parameters and the withincluster pairs. Model goodnessoffit criteria are shown in Output 42.6.2. The QIC for the ALR model shown in Output 42.6.2 is 511.86, whereas the QIC for the unstructured working correlation model shown in Output 42.5.4 is 512.34, indicating that the ALR model is a slightly better fit.
Output 42.6.1: Results of Model Fitting
Log Odds Ratio Parameter Information 


Parameter  Group 
Alpha1  (1, 2) 
Alpha2  (1, 3) 
Alpha3  (1, 4) 
Alpha4  (2, 3) 
Alpha5  (2, 4) 
Alpha6  (3, 4) 
Analysis Of GEE Parameter Estimates  

Empirical Standard Error Estimates  
Parameter  Estimate  Standard Error  95% Confidence Limits  Z  Pr > Z  
Intercept  0.9266  0.4513  1.8111  0.0421  2.05  0.0400  
treatment  A  1.2611  0.3406  0.5934  1.9287  3.70  0.0002 
center  2  0.6287  0.3486  0.0545  1.3119  1.80  0.0713 
sex  F  0.1024  0.4362  0.7526  0.9575  0.23  0.8144 
age  0.0162  0.0125  0.0407  0.0084  1.29  0.1977  
baseline  1  1.8980  0.3404  1.2308  2.5652  5.58  <.0001 
Alpha1  1.6109  0.4892  0.6522  2.5696  3.29  0.0010  
Alpha2  1.0771  0.4834  0.1297  2.0246  2.23  0.0259  
Alpha3  1.5875  0.4735  0.6594  2.5155  3.35  0.0008  
Alpha4  2.1224  0.5022  1.1381  3.1068  4.23  <.0001  
Alpha5  1.8818  0.4686  0.9634  2.8001  4.02  <.0001  
Alpha6  2.1046  0.4949  1.1347  3.0745  4.25  <.0001 
You can fit the same model by fully specifying the matrix. The following statements create a data set containing the full matrix:
data zin; keep id center z1z6 y1 y2; array zin(6) z1z6; set resp; by center id; if first.id then do; t = 0; do m = 1 to 4; do n = m+1 to 4; do j = 1 to 6; zin(j) = 0; end; y1 = m; y2 = n; t + 1; zin(t) = 1; output; end; end; end; run;
proc print data=zin (obs=12); run;
Output 42.6.3 displays the full matrix for the first two clusters. The matrix is identical for all clusters in this example.
Output 42.6.3: Full Matrix Data Set
Obs  z1  z2  z3  z4  z5  z6  center  id  y1  y2 

1  1  0  0  0  0  0  1  1  1  2 
2  0  1  0  0  0  0  1  1  1  3 
3  0  0  1  0  0  0  1  1  1  4 
4  0  0  0  1  0  0  1  1  2  3 
5  0  0  0  0  1  0  1  1  2  4 
6  0  0  0  0  0  1  1  1  3  4 
7  1  0  0  0  0  0  1  2  1  2 
8  0  1  0  0  0  0  1  2  1  3 
9  0  0  1  0  0  0  1  2  1  4 
10  0  0  0  1  0  0  1  2  2  3 
11  0  0  0  0  1  0  1  2  2  4 
12  0  0  0  0  0  1  1  2  3  4 
The following statements fit the model for fully parameterized clusters by fully specifying the matrix. The results are identical to those shown previously.
proc genmod data=resp descend; class id treatment(ref="P") center(ref="1") sex(ref="M") baseline(ref="0") / param=ref; model outcome=treatment center sex age baseline / dist=bin; repeated subject=id(center) / logor=zfull zdata=zin zrow =(z1z6) ypair=(y1 y2); run;