The PHREG Procedure

The CONTRAST statement provides a mechanism for obtaining customized hypothesis tests. It is similar to the CONTRAST statement in PROC GLM and PROC CATMOD, depending on the coding schemes used with any categorical variables involved.

The CONTRAST statement enables you to specify a matrix, , for testing the hypothesis . You must be familiar with the details of the model parameterization that PROC PHREG uses (for more information, see the PARAM= option in the section CLASS Statement). Optionally, the CONTRAST statement enables you to estimate each row, , of and test the hypothesis . Computed statistics are based on the asymptotic chi-square distribution of the Wald statistic.

There is no limit to the number of CONTRAST statements that you can specify, but they must appear after the MODEL statement.

The syntax of a row-description is:

effect values <,…,effect values>

The following parameters are specified in the CONTRAST statement:

The rows of are specified in order and are separated by commas. Multiple degree-of-freedom hypotheses can be tested by specifying multiple row-descriptions. For any of the full-rank parameterizations, if an effect is not specified in the CONTRAST statement, all of its coefficients in the matrix are set to 0. If too many values are specified for an effect, the extra ones are ignored. If too few values are specified, the remaining ones are set to 0.

When you use effect coding (by specifying PARAM=EFFECT in the CLASS statement), all parameters are directly estimable (involve no other parameters). For example, suppose an effect coded CLASS variable A has four levels. Then there are three parameters () representing the first three levels, and the fourth parameter is represented by

To test the first versus the fourth level of A, you would test

or, equivalently,

which, in the form , is

Therefore, you would use the following CONTRAST statement:

contrast '1 vs. 4' A 2 1 1;

To contrast the third level with the average of the first two levels, you would test

or, equivalently,

Therefore, you would use the following CONTRAST statement:

contrast '1&2 vs. 3' A 1 1 -2;

Other CONTRAST statements involving classification variables with PARAM=EFFECT are constructed similarly. For example:

contrast '1 vs. 2    '  A  1 -1  0;
contrast '1&2 vs. 4  '  A  3  3  2;
contrast '1&2 vs. 3&4'  A  2  2  0;
contrast 'Main Effect'  A  1  0  0,
                        A  0  1  0,
                        A  0  0  1;

When you use the less-than-full-rank parameterization (by specifying PARAM=GLM in the CLASS statement), each row is checked for estimability. If PROC PHREG finds a contrast to be nonestimable, it displays missing values in corresponding rows in the results. PROC PHREG handles missing level combinations of categorical variables in the same manner as PROC GLM. Parameters corresponding to missing level combinations are not included in the model. This convention can affect the way in which you specify the matrix in your CONTRAST statement. If the elements of are not specified for an effect that contains a specified effect, then the elements of the specified effect are distributed over the levels of the higher-order effect just as the GLM procedure does for its CONTRAST and ESTIMATE statements. For example, suppose that the model contains effects A and B and their interaction A*B. If you specify a CONTRAST statement involving A alone, the matrix contains nonzero terms for both A and A*B, since A*B contains A.

The Cox model contains no explicit intercept parameter, so it is not valid to specify one in the CONTRAST statement. As a consequence, you can test or estimate only homogeneous linear combinations (those with zero-intercept coefficients, such as contrasts that represent group differences) for the GLM parameterization.

The degrees of freedom are the number of linearly independent constraints implied by the CONTRAST statement—that is, the rank of .

You can specify the following options after a slash (/).