Example 58.1 Cochran-Armitage Test with Permutation Resampling

This example, from Keith Soper at Merck, illustrates the exact permutation Cochran-Armitage test carried out on permutation resamples. In the following data set, each observation represents an animal. The binary variables S1 and S2 indicate two tumor types, with 0s indicating no tumor (failure) and 1 indicating a tumor (success); note that they have perfect negative association. The grouping variable is Dose.

   data a;
      input S1 S2 Dose @@;
      datalines;
   0 1 1   1 0 1   0 1 1
   0 1 1   0 1 1   1 0 1
   1 0 2   1 0 2   0 1 2
   1 0 2   0 1 2   1 0 2
   1 0 3   1 0 3   1 0 3
   0 1 3   0 1 3   1 0 3
   ;

   proc multtest data=a permutation nsample=10000 seed=36607 outperm=pmt;
      test ca(S1 S2 / permutation=10 uppertailed);
      class Dose;
      contrast 'CA Linear Trend' 0 1 2;
   run;
   proc print data=pmt;
   run;

The PROC MULTTEST statement requests 10,000 permutation resamples. The OUTPERM= option creates an output SAS data set pmt used for the exact permutation distribution computed for the CA test.

The TEST statement specifies an upper-tailed Cochran-Armitage linear trend test for S1 and S2. The cutoff for exact permutation calculations is 10, as specified with the PERMUTATION= option in the TEST statement. Since S1 and S2 have 10 and 8 successes, respectively, PROC MULTTEST uses exact permutation distributions to compute the p-values for both variables.

The groups for the CA test are the levels of Dose from the CLASS statement. The trend coefficients applied to these groups are 0, 1, and 2, respectively, as specified in the CONTRAST statement.

Finally, the PROC PRINT statement displays the SAS data set pmt, which contains the permutation distributions.

The results from this analysis are displayed in Output 58.1.1 through Output 58.1.5. You should check the following "Model Information" table to verify that the analysis specifications are correct.