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The MULTTEST Procedure 
This example, from Keith Soper at Merck, illustrates the exact permutation CochranArmitage test carried out on permutation resamples. In the following data set, the 0s represent failures and the 1s represent successes. Note that the binary variables S1 and S2 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 pvals; 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=PMT option requests an output SAS data set for the exact permutation distribution computed for the CA test.
The TEST statement specifies an uppertailed CochranArmitage 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 ten and eight successes, respectively, PROC MULTTEST uses exact permutation distributions to compute the pvalues for both variables.
The groups for the CA test are the levels of Dose from the CLASS statement. The coefficients applied to these groups are 0, 1, and 2, respectively, as specified in the CONTRAST statement.
Finally, the invocation of PROC PRINT displays the SAS data set containing the permutation distributions.
The results from this analysis are listed in Output 43.1.1.
Output 43.1.1: CochranArmitage Test with Permutation Resampling


The preceding table contains summary statistics for the two test variables, S1 and S2. The Count column lists the number of successes for each level of the class variable, Dose. The NumObs column is the sample size, and the Percent column is the percentage of successes in the sample.

This table shows that, for S1, the adjusted pvalue is almost twice the raw pvalue. In fact, from theoretical considerations, the permutationadjusted pvalue for S1 should be 2 ×0.1993 = 0.3986. For S2, the raw pvalue is 0.9220, and the adjusted pvalue equals 1, as you would expect from theoretical considerations. The permutation pvalues for S1 and S2 also happen to be the Bonferroniadjusted pvalues for this example.

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