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The MULTTEST Procedure |
This example, from Keith Soper at Merck, illustrates the exact permutation Cochran-Armitage 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 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 ten and eight 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 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: Cochran-Armitage Test with Permutation Resampling
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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.
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This table shows that, for S1, the adjusted p-value is almost twice the raw p-value. In fact, from theoretical considerations, the permutation-adjusted p-value for S1 should be 2 ×0.1993 = 0.3986. For S2, the raw p-value is 0.9220, and the adjusted p-value equals 1, as you would expect from theoretical considerations. The permutation p-values for S1 and S2 also happen to be the Bonferroni-adjusted p-values for this example.
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