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The MULTTEST Procedure 
data Drug; input Dose$ SideEff1SideEff10; datalines; 0MG 0 0 1 0 0 1 0 0 0 0 0MG 0 0 0 0 0 0 0 0 0 1 0MG 0 0 0 0 0 0 0 0 1 0 0MG 0 0 0 0 0 0 0 0 0 0 0MG 0 1 0 0 0 0 0 0 0 0 1MG 1 0 0 1 0 1 0 0 1 0 1MG 0 0 0 1 1 0 0 1 0 1 1MG 0 1 0 0 0 0 1 0 0 0 1MG 0 0 1 0 0 0 0 0 0 1 1MG 1 0 1 0 0 0 0 1 0 0 2MG 0 1 1 1 0 1 1 1 0 1 2MG 1 1 1 1 1 1 0 1 1 0 2MG 1 0 0 1 0 1 1 0 1 0 2MG 0 1 1 1 1 0 1 1 1 1 2MG 1 0 1 0 1 1 1 0 0 1 ;
The increasing incidence of 1s for higher dosages in the preceding data set provides an initial visual indication that the drug has an effect. To explore this statistically, you decide to perform an analysis in which the possibility of side effects increases linearly with drug level. You can analyze the data for each side effect separately, but you are concerned that, with so many tests, there may be a high probability of incorrectly declaring some drug effects significant. You want to correct for this multiplicity problem in a way that accounts for the discreteness of the data and for the correlations between observations on the same unit.
PROC MULTTEST addresses these concerns by processing all of the data simultaneously and adjusting the pvalues. The following statements perform a typical analysis:
proc multtest bootstrap nsample=20000 seed=41287 notables pvals; class Dose; test ca(SideEff1SideEff10); contrast 'Trend' 0 1 2; run;
This analysis uses the BOOTSTRAP option to adjust the pvalues. The NSAMPLE= option requests 20,000 samples for the bootstrap analysis, and the starting seed for the random number generator is 41287. The NOTABLES option suppresses the display of summary statistics for each side effect and drug level combination.
The CLASS statement is used to specify the grouping variable, Dose. The CA(SIDEEFF1SIDEEFF10) specification in the TEST statement requests a CochranArmitage linear trend test for all 10 characteristics. The CONTRAST statement gives the coefficients for the linear trend test.
The results from this analysis are as follows.
Figure 43.1 describes the statistical tests performed by PROC MULTTEST. For this example, PROC MULTTEST carries out a twotailed CochranArmitage linear trend test with no continuity correction or strata adjustment. This test is performed on the raw data and on 20,000 bootstrap samples.

Figure 43.2 displays the coefficients for the CochranArmitage test. They are 0, 1, and 2, as specified in the CONTRAST statement.

Figure 43.3 lists the pvalues for the drug example. The Raw column lists the pvalues for the CochranArmitage test on the original data, and the Bootstrap column provides the bootstrap adjustment of the raw pvalues.
Note that the raw pvalues lead you to reject the null hypothesis of no linear trend for 3 of the 10 characteristics at the 5% level and for 7 of the 10 characteristics at the 10% level. The bootstrap pvalues, however, lead to this conclusion for 0 of the 10 characteristics at the 5% level and only 2 of the 10 characteristics at the 10% level. The bootstrap adjustment gives the probability of observing a pvalue as extreme as each given pvalue, considering all ten tests simultaneously. This adjustment incorporates the correlation of the raw pvalues, the discreteness of the data, and the multiple testing problem. Failure to account for these issues can certainly lead to misleading inferences for these data.
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