Example 58.4 Fisher Test with Permutation Resampling

The following data, from Brown and Fears (1981), are the results of an 80-week carcinogenesis bioassay with female mice. Six tissue sites are examined at necropsy; 1 indicates the presence of a tumor and 0 the absence. A frequency variable Freq is included. A control and four different doses of a drug (in parts per milliliter) make up the levels of the grouping variable Dose.

   data a;
      input Liver Lung Lymph Cardio Pitui Ovary Freq Dose$ @@;
      datalines;
   1 0 0 0 0 0 8  CTRL   0 1 0 0 0 0 7  CTRL   0 0 1 0 0 0 6  CTRL
   0 0 0 1 0 0 1  CTRL   0 0 0 0 0 1 2  CTRL   1 1 0 0 0 0 4  CTRL
   1 0 1 0 0 0 1  CTRL   1 0 0 0 0 1 1  CTRL   0 1 1 0 0 0 1  CTRL
   0 0 0 0 0 0 18 CTRL
   1 0 0 0 0 0 9  4PPM   0 1 0 0 0 0 4  4PPM   0 0 1 0 0 0 7  4PPM
   0 0 0 1 0 0 1  4PPM   0 0 0 0 1 0 2  4PPM   0 0 0 0 0 1 1  4PPM
   1 1 0 0 0 0 4  4PPM   1 0 1 0 0 0 3  4PPM   1 0 0 0 1 0 1  4PPM
   0 1 1 0 0 0 1  4PPM   0 1 0 1 0 0 1  4PPM   1 0 1 1 0 0 1  4PPM
   0 0 0 0 0 0 15 4PPM
   1 0 0 0 0 0 8  8PPM   0 1 0 0 0 0 3  8PPM   0 0 1 0 0 0 6  8PPM
   0 0 0 1 0 0 3  8PPM   1 1 0 0 0 0 1  8PPM   1 0 1 0 0 0 2  8PPM
   1 0 0 1 0 0 1  8PPM   1 0 0 0 1 0 1  8PPM   1 1 0 1 0 0 2  8PPM
   1 1 0 0 0 1 2  8PPM   0 0 0 0 0 0 19 8PPM
   1 0 0 0 0 0 4  16PPM  0 1 0 0 0 0 2  16PPM  0 0 1 0 0 0 9  16PPM
   0 0 0 0 1 0 1  16PPM  0 0 0 0 0 1 1  16PPM  1 1 0 0 0 0 4  16PPM
   1 0 1 0 0 0 1  16PPM  0 1 1 0 0 0 1  16PPM  0 1 0 1 0 0 1  16PPM
   0 1 0 0 0 1 1  16PPM  0 0 1 1 0 0 1  16PPM  0 0 1 0 1 0 1  16PPM
   1 1 1 0 0 0 2  16PPM  0 0 0 0 0 0 14 16PPM  
   1 0 0 0 0 0 8  50PPM  0 1 0 0 0 0 4  50PPM  0 0 1 0 0 0 8  50PPM
   0 0 0 1 0 0 1  50PPM  0 0 0 0 0 1 4  50PPM  1 1 0 0 0 0 3  50PPM
   1 0 1 0 0 0 1  50PPM  0 1 1 0 0 0 1  50PPM  0 1 0 0 1 1 1  50PPM
   0 0 0 0 0 0 19 50PPM
   ;

   proc multtest data=a order=data notables out=p 
                 permutation nsample=1000 seed=764511;
      test fisher(Liver Lung Lymph Cardio Pitui Ovary /
                  lowertailed);
      class Dose;
      freq Freq;
   run;
   proc print data=p;
   run;

In the PROC MULTTEST statement, the ORDER=DATA option is required to keep the levels of Dose in the order in which they appear in the data set. Without this option, the levels are sorted by their formatted value, resulting in an alphabetic ordering. The NOTABLES option suppresses the display of summary statistics, and the OUT= option produces an output data set p containing the p-values. The PERMUTATION option specifies permutation resampling, NSAMPLE=1000 requests 1000 samples, and SEED=764511 option provides a starting value for the random number generator. You should specify a seed if you need to duplicate resampling results.

To test for higher rates of tumor occurrence in the treatment groups compared to the control group, the LOWERTAILED option is specified in the FISHER option of the TEST statement to produce a lower-tailed Fisher exact test for the six tissue sites. The Fisher test is appropriate for comparing a treatment and a control, but multiple testing can be a problem. Brown and Fears (1981) use a multivariate permutation to evaluate the entire collection of tests. PROC MULTTEST adjusts the p-values by simulation.

The treatments make up the levels of the grouping variable Dose, listed in the CLASS statement. Since no CONTRAST statement is specified, PROC MULTTEST uses the default pairwise contrasts with the first level of Dose. The FREQ statement is used since these are summary data containing frequency counts of occurrences.

The results from this analysis are listed in Output 58.4.1 through Output 58.4.4. First, the PROC MULTTEST specifications are displayed in Output 58.4.1.