Example 35.10 Cochran’s Q Test

When a binary response is measured several times or under different conditions, Cochran’s tests that the marginal probability of a positive response is unchanged across the times or conditions. When there are more than two response categories, you can use the CATMOD procedure to fit a repeated-measures model.

The data set Drugs contains data for a study of three drugs to treat a chronic disease (Agresti 2002). Forty-six subjects receive drugs A, B, and C. The response to each drug is either favorable ('F') or unfavorable ('U').

   proc format;
      value $ResponseFmt 'F'='Favorable'
                         'U'='Unfavorable';
   run;

   data drugs;
      input Drug_A $ Drug_B $ Drug_C $ Count @@;
      datalines;
   F F F  6   U F F  2   
   F F U 16   U F U  4    
   F U F  2   U U F  6   
   F U U  4   U U U  6  
   ;

The following statements create one-way frequency tables of the responses to each drug. The AGREE option produces Cochran’s and other measures of agreement for the three-way table. These statements produce Output 35.10.1 through Output 35.10.5.

   proc freq data=Drugs;
      tables Drug_A Drug_B Drug_C / nocum;
      tables Drug_A*Drug_B*Drug_C / agree noprint;
      format Drug_A Drug_B Drug_C $ResponseFmt.;
      weight Count;
      title 'Study of Three Drug Treatments for a Chronic Disease';
   run;

The one-way frequency tables in Output 35.10.1 provide the marginal response for each drug. For drugs A and B, 61% of the subjects reported a favorable response while 35% of the subjects reported a favorable response to drug C. Output 35.10.2 and Output 35.10.3 display measures of agreement for the 'Favorable' and 'Unfavorable' levels of drug A, respectively. McNemar’s test shows a strong discordance between drugs B and C when the response to drug A is favorable.