|The FREQ Procedure|
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.
Output 35.10.4 displays the overall kappa coefficient. The small negative value of kappa indicates no agreement between drug B response and drug C response.
Cochran’s is statistically significant (=0.0144 in Output 35.10.5), which leads to rejection of the hypothesis that the probability of favorable response is the same for the three drugs.