The FREQ Procedure
 Agreement Study

Medical researchers are interested in evaluating the efficacy of a new treatment for a skin condition. Dermatologists from participating clinics were trained to conduct the study and to evaluate the condition. After the training, two dermatologists examined patients with the skin condition from a pilot study and rated the same patients. The possible evaluations are terrible, poor, marginal, and clear. Table 3.2 contains the data.

 Dermatologist 2 Dermatologist 1 Terrible Poor Marginal Terrible 10 4 1 0 Poor 5 10 12 2 Marginal 2 4 12 5 Clear 0 2 6 13

The following DATA step statements create the SAS dataset SkinCondition. The dermatologists’ evaluations of the patients are contained in the variables Derm1 and Derm2; the variable Count is the number of patients given a particular pair of ratings.

```data SkinCondition;
input Derm1 \$ Derm2 \$ Count;
datalines;
terrible terrible 10
terrible     poor 4
terrible marginal 1
terrible    clear 0
poor     terrible 5
poor         poor 10
poor     marginal 12
poor        clear 2
marginal terrible 2
marginal     poor 4
marginal marginal 12
marginal    clear 5
clear    terrible 0
clear        poor 2
clear    marginal 6
clear       clear 13
;
```

The following PROC FREQ statements request an agreement analysis of the skin condition data. In order to evaluate the agreement of the diagnoses (a possible contribution to measurement error in the study), the kappa coefficient is computed. The AGREE option in the TABLES statement requests the kappa coefficient, together with its standard error and confidence limits. The KAPPA option in the TEST statement requests a test for the null hypothesis that kappa equals zero, or that the agreement is purely by chance.

```proc freq data=SkinCondition order=data;
tables Derm1*Derm2 / agree noprint;
test kappa;
weight Count;
run;
```

Figure 3.10 shows the results. The kappa coefficient has the value 0.3449, which indicates slight agreement between the dermatologists, and the hypothesis test confirms that you can reject the null hypothesis of no agreement. This conclusion is further supported by the confidence interval of (0.2030, 0.4868), which suggests that the true kappa is greater than zero. The AGREE option also produces Bowker’s test for symmetry and the weighted kappa coefficient, but that output is not shown here.

Figure 3.10 Agreement Study
The FREQ Procedure

Statistics for Table of Derm1 by Derm2

Simple Kappa Coefficient
Kappa 0.3449
ASE 0.0724
95% Lower Conf Limit 0.2030
95% Upper Conf Limit 0.4868

Test of H0: Kappa = 0
ASE under H0 0.0612
Z 5.6366
One-sided Pr > Z <.0001
Two-sided Pr > |Z| <.0001

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