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The University of Texas M. D. Anderson Cancer Center Houston, TX 77030
Thank you for giving us the opportunity of responding to Dr. Erturk's letter regarding our article published in the December 2004 issue of the AJR [1]. Dr. Erturk's letter seems to be based on two issues: first, the use of the chi-square test versus the McNemar test; and, second, the use (lack thereof) of the kappa statistic for agreement.
Dr. Erturk suggests that the chi-square test is not appropriate because the study has a matched design and includes data of repeated measurements in the same patient population. It is true that the data were measured before and after treatment for each of the response variables (maximum standardized uptake value [SUV-max], tumor density, and tumor size); however, in our analysis, we computed the change in each independent variable—thus reducing the dependency to a single measure—and categorized the change into four discrete groups for each variable before assessing the association between the categories of one variable versus the categories of another variable. We assumed that each categorical variable for each change (i.e., SUVmax, tumor density, and tumor size) was independent of the other; thus, a chi-square test was appropriate. This approach is similar to any study in which the association of two independent variables is assessed.
As Dr. Eurtuk points out, the McNemar test [2] is used in the 2 x 2 contingency table for dichotomous outcomes in which the data are repeated or dependent, such as a response variable measured before and after treatment of the same patient. For nondichotomous outcomes in a 4 x 4 contingency table, a similar test such as Bowker's test for symmetry [3] or the Stuart-Maxwell test of homogeneity can be used. In order to use McNemar or Bowker's test, the contingency table must be square (i.e., have the same number of rows and columns), which our tables were not. Note that Table 3 is really a 4 x 3 table because there are no patients with complete remission.
The kappa statistic [4] is a statistic used to measure agreement. As Dr. Erturk described, the kappa statistic is used to measure agreement between raters, but mathematically it could be used to measure the agreement between the two different response variables. Again, to compute the kappa statistic, the table must be square (have the same number of rows and columns). Dr. Erturk provided the kappa statistic and corresponding 95% confidence intervals for Table 3, but because that table is not square, the software was "tricked" into assuming that the table was square by replacing the counts in the Complete Remission column with a small number (0.001). The kappa statistics and corresponding 95% confidence intervals we computed are the same for Table 4 and are similar for Table 3. These statistics would have actually strengthened the value of our study in which we tried to show the quantitative CT parameter and tumor density measurement (H) in addition to the conventional tumor size measurement that would provide more accurate information in the evaluation of response in patients with gastrointestinal stromal tumors treated with imatinib mesylate.
We appreciate Dr. Erturk's insight into reviewing our data from a different perspective.
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