Receiver Operating Characteristic (ROC) analysis has been used as a popular technique of comparing the performance of two paired diagnostic tests data while the area under the curve (AUC) summarizes the overall activities between two ROC curves. In other to assess a difference in the AUCs of paired data as well as to tackle the problem of exchangeability of the labels between two diagnostic tests within subject which characterizes previous studies, we propose a modified Wilcoxon signed-rank test to accommodate the presence of tied absolute values of differences for assessing a difference in the AUCs in a continuous matched pair of data. This assessment is based on between-subjects permutations particularly by exchanging the non-diseased and diseased labels of the subjects within each diagnostic test procedure, thus validating the permutation test since test results for each diagnostic test can be taken on a different scale. We as well derive the asymptotic normal approximation to the permutation test. In applying real life data, the proposed test has the more likelihood of rejecting null hypothesis of equality of at nominal level of 0.05 with the proposed test having a p-value of 0.0312 against the Braun and Alonzo’s test with a p-value of 0.0387. Also the estimates of for the two diagnostic tests are 0.668 and 0.887 respectively showing that,that is 2 hours 100g Oral Glucose Tolerance Test (OGTT) is superior to (2 hours 70g OGTT) at a time that the specificity is greater than 0.7.
Keywords: Modified Wilcoxon signed rank test, Permutation Test, area under the ROC curve (AUC), asymptotic normal approximation, exchangeability, receiver operating characteristic (ROC) curve, two diagnostic test procedures