New diagnostic tools developed for the non-invasive diagnosis of serious illnesses require evaluation and should be compared against standard diagnostic tools. Receiver operating characteristic (ROC) analysis has become established as the appropriate method for such comparisons and much of the research has been focused on comparing the areas under the ROC curves. The general purpose of this proposal is to extend a distribution-free permutation test procedure that compares entire ROC curves for two diagnostic tests based on continuous data from a paired design. The novelty of this new approach is that it permits a valid comparison of the tests without any assumptions other than that the pairs of observations are independent and identically distributed within disease status. Specifically we will develop asymptotic expressions to allow easier computation of the significance level of the proposed test statistic which is currently accomplished by resampling. We will generalize the test statistic to the unpaired data case, derive the appropriate resampling scheme for the evaluation of the significance level as well as an asymptotic expression for it, and study its properties. We will extend the methods for comparing diagnostic tests to the setting in which the results are in a rating scale (for example radiologic data) and study the effect of the models-used to generate the ROC curve from the discrete points on the rating scale. Finally, we will develop methods for adjusting for covariates that affect the performance of the diagnostic tests.
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