Daryl Morris
The accuracy of a diagnostic test can be summarized in a receiver operating characteristic (ROC) curve, a plot of the true positive (TP) versus false positive (FP) rates associated with varying thresholds c for the test results Y: TP(c) = P[Y > c | disease present] and FP(c) = P[Y > c | disease not present]. ROC curves have become well accepted measures of accuracy in diagnostic medicine. They display the trade-offs possible between increasing true positive and increasing false positive rates as the positivity criterion varies. They describe the inherent capacity of a test for discriminating diseased from non-diseased subjects without linking the test to any specific positivity criterion. ROC curves are particularly useful for comparing diagnostic tests since tests are put on the same scale (even if the test result variables themselves are on entirely different scales) and the scale relates directly to the notion of accuracy.
Methods for estimating and comparing ROC curves have long been available. ROC regression methodology offers the opportunity to investigate how factors such as characteristics of the study subjects or test environment influence test accuracy. For ordinal outcomes, Tosteson and Begg (1988) proposed the use of ordinal regression models to induce regression models for ROC curves. For continuous markers, we have proposed direct modeling of the ROC curves themselves (“Placement Value methods”). We have not previously applied the direct modeling in the case of ordinal outcomes.
In this talk we compare and contrast joint ordinal regression method models (a la Tosteson & Begg) and direct modeling of the ROC curves when applied to ordinal outcomes.