Anticipated Date of Graduation

Summer 2022

Document Type

Thesis

Degree Name

Master of Science in Mathematical Sciences

Department

Mathematical Sciences

First Advisor

Douglas Darbro

Abstract

In 2017, Ilker Unal presented the Index of Union method for obtaining optimal cut-points in ROC analysis and claimed that it outperformed other methods, including the historied Youden Index. This is an investigation into that claim using generated data. It specifically pits the Youden Index method against the Index of Union (IU) method under various circumstances. The data sets have different ratios of diseased and non-diseased data points along with different ratios of true and false results based on a theoretical true cutpoint. The data was analyzed to see if any patterns emerged as to when the Youden Index obtain a cut-point closer to the theoretical true cut-point and when the IU method does. Although the IU method performed better in the majority of data sets, the Youden Index method did outperform the IU method at times. The IU method had a clear advantage in the case that the specificity and sensitivity were equal, while the Youden Index had an advantage when the area under the ROC curve was between 0.27 and 0.47. The results imply that there is good reason for the uncertainty in the landscape of methods for obtaining optimal cut-points, but there may be a good argument as to when to use one over another. More research should be done into the relationship between the area under the curve and these methods. In the meantime, medical researchers should not rely on a single method but rather take into the range of cut-points obtained by various methods.

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