Development and Evaluation of Concavity-Respecting ROC Curve Estimators Open Access

Zhao, Xiwen (Spring 2018)

Permanent URL: https://etd.library.emory.edu/concern/etds/sn009x77v?locale=en
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Abstract

 

Biomarkers are widely used for the diagnosis of a specific disease. To evaluate the diagnostic accuracy of a biomarker, the Receiver Operating Characteristic (ROC) curve analysis is one of the best developed statistical tools. In clinical context, typically higher biomarker value indicates larger possibility of the disease and then the corresponding ROC curve should be strictly concave. However, the empirical ROC curve, as often adopted, does not necessarily respect the concavity property. In this study, we developed two methods to modify the empirical ROC curve in order to restore the concavity. Extensive simulations were conducted, and they showed that our modified ROC estimators for the area under curve (AUC) and the specificity at a fixed sensitivity have performance comparable to the empirical estimators.

 

Table of Contents

1.Introduction.............................................................................................................. 1

2.Problem and Notation ...................................................................................................... 4

3.Algorithm.................................................................................................................. 7

Constructing Empirical ROC Curve ............................................................................... 7

Identifying and Restoring Concavity.............................................................................. 7

4.Simulation Study.............................................................................................................. 9

Area Under Curve ............................................................................................. 9

Specificity at Fixed Level of Sensitivity....................................................................... 17

5.Real Data Application............................................................................................ 28

6.Discussion........................................................................................................... 30

Reference .............................................................................................................. 31

Figures................................................................................................................... 32

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