Biomarker assessment in ROC curve analysis using the length of the curve as an index of diagnostic accuracy: the binorma
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Biomarker assessment in ROC curve analysis using the length of the curve as an index of diagnostic accuracy: the binormal model framework Alba M. Franco‑Pereira1 · Christos T. Nakas2,3 · M. Carmen Pardo1 Received: 7 August 2019 / Accepted: 15 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In receiver operating characteristic (ROC) curve analysis, the area under the curve (AUC) is undoubtedly the most widely used index of diagnostic accuracy for the assessment of the utility of a biomarker or for the comparison of competing biomarkers. Along with the AUC, the maximum of the Youden index, J, is often used both as an index of diagnostic accuracy and as a tool useful for the estimation of an optimal cutoff point that can be used for diagnostic purposes based on the biomarker under consideration. In this work, we study the utility of the length of the binormal model-based ROC curve (LoC) as an index of diagnostic accuracy for biomarker evaluation. Estimation procedures for LoC, described in this article, are based either on normality assumptions or on the same assumptions after a Box–Cox transformation to normality. Two simulation studies are considered. In the first, the estimation procedures for LoC are compared in terms of bias and root mean squared error, while in the second one, the performance of LoC is compared with approaches based on AUC and J, both for the case of the assessment of a single biomarker and for the comparison of two biomarkers, in a parametric framework. We provide an interpretation for the proposed index and illustrate with an application on biomarkers from a colorectal cancer study. Keywords Area under the ROC curve (AUC) · Length of the ROC curve (LoC) · Binormal ROC curve · Maximum of the Youden index (J) · Diagnostic likelihood ratio (DLR)
* Alba M. Franco‑Pereira [email protected] 1
Department of Statistics and O.R., Complutense University of Madrid, 28040 Madrid, Spain
2
Laboratory of Biometry, University of Thessaly, Phytokou Street, 38446 Volos, Greece
3
University Institute of Clinical Chemistry, Inselspital, Bern University Hospital, University of Bern, Freiburgstrasse, 3010 Bern, Switzerland
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1 Introduction The development of disease-specific biomarkers is of major interest in cancer research (Baker 2003). Receiver operating characteristic (ROC) curve analysis is the most widespread methodology used in biomarker validation when there are two conditions or disease states, e.g., non-diseased and diseased subjects, (see Pepe 2003, and Zhou et al. 2011). Suppose that, for biomarker measurements for the non-diseased subjects, X ∼ F , while for diseased subjects, Y ∼ G , respectively. We consider, without loss of generality, that high biomarker measurements are indicative of disease. For a given cutoff point, c, in the continuum of the biomarker measurement support, any measurement greater than c will be considered as arising from a diseased individual; otherwise, it will be considered as indi
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