Estimation and inference on the partial volume under the receiver operating characteristic surface

Abstract

Summary measures of biomarker accuracy that employ the receiver operating characteristic surface have been proposed for biomarkers that classify patients into one of three groups: healthy, benign, or aggressive disease. The volume under the receiver operating characteristic surface summarizes the overall discriminatory ability of a biomarker in such configurations, but includes cutoffs associated with clinically irrelevant true classification rates. Due to the lethal nature of pancreatic cancer, cutoffs associated with a low true classification rate for identifying patients with pancreatic cancer may be undesirable and not appropriate for use in a clinical setting. In this project, we study the properties of a more focused criterion, the partial volume under the receiver operating characteristic surface, that summarizes the diagnostic accuracy of a marker in the three-class setting for regions restricted to only those of clinical interest. We propose methods for estimation and inference on the partial volume under the receiver operating characteristic surface under parametric and non-parametric frameworks and apply these methods to the evaluation of potential biomarkers for the diagnosis of pancreatic cancer.

Keywords

Biomarkers classification delta Method kernels receiver operating characteristic surface

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References

Capello

Bantis

Scelo

et al. Sequential validation of blood-based protein biomarker candidates for early-stage pancreatic cancer. J Natl Cancer Inst 2017; 109: djw266.

Deshwar

Sugar

Torto

et al. Diagnostic intervals and pancreatic ductal adenocarcinoma (PDAC) resectability: a single-center retrospective analysis. Ann Pancreat Cancer 2018; 1: 13–13.

Vujasinovic

Dugic

Maisonneuve

et al. Risk of developing pancreatic cancer in patients with chronic pancreatitis. J Clin Med 2020; 9: 3720.

Nakas

Dalrymple-Alford

Anderson

et al. Generalization of Youden index for multiple-class classification problems applied to the assessment of externally validated cognition in Parkinson disease screening. Stat Med 2013; 32: 995–1003.

Wang

Chang

YCI

. Marker selection via maximizing the partial area under the ROC curve of linear risk scores. Biostatistics 2011; 12: 369–385.

Dodd

Pepe

. Partial AUC estimation and regression. Biometrics 2003; 59: 614–623.

McClish

. Analyzing a portion of the ROC curve. Med Decis Making 1989; 9: 190–195.

Huang

. Weighted volume under the three-way receiver operating characteristic surface. Stat Methods Med Res 2019; 28: 3627–3648.

Xiong

van Belle

Miller

et al. Measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups. Stat Med 2006; 25: 1251–1273.

10.

Xiong

van Belle

Miller

et al. A parametric comparison of diagnostic accuracy with three ordinal diagnostic groups. Biometrical Journal 2007; 49: 682–693.

11.

Mosier

Bantis

. Estimation and construction of confidence intervals for biomarker cutoff-points under the shortest Euclidean distance from the ROC surface to the perfection corner. Stat Med 2021; 40: 4522–4539.

12.

Lloyd

Yong

. Kernel estimators of the ROC curve are better than empirical. Stat Probab Lett 1999; 44: 221–228.

13.

Zhou

Harezlak

. Comparison of bandwidth selection methods for kernel smoothing of ROC curves. Stat Med 2002; 21: 2045–2055.

14.

Mossman

. Three-way ROCs. Med Decis Making 1999; 19: 78–89.

15.

Nakas

Yiannoutsos

. Ordered multiple-class ROC analysis with continuous measurements. Stat Med 2004; 23: 3437–3449.

16.

Bantis

Feng

. Comparison of two correlated ROC surfaces at a given pair of true classification rates: comparing two ROC surfaces at given pairs of TCRs. Stat Med 2018; 37: 4022–4035.

17.

Flanders

. Differentiation under the integral sign. Am Math Mon 1973; 80: 615.

18.

Box

GEP

Cox

. An analysis of transformations. J R Stat Soc: Ser B (Methodological) 1964; 26: 211–243.

19.

Bantis

Nakas

Reiser

. Construction of confidence regions in the ROC space after the estimation of the optimal Youden index-based cut-off point: construction of confidence regions in the ROC space after the estimation of the cut-off point. Biometrics 2014; 70: 212–223.

20.

Bantis

Nakas

Reiser

et al. Construction of joint confidence regions for the optimal true class fractions of receiver operating characteristic (ROC) surfaces and manifolds. Stat Methods Med Res 2017; 26: 1429–1442.

21.

Silverman

. Density Estimation for Statistics and Data Analysis. Number 26 in Monographs on statistics and applied probability, Boca Raton: Chapman & Hall/CRC, 1998. ISBN 978-0-412-24620-3.

22.

Dreiseitl

Ohno-Machado

Binder

. Comparing three-class diagnostic tests by three-way ROC analysis. Med Decis Making 2000; 20: 323–331.

23.

Bantis

Tsimikas

. On optimal biomarker cutoffs accounting for misclassification costs in diagnostic trilemmas with applications to pancreatic cancer. Stat Med 2022: sim.9432. DOI: 10.1002/sim.9432. https://onlinelibrary-wiley-com-443.web.bisu.edu.cn/doi/10.1002/sim.9432.

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