Receiver operating characteristics (ROC) curves play a pivotal role in the analyses of data collected in applications involving machine vision, machine learning and clinical diagnostics. The importance of ROC curves lies in the fact that all decision-making strategies rely on the interpretations of the curves and features extracted from them. Such analyses become simple and straightforward if it is possible to have a statistical fit for the empirical ROC curve. A methodology is developed and demonstrated to obtain a parametric fit for the ROC curves using multiple tools in statistics such as chi square testing, bootstrapping (parametric and non-parametric) and -testing. Relying on three data sets and an ensemble of density functions used in modeling sensor and econometric data, statistical modeling of the ROC curves (best fit) is accomplished. While the reported research relied on simulated data sets, the approaches implemented and demonstrated in this work can easily be adapted to data collected in clinical as well as non-clinical settings.
DemidenkoE. (2012). Confidence intervals and bands for the binormal ROC curve revisited. Journal of Applied Stat, 39(1), 67-79.
9.
DestrempesF., & CloutierG. (2010). A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope. Ultrasound in Medicine and Biology, 36(7), 1037-1051.
HanleyJ.A. (1988). The robustness of the “binormal” assumptions used in fitting ROC curves. Medical decision Making, 8(3), 197-203.
12.
HanleyJ.A. (1996). The use of the ‘binormal’ model for parametric ROC analysis of quantitative diagnostic tests. Statistics in medicine, 15(14), 1575-1585.
13.
HoggR.V., & KlugmanS.A. (1983). On the estimation of long tailed skewed distributions with actuarial applications. Journal of Econometrics, 23(1), 91-102.
14.
HoyerA., & KussO. (2020). Meta analysis of full ROC curves with flexible parametric distributions of diagnostic test values. Res Syn Meth, 11(2), 301-313.
KochańskiB. (2022). Which curve fits best: Fitting ROC curve models to empirical credit-scoring data. Risks, 10(10), 184.
17.
LiuX. (2012). Classification accuracy and cut point selection. Statistics in Medicine, 31(23), 2676-2686.
18.
LipovetskyS., & ConklinM.W. (2020). Bayesian sensitivity-specificity and ROC analysis for finding key drivers. Journal of Modern Applied Statistical Methods, 19(1), eP3023.
19.
LtifiH.BenmohamedE.KolskiC., & Ben AyedM. (2020). Adapted visual analytics process for intelligent decision-making: application in a medical context. International Journal of Information Technology and Decision Making, 19(1), 241-282.
20.
MetzC.E. (1989). Some practical issues of experimental design and data analysis in radiological ROC studies. Investigative Radiology, 24(3), 234-245.
21.
ObuchowskiN.A., & BullenJ.A. (2018). Receiver operating characteristic (ROC) curves: review of methods with applications in diagnostic medicine. Physics in Medicine and Biol, 63(7), 07TR01.
PundirS., & AmalaR. (2014). Parametric receiver operating characteristic modeling for continuous data: A glance. Model Assisted Statistics and Applications, 9(2), 121-135.
24.
RohatgiV.K., & SalehA.K. (2000). An Introduction to Probability and Statistics. 2 Edition. Wiley.
25.
RotaM., & AntoliniL. (2014). The optimal cut-point for Gaussian and Gamma distributed biomarkers. Computational Statistics and Data Analysis, 69, 1-14.
26.
SchistermanE.F.PerkinsN.J.LiuA., & BondellH. (2005). Optimal cut-point, and its corresponding Youden Index to discriminate individuals using pooled blood samples. Epidemiology, 16(1), 73-81.
27.
SimonM.K., & AlouiniM.S. (2001). Digital communication over fading channels. New York: Wiley.
28.
SivaG.Vishnu VardhanR., & ChesneauC. (2023). Estimating the AUC of mixture MROC curve in the presence of measurement errors. Model Assisted Statistics and Applications, 18(3), 237-244.
29.
SwetsJ.A. (1988). Measuring the accuracy of diagnostic systems. Science, 240(4857), 1285-1293.
30.
TilburyJ.B.Van EetveltW.J.GaribaldiJ.M.CurnswJ.S., & IfeachorE.C. (2000). Receiver operating characteristic analysis for intelligent medical systems-a new approach for finding confidence intervals. IEEE Transactions on Biomedical Engineering, 47(7), 952-963.
31.
VickersA.J. (2008). Decision analysis for the evaluation of diagnostic tests, prediction models, and molecular markers. The American Statistician, 62(4), 314-320.
32.
WalshS.J. (1999). Goodness-of-fit issues in ROC curve estimation. Medical decision making, 19(2), 193-201.
33.
WatsonG.S. (1958). On chi-square goodness-of-fit tests for continuous distributions. J of the Royal Statistical Society. Series B (Methodological), 20(1), 44-72.
34.
ZweigM.H., & CampbellG. (1993). Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry, 39(4), 561-577.
