Estimation of Volume Under Receiver Operating Characteristic Surface and Asymptotic Variance for Diagnostic Classifier Following Log-Normal Distribution

G  Kumarapandiyan; T. S.  Sahana

doi:10.18502/jbe.v11i3.21371

G Kumarapandiyan Department of Statistics, Madras Christian College, University of Madras, Chennai, India.
T. S. Sahana Department of Statistics, Madras Christian College, University of Madras, Chennai, India.

DOI: https://doi.org/10.18502/jbe.v11i3.21371

Keywords: Biomarker; Gold standard; Three class classification; Receiver operating characteristics; Volume under the ROC surface and asymptotic variance

Abstract

Introduction: Clinical diagnosis highlights the essential need to assess biomarker performance for effective diseasescreening and diagnosis. The Receiver Operating Characteristic (ROC) curve serves as a fundamental tool for assessingand interpreting biomarker effectiveness. Numerous models and techniques have been developed to analyze biomarkersin binary classification settings (Non-Diseased vs. Diseased). This research article seeks to expand the binary classificationframework to a three-class scenario, incorporating Diseased, Suspicious, and Non-Diseased categories under a Log-Normaldistribution.

Methods: It introduces a three-class Log-Normal ROC model based on a Parametric approach, deriving metrics such asVolume Under the ROC Surface (VUS) and Asymptotic Variance, as well as an alternative Non-Parametric approach. Themodel was validated using simulated data generated for the underlying distribution, and a real-life dataset was used to fitthe VUS and ROC curves.

Results: The simulation study was conducted using four sets with varying parameters. In the fourth set, the Non-ParametricVUS (0.9966) exceeded the Parametric VUS (0.8058), though the difference was smaller compared to the other sets. Thelow Standard Error (SE) (0.0472) across all sets indicates high precision in the estimates. Additionally, for the real-life (Themultiple sclerosis (ms) disease) dataset the VUS value is 0.6782 which gives moderate fit of the model.

Conclusion: In this study, we derived the asymptotic variance and VUS for the Log-Normal distribution using simulateddata with varying parameters. The analysis compares diagnostic performance across parameter sets, highlighting thesuperiority of Non-Parametric VUS over Parametric VUS. Set 4 demonstrated the highest reliability with the lowest standarderror (SE = 0.0472). The real-life MS dataset provided a moderate fit to the proposed model