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<p>We contribute to the literature by developing point estimators for the volume under a three-class receiver operator characteristics (ROC) surface (VUS) when the biomarker distribution in each subclass follows a two-parameter exponential distribution with a known scale parameter under simple random sampling (SRS) and minima nomination sampling (MinNS). Specifically, we derive the uniformly minimum variance unbiased estimators (UMVUEs) under the perfect ranking assumption when either SRS or MinNS is applied to each subpopulation. We then compare the performance of the estimators using Monte Carlo simulation for both perfect and imperfect ranking cases. Our simulation results show significant efficiency gains in many of the considered cases. Finally, we apply our proposed methodology to a real HIV dataset to demonstrate its practical utility.</p>

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Estimation of the volume under a three-class ROC surface (VUS) for two-parameter exponential distribution with an application

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Samira Nasr Esfahani,
  • Ehsan Zamanzade,
  • Omid Naghshineh A.

摘要

We contribute to the literature by developing point estimators for the volume under a three-class receiver operator characteristics (ROC) surface (VUS) when the biomarker distribution in each subclass follows a two-parameter exponential distribution with a known scale parameter under simple random sampling (SRS) and minima nomination sampling (MinNS). Specifically, we derive the uniformly minimum variance unbiased estimators (UMVUEs) under the perfect ranking assumption when either SRS or MinNS is applied to each subpopulation. We then compare the performance of the estimators using Monte Carlo simulation for both perfect and imperfect ranking cases. Our simulation results show significant efficiency gains in many of the considered cases. Finally, we apply our proposed methodology to a real HIV dataset to demonstrate its practical utility.