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Statistical inference on optimal operating characteristics for operational markers when the likelihood ratio is unimodal: A parametric approach

Author

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  • Anastasiou, Achilleas
  • Tsimikas, John

Abstract

Misclassification cost analysis is integrated into decision making and statistical inference using optimal Receiver Operating Characteristics (ROC) curves. The focus is on distribution families with the unimodal likelihood ratio property where the optimal ROC curve is simply a two cutpoint ROC curve. The notion of marker operationality is explored in the presence of the prevalence-adjusted misclassification cost ratio and a Relative Benefit index for a given marker is defined. Results concerning statistical testing for the operationality of a marker and the estimation of optimal thresholds and the corresponding optimal operational characteristics are derived. Details for some common parametric families that exhibit the unimodal likelihood ratio property are presented. Implicit differentiation, the envelop theorem and Leibniz integral differentiation are the mathematical tools utilized to develop a general delta method inferential procedure. The techniques are applied on a real dataset with mRNA expression measurements.

Suggested Citation

  • Anastasiou, Achilleas & Tsimikas, John, 2026. "Statistical inference on optimal operating characteristics for operational markers when the likelihood ratio is unimodal: A parametric approach," Computational Statistics & Data Analysis, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:csdana:v:220:y:2026:i:c:s0167947326000381
    DOI: 10.1016/j.csda.2026.108369
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