Integrated Framework for the Optimal Determination of Diagnostic Cut-off Points through Empirical Interpolation, Logistic Modeling Optimized by Dual Annealing, and Combinatorial Optimization with ThresholdXpert: Application to Hepatocellular Carcinoma

IntroductionThe precise determination of diagnostic cut-off points is essential for the development of multimarker panels in oncology. In previous work on pulmonary nodules, it was observed that the standard two-parameter logistic fit could be insufficient for biomarkers with asymmetric distributions. Furthermore, the calculation of empirical cut-off points based on graphical visualization presented limitations in precision and reproducibility. ObjectiveThis study presents a methodological advancement in the data analysis phase (Stage 1), introducing new Python algorithms for the direct analytical calculation of empirical intersections and robust mathematical modeling using Dual Annealing with both two-parameter and four-parameter logistic functions. This improved methodology feeds into the ThresholdXpert 1.0 software tool for combinatorial optimization of biomarker panels (Stage 2), and is applied here to the diagnostic challenge of hepatocellular carcinoma (HCC). MethodsThe methodology was first validated by re-analyzing a dataset of patients with pulmonary nodules (N=895). It was subsequently applied to an HCC dataset derived from the cohort of Jang et al. (208 HCC, 193 cirrhosis, 401 total), randomly divided into a training set (280) and an independent test set (121). Scripts were developed to compare the previous two-parameter logistic fit with the new two- and four-parameter logistic models. Finally, ThresholdXpert 1.0 was used for multimarker panel optimization. ResultsThe integration of empirical calculation, logistic modeling, and combinatorial optimization through ThresholdXpert 1.0 provides a robust and coherent framework for the development of multimarker diagnostic panels. The four-parameter logistic model provided additional validation without substantially modifying cut-off values for most biomarkers, confirming the stability of the approach while offering greater flexibility for complex distributions. When applied to hepatocellular carcinoma, the framework identified a molecular panel composed of AFP, PIVKA-II, OPN, and DKK-1 with sensitivity of 0.77 and specificity of 0.72, and an optimized panel incorporating inverse MELD that achieved the best overall balance (sensitivity 0.73, specificity 0.75) in independent external validation. These results demonstrate the potential of this approach as a generalizable tool for the optimized design of binary diagnostic systems in oncology. ConclusionThe integration of complementary mathematical modeling enhances the capability of ThresholdXpert 1.0 to identify robust diagnostic panels, as in some cases a single biomarker may outperform biomarker combinations, and vice versa. This approach enabled the integration of molecular biomarkers and clinical variables under a unified mathematical framework. Contactroberto117343@gmail.com