Quantificational evaluation of the resolving power of qualitative biomarkers with different cardinal numbers based on a magnitude-standardized index.

Biomarkers are used for clinical diagnostic purposes, but existing indexes exhibit limitations in terms of the resolving power of biomarkers. This paper proposes a new index, the magnitude-standardized index (MSI), to describe the quantitative variations and resolving powers of different biomarkers. In MSI analysis models, variation scales for ratios and differences are considered simultaneously, and a higher MSI value implies a stronger risk or effect for a biological factor. We explain the rationale for the MSI via hybrid and geometric methods and verify its efficacy through simulation experiments. Our results indicate that the MSI is superior to the Youden index and odds ratio for describing resolving power. When two biomarkers with similar Youden index values, odds ratios, or MSI values but different positive test rates (or cardinal numbers) were combined, all three index values increased; however, only the MSI value remained relatively stable. For a very small cardinal number, such as that of a single nucleotide polymorphism, the MSI value is at most half of the maximum value (0.5), allowing comparisons between MSI values for biomarkers with different cardinal numbers. The MSI can thus provide a better quantifiable evaluation of the resolving power of biomarkers with different cardinal numbers.