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.

中文翻译：

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基于幅度标准化指数的不同基数定性生物标志物分辨能力的量化评估

生物标志物用于临床诊断目的，但现有指标在生物标志物的分辨能力方面存在局限性。本文提出了一种新的指标，即幅度标准化指数（MSI），用于描述不同生物标志物的定量变化和分辨能力。在 MSI 分析模型中，比率和差异的变化尺度被同时考虑，更高的 MSI 值意味着对生物因素的风险或影响更大。我们通过混合和几何方法解释 MSI 的基本原理，并通过模拟实验验证其功效。我们的结果表明，MSI 在描述分辨能力方面优于约登指数和优势比。当两个生物标志物具有相似的约登指数值、优势比、或 MSI 值但不同的阳性检测率（或基数）相结合，三个指标值均增加；然而，只有 MSI 值保持相对稳定。对于非常小的基数，例如单核苷酸多态性的基数，MSI 值最多为最大值 (0.5) 的一半，从而可以比较具有不同基数的生物标志物的 MSI 值。因此，MSI 可以更好地量化评估具有不同基数的生物标志物的分辨能力。允许比较具有不同基数的生物标志物的 MSI 值。因此，MSI 可以更好地量化评估具有不同基数的生物标志物的分辨能力。允许比较具有不同基数的生物标志物的 MSI 值。因此，MSI 可以更好地量化评估具有不同基数的生物标志物的分辨能力。