发表机构
Department of Biostatistics, College of Public Health, University of Kentucky（肯塔基大学公共卫生学院生物统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将严格标准化均数差扩展到多变量线性组合，提出闭式解优化系数，证明其与Fisher判别等方法的关联，并构建估计与置信区间，为多变量生物标志物提供可解释框架。
AI 中文摘要
严格标准化均数差（SSMD）是一种可解释、无单位的效果量，最初为高通量筛选中的质量控制和命中选择而开发，随后扩展到效果量评估和错误率控制。现有的SSMD理论一次只考虑一个变量。在此，我们将SSMD扩展到多个变量的线性组合，并确定使所得SSMD最大化的系数。我们证明该优化可以表述为具有闭式解的广义瑞利商，并确定了最优方向与Fisher线性判别一致的条件。我们推导了最大化SSMD的矩估计、偏差校正和最大似然估计量，并在不同相关性和方差结构下基于Hotelling的T平方统计量和非中心F分布构建置信区间。我们还刻画了所得线性评分的分类截断值，并建立了其与受试者工作特征曲线下面积（AUROC）的关系。模拟表明，在等协方差下，SSMD最大化与Fisher线性判别和逻辑回归一致，但在不等协方差和类别不平衡下则出现分歧。在配对设计中，SSMD最大化独特地纳入了互协方差信息。线性支持向量机也被作为现代比较器进行评估。该框架为高通量筛选、细胞因子谱分析、代谢组学、唾液诊断和连续监测应用构建多变量生物标志物和特征提供了可解释的方法。
英文摘要
The strictly standardized mean difference (SSMD) is an interpretable, unit-free effect size originally developed for quality control and hit selection in high-throughput screening and subsequently extended to effect-size assessment and error-rate control. Existing SSMD theory considers one variable at a time. Here, we extend SSMD to a linear combination of multiple variables and determine the coefficients that maximize the resulting SSMD. We show that this optimization can be formulated as a generalized Rayleigh quotient with a closed-form solution and identify conditions under which the optimal direction coincides with Fisher's linear discriminant. We derive method-of-moments, bias-corrected, and maximum-likelihood estimators of the maximized SSMD and construct confidence intervals based on Hotelling's T-squared statistic and the noncentral F distribution under different correlation and variance structures. We also characterize classification cutoffs for the resulting linear score and establish its relationship with the area under the receiver operating characteristic curve (AUROC). Simulations show that SSMD maximization coincides with Fisher's linear discriminant and logistic regression under equal covariance but diverges under unequal covariance and class imbalance. In paired designs, SSMD maximization uniquely incorporates cross-covariance information. Linear support vector machines are also evaluated as a modern comparator. This framework provides an interpretable approach to constructing multivariable biomarkers and signatures for high-throughput screening, cytokine profiling, metabolomics, salivary diagnostics, and continuous-monitoring applications.
Comments29 pages, 3 figures, 3 tables
