Guan Calvin, Gangopadhyay Ashis
Department of Mathematics & Statistics, Boston University.
bioRxiv. 2025 May 18:2023.12.19.572366. doi: 10.1101/2023.12.19.572366.
Although there are many methods available in the literature to compare the covariance structures of two populations, few are suitable for clinical application due to the inability to account for covariate(s) that affect the dependence structure of the variables being investigated. A common method is to adjust the effect of the covariates via a linear model and work with the resulting residuals. However, removing the effects of the covariates could potentially eliminate valuable information from the analysis. We propose a functional nonparametric covariance matrix estimator to account for any given value in the covariate(s), which allows a comparison of the functional covariance structures of the multivariate data. This comparison is facilitated via a test statistic involving the first eigenvalue of the combined form of covariance matrices of the two groups. Three different approaches, namely, the parametric Tracy-Widom, the semi-parametric Forkman's test, and the nonparametric Permutation method, are used to compute the approximate p-values of the test statistic. We have conducted extensive simulation studies to determine the type I error and power of the proposed hypothesis testing methods and developed practical recommendations for implementing this novel approach. Finally, we apply our methods to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study to compare cerebrospinal fluid (CSF) biomarkers between dementia and non-dementia cohorts, which offers a fascinating insight into the differences between covariance structures of biomarkers amyloid , total tau (tau), and phosphorylated tau (ptau) for given values of age, sex, and years of education.
虽然文献中有许多方法可用于比较两个总体的协方差结构，但由于无法考虑影响所研究变量依赖结构的协变量，很少有方法适用于临床应用。一种常见的方法是通过线性模型调整协变量的影响，并处理由此产生的残差。然而，去除协变量的影响可能会从分析中潜在地消除有价值的信息。我们提出了一种函数非参数协方差矩阵估计器，以考虑协变量中的任何给定值，这使得能够比较多变量数据的函数协方差结构。通过涉及两组协方差矩阵组合形式的第一个特征值的检验统计量来促进这种比较。使用三种不同的方法，即参数化的特雷西 - 威多姆方法、半参数化的福克曼检验和非参数化的置换方法，来计算检验统计量的近似p值。我们进行了广泛的模拟研究，以确定所提出的假设检验方法的I型错误和功效，并为实施这种新方法制定了实用建议。最后，我们将我们的方法应用于阿尔茨海默病神经影像学倡议（ADNI）研究，以比较痴呆症和非痴呆症队列之间的脑脊液（CSF）生物标志物，这为在年龄、性别和受教育年限的给定值下，生物标志物淀粉样蛋白、总tau蛋白（tau）和磷酸化tau蛋白（ptau）的协方差结构差异提供了引人入胜的见解。
