Statistical methods of multivariate analysis for large and complex data

生物数据的复杂性推动了统计方法的巨大发展。这项研究计划的长期目标是开发新的多变量统计方法来分析高维生物数据。更直接的目标是开发三种方法来检测涉及疾病发病机制的相关变量组。我的第一个短期目标是使用惩罚估计法确定调节风险因素和结果之间关系的变量组。它的动机是从数百种测量的代谢物中确定BMI和乳腺癌之间联系的中介。我计划利用一个稀疏潜在因素模型来描述多变量代谢物，它们之间的相关性将用一个稀疏因素加载矩阵来描述。然后，每个因素将只与一小部分变量联系在一起，因此这将增强生物结构的可解释性。为了恢复BMI与乳腺癌之间的中介关系，我计划对BMI对中介因素的影响和中介因素对乳腺癌的影响的回归系数向量实施额外的惩罚。解决中介分析中的高维问题是方法论发展的关键。我的第二个短期目标是找到与变量组相关的变量组，这是一个潜在的因素，支撑着连续和多变量结果的混合。它的动机是研究与精神障碍相关的遗传变异。由于精神障碍的复杂性，人们一直认为，绝对的精神诊断不能准确地描述这种疾病的性质。内表型是假设潜在疾病症状的可测量的数量性状，已被认为是分类疾病表型的替代。我最近的工作利用惩罚结构方程模型来检测与多种定量内表型的潜在疾病综合征相关的遗传变异。我计划将该方法扩展到连续和多裂型的混合表型，以增强其在精神病学遗传学研究中的适用性。我的第三个短期目标是建立一个测试统计数据，以确定与结果子集相关的一组变量，其中特定的子集是未知的。基因应用的目的是检测与一组遗传变异相关的多种疾病的子集的存在。在建立了这些方法之后，我将构建R包与科学界共享。随着生物技术的发展，将会出现更多的统计问题，这项研究计划将同时发展到这个五年计划之外。

The complexity of biological data has driven tremendous developments of statistical methods. The long-term goal of this research program is to develop new multivariate statistical methods for analyzing high dimensional biological data. The more immediate goal is to develop three methods for detecting groups of related variables that involved with disease pathogenesis. My first short-term objective is to identify the groups of variables that mediate the relationship between a risk factor and an outcome using penalized estimation approach. It is motivated by the identification of mediators for the association between BMI and breast cancer from hundreds of measured metabolites. I plan to utilize a sparse latent factor model for the multivariate metabolites, and the dependency among them will be described by a sparse factor loading matrix. Then each factor will link to only a small subset of variables so this will enhance the interpretability of the biological structure. To recover the factors that mediate the relationship among BMI and breast cancer, I plan to implement additional penalties on the regression coefficient vectors for the effect of BMI on mediating factors and for the effect of mediating factors on breast cancer. The key methodological development is to address the high dimensional problems in mediation analysis. My second short-term objective is to find the group of variables associated a latent factor underlying a mixture of continuous and polytomous multivariate outcomes. It is motivated by the study of the genetic variants associated with psychiatric disorders. Because of the complexity of psychiatric disorders, the categorical psychiatric diagnoses have been believed to be imprecise to characterize the nature of the disorder. Endophenotypes, which are measurable quantitative traits hypothesized to the underlying disease syndromes, have been considered as an alternative to the categorical disease phenotypes. My recent work utilized a penalized structural equation modelling to detect the genetic variants associated with the underlying disease syndromes for multiple quantitative endophenotypes. I plan to extend the method for a mixture of continuous and polytomous phenotypes to enhance its applicability in psychiatric genetic studies. My third short-term objective is to build a test statistic to identify a group of variables associated with a subset of outcomes, where the specific subset is unknown. It is motivated by a genetic application to detect the existence of a subset of multiple diseases associated with a group of genetic variants. After establishing those methods, I will build R packages to share with the scientific community. With the development of biotechnology, more statistical problems will emerge and this research program will grow concurrently beyond this five-year proposal.