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发展新的多元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与疾病发病机制有关的相关变量组。我的第一个短期目标是使用惩罚估计方法确定调节风险因素和结果之间关系的变量组。这项研究的动机是从数百种测量的代谢物中发现BMI和乳腺癌之间的关联介质。我计划对多变量代谢物使用稀疏潜在因子模型，它们之间的依赖关系将用稀疏因子加载矩阵来描述。然后，每个因素将链接到变量的一个小子集，因此这将增强生物结构的可解释性。为了恢复BMI与乳腺癌之间关系的中介因素，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进行额外的处罚。关键的方法发展是解决调解分析中的高维问题。我的第二个短期目标是找到与连续和多变量结果混合的潜在因素相关的一组变量。它的动机是研究与精神疾病相关的遗传变异。由于精神疾病的复杂性，精神疾病的分类诊断被认为是不精确的表征障碍的性质。内表型是假设潜在疾病综合征的可测量的定量性状，已被认为是分类疾病表型的替代方法。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。我计划扩展连续和多染色体表型混合的方法，以增强其在精神病学遗传研究中的适用性。我的第三个短期目标是构建一个测试统计，以识别与结果子集相关的一组变量，其中特定子集是未知的。它的动机是遗传应用，以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包与科学界分享。随着生物技术的发展，将会出现更多的统计问题，这项研究计划将在五年计划之外同步发展。

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.