Modeling Longitudinal Data with Complex Structures

纵向数据是指从同一组个体中连续收集的数据，它们是理解生物过程等现象的全球演变的关键。在大数据时代，纵向数据分析面临着高维、不规则、异构和计算负担等新的挑战。此外，多视角纵向数据在许多研究领域变得越来越普遍。这类数据是指从多个来源收集的描述同一组个体的纵向数据。例如，多视图纵向数据可以包括不同类型的组学（基因组学、转录组学、蛋白质组学）数据、电子医疗记录数据以及在多次随访期间对同一组患者测量的临床症状。我的研究计划的长期目标是开发灵活，可推广和可解释的统计学习方法，以模拟从多个来源收集的生物医学数据，并具有复杂的（例如高维，不完整，异构）结构。 在短期内，我的研究计划将有助于通过三个目标推进数学和统计领域。第一个目标是开发可扩展的贝叶斯方法，用于聚类具有不同结构的多变量纵向数据。我们将开发数据驱动的方法来确定集群的数量，基于Dirichlet过程混合物模型和有限混合物模型的混合物等方法。变分推理算法将推导和执行软件包将开发，以促进快速和有效的计算。第二个目标是开发可扩展的贝叶斯方法动态聚类的多变量纵向数据与未知数量的集群。我们将开发一类动态聚类模型，通过将在每个时间间隔更新的时间相关变量的信息，直接分配每个时间间隔的类成员资格。第三个目标是开发一类可扩展的贝叶斯模型，用于聚类具有未知数量的聚类的多视图纵向数据。所提出的方法将使用模拟和真实的数据集进行评估。这些真实的数据集将从皇后大学加拿大癌症试验组和儿童队列研究等研究平台获得。我的研究计划承诺在数学和统计学方面取得显着的进步和创新，因为该研究计划创新了新的统计方法和可扩展的计算工具，以解决与分析具有复杂结构的纵向数据相关的一系列问题。从我们的计划开发的开源和用户友好的软件包将促进我们提出的模型的广泛应用，并将在加拿大和世界范围内的自然科学和工程研究界产生更大的影响。

Longitudinal data refer to data collected sequentially from the same set of individuals over time and they are key to understanding the global evolution of a phenomenon such as biological processes. In the era of big data, analysis of longitudinal data is faced with new challenges, such as high dimensionality, irregularity, heterogeneity and computational burden. Moreover, multi-view longitudinal data have become increasingly common in many research areas. This type of data refers to longitudinal data collected from multiple sources describing the same set of individuals. For example, multi-view longitudinal data may include different types of omics (genomics, transcriptomics, proteomics) data, electronic medical record data, and clinical symptoms measured on the same set of patients during multiple follow-up visits. The long-term goal of my research program is to develop flexible, generalizable and interpretable statistical learning methods to model biomedical data collected from multiple sources and with complex (e.g. high-dimensional, incomplete, heterogeneous) structures. In the short term, my research program will contribute to advancing the field of mathematics and statistics via three objectives. The first objective is to develop scalable Bayesian methods for clustering multivariate longitudinal data with distinct structures. We will develop data-driven approaches to determine the number of clusters, based on methods such as the Dirichlet process mixture model and mixtures of finite mixtures model. Variational inference algorithms will be derived and implementation software packages will be developed to facilitate fast and efficient computation. The second objective is to develop scalable Bayesian methods for dynamic clustering of multivariate longitudinal data with an unknown number of clusters. We will develop a class of dynamic clustering model that directly assigns class membership for each time interval by incorporating information from time-dependent variables that are updated in each time interval. The third objective is to develop a class of scalable Bayesian models for clustering multi-view longitudinal data with an unknown number of clusters. The proposed methods will be evaluated using both simulated and real datasets. These real datasets will be obtained from research platforms such as the Canadian Cancer Trials Group at Queen's University and the CHILD Cohort Study. My research program promises a notable advancement and innovation in mathematics and statistics in that this research program innovates new statistical methodologies and scalable computational tools to tackle a range of problems related to analyzing longitudinal data with complex structures. The open sources and user-friendly software packages developed from our program will facilitate a wide application of our proposed models and will create an even larger impact on the natural sciences and engineering research community in Canada and worldwide.