Modeling Longitudinal Data with Complex Structures

对具有复杂结构的纵向数据进行建模

• 批准号: RGPIN-2022-03333
• 负责人: Lu, Zihang
• 金额: $ 1.38万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=764371
• 关键词: Modeling; Longitudinal; Data; Complex; Structures

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.

纵向数据是指在一段时间内从同一组个体连续收集的数据，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，纵向数据的分析面临着高维、不规则、异构性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中已经变得越来越常见。这类数据是指从描述同一组个体的多个来源收集的纵向数据。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、电子病历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，以对从多个来源收集的具有复杂(如高维、不完整、异质)结构的生物医学数据进行建模。在短期内，我的研究计划将通过三个目标促进数学和统计领域的发展。第一个目标是开发具有不同结构的多变量纵向数据的可伸缩贝叶斯方法。我们将基于Dirichlet过程混合模型和有限混合模型等方法，开发数据驱动的方法来确定簇的数量。将推导出变分推理算法，并开发实现软件包，以促进快速和高效的计算。第二个目标是发展可伸缩的贝叶斯方法，用于具有未知聚类数目的多变量纵向数据的动态聚类。我们将开发一类动态聚类模型，通过结合每个时间间隔中更新的依赖于时间的变量的信息，直接为每个时间间隔分配类成员资格。第三个目标是开发一类可伸缩的贝叶斯模型，用于对具有未知聚类数的多视点纵向数据进行聚类。所提出的方法将使用模拟数据集和真实数据集进行评估。这些真实的数据集将从研究平台获得，如女王大学的加拿大癌症试验小组和儿童队列研究。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，因为这个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。根据我们的计划开发的开源和用户友好的软件包将促进我们建议的模型的广泛应用，并将对加拿大和世界各地的自然科学和工程研究社区产生更大的影响。