Modeling Longitudinal Data with Complex Structures

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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.