Analysis and Modeling of Functional Data in Biostatistics

我的新研究计划的长期目标是开发有用的计算工具和新的统计方法，用于对生物统计学中不同领域的复杂功能和纵向数据进行建模和分析，例如医学成像、生存分析和临床试验设计。在接下来的5年里，我的团队将在三个应用领域解决三个短期目标。领域1：生物统计学应用功能数据分析的新方法发展。功能数据在生物统计学中广泛存在，特别是在医学成像和癌症生物标记物分析领域。例如，传统的对脑扫描图像进行功能数据分析的方法可能会在时间和机器内存方面招致高昂的成本。此外，在癌症生物标志物分析中，轨迹经常受到扰动和遗漏的影响，传统的函数主成分分析方法可能不能有效地工作。为了避免这样的计算困难，我们将使用基于回归的正交逼近方法来开发进行泛函主成分分析的新方法。区域2：生存模型的功能性数据分析的组合。现有的涉及功能协变量的生存模型通常依赖于Cox比例风险结构和正确审查的假设。为了从生物标记物的轨迹预测转化为阿尔茨海默病的时间，我们将结合函数回归框架和广义混合治愈模型来开发几类功能生存模型。该模型将是通用的，并能够处理函数协变量和标量协变量，各种类型的审查方案，以及密集和稀疏抽样结构。区域3：试验设计中功能数据信息的利用。这与针对大流行性疾病的新颖统计试验设计特别相关，例如当前的新冠肺炎大流行。这种疾病的疗效终点通常是纵向顺序的。对于每个患者，在整个时间跨度内每天观察这些顺序结果，形成一系列功能数据对象。我们将应用贝叶斯自适应序贯方法来开发新的统计设计，以从纵向数据中提取信息，这将使有效和有效的测试和识别有用的治疗策略。综上所述，拟议目标的结果将引起生物统计和药物统计等领域的研究人员和开发人员的兴趣，在这些领域，需要分析复杂的功能和纵向数据。最终，由开发的统计方法实现的分析将带来有利于加拿大人健康和福祉的新技术，并提高加拿大在世界舞台上统计研究的声誉。

The long-term goal of my new research program is to develop useful computational tools and new statistical methodologies for modeling and analysis of complex functional and longitudinal data in various areas in biostatistics, such as medical imaging, survival analysis, and clinical trial design.  Over the next 5 years, my team will address three short-term objectives in three areas of application. Area 1: Novel methodological development of functional data analysis for biostatistics application. Functional data has wide a presence in biostatistics, in particular in the field of medical imaging and cancer biomarkers analysis. For example, conventional methods for functional data analysis on images of brain scans may incur high costs in terms of time and machine memory. Moreover, in cancer biomarkers analysis, trajectories are often subject to perturbation and missingness, and conventional methods for functional principal component analysis might not work effectively. To circumvent such computational difficulties, we will use a regression-based orthogonal approximation method to develop novel approaches for conducting functional principal component analysis. Area 2: Combination of functional data analysis for survival models. Existing survival models involving functional covariates typically rely on the Cox proportional hazards structure and the assumption of right censorship. Motivated by the aim of predicting the time of conversion to Alzheimer's disease from biomarker trajectories, we will combine the framework of functional regression and a generalized mixture cure model to develop several classes of functional survival models. The models will be versatile and able to handle both functional and scalar covariates, various types of censoring schemes, and both dense and sparse sampling structure. Area 3: Utilization of functional data information in trial design. This is particularly relevant for novel statistical trial designs for pandemic diseases such as the current COVID-19 pandemic. The efficacy endpoints for this type of disease is typically longitudinally ordinal. For each patient, these ordinal outcomes are observed daily across the entire timespan, forming a series of functional data objects. We will apply the methodologies of Bayesian adaptive sequential method to develop novel statistical designs for extracting information from the longitudinal data, which would enable efficient and effective testing and identification of useful treatment strategies. Taken together, the results of the proposed objectives will be of interest to researchers and developers in fields such as biostatistics and pharmaceutical statistics, in which the analysis of complex functional and longitudinal data is required. Ultimately, the analyses enabled by the developed statistical methodologies will bring new technologies that will benefit the health and well-being of Canadians and elevate Canada's reputation for statistical research on the world-stage.