Analysis and Modeling of Functional Data in Biostatistics

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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.