Presented by Andres Arguedas Leiva
Ph.D. Candidate in Biostatistics
Ph.D. Advisers: Dr. Mark Fiecas & Dr. Erjia Cui

Longitudinal data are commonly collected in biomedical studies and used to measure change or progression over time. They can be used for diagnosis, prognosis, or even stratification in clinical trials. When the longitudinal data are multivariate, the modeling complexity is increased due to potential correlations across time within and between variables. Data may also be collected sparsely and irregularly, decreasing the amount of information available for each subject. One approach to deal with these data is functional data analysis (FDA) methods. These can be used to flexibly model the trajectory over time of these sparsely observed data without strong distributional assumptions. Motivated by a collaboration with the ALS Natural History Consortium, we propose a series of approaches developed to better understand longitudinal trajectories and their relationship with time-to-event outcomes. First, we apply a semi-competing risks model to jointly account for death and intermediate disease milestones in ALS progression. Second, we present a dynamic prediction model that uses sparse multivariate functional PCA to estimate unobserved disease progression trajectories and link them to time-to-death. Finally, we propose a novel method based on a mixture model of Gaussian Processes to cluster these longitudinal trajectories in a scalable and data-driven way. Together, the methods developed in this dissertation seek to provide varied approaches to understand longitudinal disease trajectories and connect them to survival outcomes based on sparsely observed data.