Model selection in generalized functional regression: enhancing prediction and identifying key longitudinal predictors

For a single subject in biomedical research, many different continuous biological processes can be observed over time via lab assays or clinical measurement. Connecting the effects of these processes to patient outcomes could give researchers new tools for predicting morbidity and mortality in vulnerable populations such as pre-term infants. Oftentimes this type of functional data is observed simultaneously across a large number of different biological processes and tools are needed to separate out only the most important processes as they relate to a patient outcome. This dissertation develops tools to connect functional data that may be observed across many dimensions with scalar outcomes, such as a binary morbidity/mortality outcome or a continuous weight at discharge outcome. More specifically, we elaborate how group penalization can be used to arrive at a small collection of important functional predictors, then develop a novel selection algorithm that allows researchers to treat a group of predictors as a single multivariate functional predictors. Using these tools, we identify select metabolic processes that predict health outcomes in a real-world cohort of pre-term infants. This research addresses a problem that is more and more present in biomedical research: how to sift through a wealth of data and identify only those variables that are most predictive of a health outcome.