UC San Diego

The objective of this thesis is to utilize statistical methods for longitudinal and functional data analysis, where repeated measures are observed. This dissertation is comprised of threemain applications. In the first study, we aimed to model developing trajectories of multiple biomarker outcomes simultaneously and predict latent disease stages of Alzheimer's disease, using data from the multicohort longitudinal Alzheimer's Disease Neuroimaging Initiative (ADNI) study. For sparsely observed outcomes over a relatively short period of time, we proposed a flexible Bayesian multivariate growth mixture model to identify distinct longitudinal patterns of disease progression and three latent trajectory patterns among ADNI participants that overlap with but do not correspond one-to-one with diagnostic status.

In the second study, we observed densely sampled physical activity (PA) data acquired from accelerometers, which are widely used for tracking human movement and provide minute-level PA records, and intended to explore its association with health outcomes related with obesity. We developed multiple multilevel functional models, based on functional principal component analysis (FPCA) approaches, to study the hierarchical structure and temporal patterns of daily PA data from 245 overweight/obese women at three visits over a one-year period. We found that the health outcomes are strongly associated with PA variation and revealed that the timing of PA during the day can also impact changes in outcomes.

We further extended the implementation to densely sampled data in both spatial and temporal domains, focusing on modeling and testing climate change effects using regional climate data from the North American Coordinated Regional Downscaling Experiment (NA-CORDEX). We constructed spatial-temporal models which incorporate geographically weight regression strategies, and performed spatial inference on trend parameters regarding temperature and precipitation change. As a result, we identified regions with significant climate change in California, Colorado and Kansas, and compared similarities and differences of global warming effects in local scales.