Title: Regression based principal component analysis for sparse functional data with applications to screening pubertal growth paths
Description: Pediatric growth paths are smooth trajectories of body-size measurements (e.g. height or weight). They are observed at irregular times due to individual needs. It is clinically important to screen such growth paths. However rigorous quantitative methods are largely missing in the literature. In the first part of this dissertation, we proposed a new screening method based on principal component analysis for growth paths (sparse functional data). An estimation algorithm using alternating regressions is developed, and the resulting component functions are shown to be uniformly consistent. The proposed method does not require any distributional assumptions, and is also computationally feasible. It is then applied to monitor the puberty growth among a group of Finnish teenagers, and yields interesting insights. A Monte-Carlo study is conducted to investigate the performance of our proposed algorithm, with comparison to existing methods. In the second part of the dissertation, the proposed screening method is further extended to incorporate subject level covariates, such as parental information.

When it is applied to the same group of Finnish teens, it shows enhanced screening performance in identifying possible abnormal growth paths. Simulation studies are also conducted to validate the proposed covariate adjusted method.