Dissertation Defense: Xiaoyang Ma

Candidate: Xiaoyang Ma

Major: Biostatistics

Advisors: Colin Wu, Ph.D. and Ming Tan, Ph.D.

Title: Regularized Local Smoothing for Longitudinal Analysis with Time-Varying Coefficient Models and Transformation Models

This dissertation concerns selecting locally influential variables in both conditional mean and conditional distribution-based models with high-dimensional longitudinal data. Motivated by a large epidemiological study for children and adolescent girls, we aim to search whether the risk factors for blood pressure change over age and find age-specific important covariates. To capture the dynamic covariate effects of the conditional mean-based models, we propose regularized kernel-based local polynomial smoothing time-varying coefficient models (TVCM) that can be used to select the locally influential covariates at the specific time range and estimate the local covariate effects. Our approach extends the local smoothing for TVCM to high-dimensional longitudinal data and is an alternative to the regularized spline methods studied by Wang et al. (2008) and Xue et al. (2020). To explore the temporal trends of outcome variable and covariates effect in conditional distribution-based model, we propose a two-step regularized smoothing time-varying transformation model. We adopt the iterative algorithm that combines the Majorize-Minimization (MM) algorithm for non-convex penalties with the Newton-Raphson algorithm. Through an application to the large epidemiological study, we demonstrate that our regularized local smoothing method has advantages over the regularized spline methods for being computationally simple and having straightforward clinical interpretations. Our simulation studies suggest that the proposed methods are capable of identifying locally influential predictors and can have consistent estimators of coefficients and conditional distribution functions at different time ranges. The proposed methods provide useful dynamic model-based tools for statistical machine learning with longitudinal data.