Details

Autor(en) / Beteiligte

• Zu, Tianhai

Titel

Two Essays on Ultra-High-Dimensional Longitudinal Data Analysis and Network Bootstrapping Method

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2023

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• The increasing prevalence of high-dimensional data in many scientific fields presents both challenges and opportunities for researchers. It requires the development of new methods and techniques to analyze and make sense of such data. This dissertation comprises two essays that tackle the challenge of analyzing high-dimensional data.In Essay I, we develop a novel penalized quantile generalized estimating equations (GEE) approach and apply it to genetics research. Despite major advances in research and treatment, identifying important genotype risk factors for high blood pressure remains challenging. Traditional genome-wide association studies (GWAS) focus on one single nucleotide polymorphism (SNP) at a time. We aim to select among over half a million SNPs along with time-varying phenotype variables via simultaneous modeling and variable selection, focusing on the most dangerous blood pressure levels at high quantiles. Taking advantage of rich data from a large-scale public health study, we develop and apply a novel penalized quantile generalized estimating equations (GEE) approach, incorporating several key aspects including ultra-high dimensional genetic SNPs, the longitudinal nature of blood pressure measurements, time-varying covariates, and conditional high quantiles of blood pressure. Importantly, we identify interesting new SNPs and some plausible SNP pathways for high blood pressure. Besides, we find blood pressure levels are likely heterogeneous, where the important risk factors identified differ among quantiles. This comprehensive picture of conditional quantiles of blood pressure can potentially allow more insights and targeted treatments. Challenges in both computation and theory arise due to the non-smooth objective function of conditional quantiles, non-convex penalty function, ultra-high dimensional SNPs, and the longitudinal data. We provide an efficient computational algorithm and establish difficult theoretical properties including consistency, asymptotic normality, and the oracle property in ultra-high dimensions for the quantile penalized GEE estimators. Moreover, we establish consistency for high-dimensional BIC. Simulation studies show the promise of the proposed approach.In Essay II, we propose a new bootstrap method for conducting inference on network parameters. Since the sampling distribution of the statistic is often unknown, we need to rely on bootstrap. However, due to the complex dependence structure among vertices, existing bootstrap methods often yield unsatisfactory performance, especially under small or moderate sample sizes. To this end, we propose a new network bootstrap procedure, termed local bootstrap, to estimate the standard errors of network statistics. We propose to resample the observed vertices along with their neighbor sets, and reconstruct the edges between the resampled vertices by drawing from the set of edges connecting their neighbor sets. We justify the proposed method theoretically with desirable asymptotic properties for statistics such as motif density, and demonstrate its excellent numerical performance in small and moderate sample sizes. Our method includes several existing methods as special cases, such as the empirical graphon bootstrap. We investigate the advantages of the proposed methods over the existing methods through the lens of edge randomness, vertex heterogeneity, and neighbor set size, which shed some light on the complex issue of network bootstrapping.