Mathematical Sciences Department PhD Dissertation Defense
Shuaichuan Feng, Statistics PhD Candidate
Thursday, July 31, 2025
10:00 am - 12:00 pm
Stratton Hall 202
Zoom: 995 8134 0101, https://wpi.zoom.us/j/99581340101
Dissertation Committee:
Prof. Zheyang Wu, WPI (Advisor)
Prof. Frank Zou, WPI
Prof. Fangfang Wang, WPI
Prof. Charlotte Fowler, WPI
Prof. Dmitry Korkin – Department of Computer Science, WPI
Title: Innovative Statistical Methods for Genetic Data Analysis: Heritability Estimation and Rare Variant Analysis by Discrete PValue Combination
Abstract: Understanding the genetic basis of complex traits and diseases remains a central challenge in statistical genetics. This dissertation addresses two key problems in the analysis of genetic data: the estimation of SNP-based heritability and the combination of discrete p-values in rare variant association studies. The first part of the work focuses on developing and evaluating statistical methods for heritability estimation using GWAS summary statistics and linkage disequilibrium (LD) information. A central contribution is a reduced-rank likelihood-based estimator that leverages the eigen decomposition of the LD matrix to construct an efficient and flexible likelihood framework. This approach improves accuracy and interpretability across both gene-level and genomewide settings. We also explore alternative strategies, including generalized linear models with gamma-distributed residuals and multiple linear regression with regularization. These methods are compared under diverse modeling assumptions, providing a comprehensive perspective on heritability inference. The second part investigates the use of discrete p-value combination methods in rare variant association studies, where the discreteness of test statistics presents unique statistical challenges. We examine a family of gamma-based combination statistics and investigate adjustment techniques grounded in the minimum Wasserstein distance framework. These methods are applied to realistic rare variant analysis scenarios, such as those involving binary phenotypes and low allele counts, where conventional approaches may fail to control type I error. To support future applications, we also provide an R package and a reproducible analysis pipeline tailored to discrete data contexts.