Date of Award

2021

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Statistics (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Kui Zhang

Committee Member 1

Qiuying Sha

Committee Member 2

Hairong Wei

Committee Member 3

Shuanglin Zhang

Committee Member 4

Xiao Zhang

Abstract

This dissertation includes three Chapters. A brief description of each chapter is organized as follows.

In Chapter 1, we proposed a new method, called MF-TOWmuT, for genome-wide association studies with multiple genetic variants and multiple phenotypes using family samples. MF-TOWmuT uses kinship matrix to account for sample relatedness. It is worth mentioning that in simulations, we considered hidden polygenic effects and varied the proportion of variance contributed by it to generate phenotypes. Simulation studies show that MF-TOWmuT can preserve the type I error rates and is more powerful than several existing methods in different simulation scenarios, MFTOWmuT is also quite robust to the proportion of variance explained by invisible polygenic effects and to the direction of effects of genetic variants.

In Chapter 2, we proposed a fast and efficient low rank penalized regression with the Elastic Net penalty for the eQTL mapping, called LORSEN. By considering the Elastic Net penalty instead of the L1 penalty, our method can overcome two crucial drawbacks of the L1 penalty, and outperforms two commonly used methods for the eQTL mapping, LORS and FastLORS, in many simulation scenarios in terms of average Area Under the Curve (AUC).

In Chapter 3, we proposed a bipartite network-based penalized regression model for the eQTL mapping, called BiNetPeR. This method takes into account the SNPgene marginal association evidence to construct the SNP-gene bipartite network, then uses such a bipartite network to obtain the projected SNP network. Based on the normalized Laplacian matrix of the projected SNP network, we then formulate the eQTL mapping into a penalized regression model. Our simulation results show that our proposed method can maintain the appropriate false positive rate and outperforms two competing methods for the eQTL mapping, FastLORS and mtLasso2G.

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