Date of Award

2018

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Shuanglin Zhang

Advisor 2

Qiuying Sha

Committee Member 1

Kui Zhang

Committee Member 2

Laura Brown

Abstract

This dissertation includes three papers with each distributed in one chapter.

In chapter 1, we proposed an Adaptive Weighting Reverse Regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compared the performance of AWRR with canonical correlation analysis (CCA), Single-TOW, and the Weighted Sum Reverse Regression (WSRR). Our results showed that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most scenarios, AWRR is more powerful than Single-TOW and WSRR.

In chapter 2, we proposed an “optimal” maximum heritability test (MHT-O) to test the association between multiple traits and a single variant. MHT-O includes a procedure of deleting traits that have weak or no association with the variant. Using extensive simulation studies, we compared the performance of MHT-O with MHT, Trait-based Association Test uses Extended Simes procedure (TATES), SUM_SCORE and MANOVA. Our results showed that, in all of the simulation scenarios, MHT-O is either the most powerful test or comparable to the most powerful test among the five tests we compared.

In chapter 3, we developed a statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is robust to the directions of effects of causal variants and is applicable to different types of traits. Using extensive simulation studies, we compared the performance of TOWmuT with the following five existing methods: gene association with multiple traits (GAMuT), multiple sequence kernel association test (MSKAT), adaptive weighting reverse regression (AWRR), single-TOW, and MANOVA. Our results showed that, in all of the simulation scenarios, TOWmuT has correct type I error rates and is consistently more powerful than the other five tests. We also illustrated the usefulness of TOWmuT by analyzing a whole-genome genotyping data from a lung function study.

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