Date of Award


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

Yeonwoo Rho

Committee Member 2

Hairong Wei


Genome-wide association studies (GWAS) have become a very effective research tool to identify genetic variants of underlying various complex diseases. In spite of the success of GWAS in identifying thousands of reproducible associations between genetic variants and complex disease, in general, the association between genetic variants and a single phenotype is usually weak. It is increasingly recognized that joint analysis of multiple phenotypes can be potentially more powerful than the univariate analysis, and can shed new light on underlying biological mechanisms of complex diseases. Therefore, developing statistical methods to test for genetic association with multiple phenotypes has become increasingly important. This dissertation contains three chapters and the three chapters include three new methods we developed for jointly analyzing multiple phenotypes.

In the first chapter of this dissertation, we propose an Adaptive Fisher’s Combination (AFC) method for joint analysis of multiple phenotypes in association studies. The AFC method combines p-values obtained in standard univariate GWAS by using the optimal number of p-values which is determined by the data. In the second chapter, we propose an Allele-Based Clustering (ABC) approach for the joint analysis of multiple non-normal phenotypes in association studies. In the ABC method, we consider the alleles at a SNP of interest as a dependent variable with two classes, and the correlated phenotypes as predictors to predict the alleles at the SNP of interest. In the third chapter, we develop a novel variable reduction method using hierarchical clustering method (HCM) for joint analysis of multiple phenotypes in association studies. HCM involves two steps. The first step applies a dimension reduction technique by using a representative phenotype for each cluster of phenotypes. Then, existing methods are used in the second step to test the association between genetic variants and the representative phenotypes rather than the individual phenotypes. We perform extensive simulations to evaluate performances of AFC, ABC, and HCM methods and compare the powers of our methods with the powers of some existing methods. Our simulation studies show that the proposed methods have correct type I error rates and are either the most powerful test or comparable with the most powerful test. Finally, we illustrate our proposed methodologies AFC and HCM by analyzing whole-genome genotyping data from a lung function study. The results of real data analysis demonstrated that the proposed methods have great potential in GWAS on complex diseases with multiple phenotypes.