Title: On Identifying Rare Variants for Complex Human Traits
Description: This thesis focuses on developing novel statistical tests for rare variants association analysis incorporating both marginal effects and interaction effects among rare variants. Compared with common variants, rare variants have lower minor allele frequencies (typically less than 5%), and hence traditional association tests for common variants will lose power for rare variants. Therefore, there is a pressing need of new analytical tools to tackle the problem of rare variants association with complex human traits. Several collapsing methods have been proposed that aggregate information of rare variants in a region and test them together. They can be divided into burden tests and non-burden tests based on their aggregation strategies. They are all variations of regression-based methods with the assumption that the phenotype is associated with the genotype via a (linear) regression model. Most of these methods consider only marginal effects of rare variants and fail to take into account gene-gene and gene-environmental interactive effects, which are ubiquitous and are of utmost importance in biological systems.

In this thesis, we propose a summation of partition approach (SPA) -- a nonparametric strategy for rare variants association analysis. Extensive simulation studies show that SPA is powerful in detecting not only marginal effects but also gene-gene interaction effects of rare variants. Moreover, extensions of SPA are able to detect gene-environment interactions and other interactions existing in complicated biological system as well. We are also able to obtain the asymptotic behavior of the marginal SPA score, which guarantees the power of the proposed method. Inspired by the idea of stepwise variable selection, a significance-based backward dropping algorithm(SDA) is proposed to locate truly influential rare variants in a genetic region that has been identified significant. Unlike traditional backward dropping approaches which remove the least significant variables first, SDA introduces the idea of eliminating the most significant variable at each round. The removed variables are collected and their effects are evaluated by an influence ratio score -- the relative p-value change.

Our simulation studies show that SDA is powerful to detect causal variables and SDA has lower false discovery rate than LASSO. We also demonstrate our method using the dataset provided by Genetic Analysis Workshop (GAW) 17 and the results support the superiority of SDA over LASSO. The general partition-retention framework can also be applied to detect gene-environmental interaction effects for common variants. We demonstrate this method using the dataset from Genetic Analysis Workshop (GAW) 18. Our nonparametric approach is able to identify a lot more possible influential gene-environmental pairs than traditional linear regression models. We propose in this thesis a "SPA-SDA" two step approach for rare variants association analysis at genomic scale: first identify significant regions of moderate sizes using SPA, and then apply SDA to the identified regions to pinpoint truly influential variables. This approach is computationally efficient for genomic data and it has the capacity to detect gene-gene and gene-environmental interactions.