Asuman Turkmen

Gene-based partial least-squares approaches for detecting rare variant associations with complex traits.

Genome-wide association studies are largely based on single-nucleotide polymorphisms and rest on the common disease/common variants (single-nucleotide polymorphisms) hypothesis. However, it has been argued in the last few years and is well accepted now that rare variants are valuable for studying common diseases. Although current genome-wide association studies have successfully discovered many genetic variants that are associated with common diseases, detecting associated rare variants remains a great challenge. Here, we propose two partial least-squares approaches to aggregate the signals of many single-nucleotide polymorphisms (SNPs) within a gene to reveal possible genetic effects related to rare variants. The availability of the 1000 Genomes Project offers us the opportunity to evaluate the effectiveness of these two gene-based approaches. Compared to results from a SNP-based analysis, the proposed methods were able to identify some (rare) SNPs that were missed by the SNP-based analysis.

Kullback–Leibler Distance Methods for Detecting Disease Association with Rare Variants from Sequencing Data

Because next generation sequencing technology that can rapidly genotype most genetic variations genome, there is considerable interest in investigating the effects of rare variants on complex diseases. In this paper, we propose four Kullback–Leibler distance‐based Tests (KLTs) for detecting genotypic differences between cases and controls. There are several features that set the proposed tests apart from existing ones. First, by explicitly considering and comparing the distributions of genotypes, existence of variants with opposite directional effects does not compromise the power of KLTs. Second, it is not necessary to set a threshold for rare variants as the KL definition makes it reasonable to consider rare and common variants together without worrying about the contribution from one type overshadowing the other. Third, KLTs are robust to null variants thanks to a built‐in noise fighting mechanism. Finally, correlation among variants is taken into account implicitly so the KLTs work well regardless of the underlying LD structure. Through extensive simulations, we demonstrated good performance of KLTs compared to the sum of squared score test (SSU) and optimal sequence kernel association test (SKAT‐O). Moreover, application to the Dallas Heart Study data illustrates the feasibility and performance of KLTs in a realistic setting.

An optimum projection and noise reduction approach for detecting rare and common variants associated with complex diseases.

Background: Despite the thrilling advances in identifying gene variants that influence common diseases, most of the heritable risk for many common diseases still remains unidentified. One of the possible reasons for this missing heritability is that the genome-wide association study (GWAS) approaches have been focusing on common rather than rare single nucleotide variants (SNVs). Consequently, there is currently a great deal of interest in developing methods that can interrogate rare variants for association with diseases. Methods: We propose a two-step method (termed rPLS) to reveal possible genetic effects related to rare as well as common variants. The procedure starts with removing irrelevant variants using penalized regression (regularization) which is followed by partial least squares (PLS) on the surviving SNVs to find an optimal linear combination of rare and common SNVs within a genomic region that is tested for its association with the trait of interest. Results: Simulation settings based on the 1000 Genomes sequencing data and reflecting real situations demonstrated that rPLS performs well compared to existing methods especially when there are a large number of noncausal variants (both rare and common) present in the gene and when causal SNVs have different effect sizes and directions.

Blocking Approach for Identification of Rare Variants in Family-Based Association Studies

With the advent of next-generation sequencing technology, rare variant association analysis is increasingly being conducted to identify genetic variants associated with complex traits. In recent years, significant effort has been devoted to develop powerful statistical methods to test such associations for population-based designs. However, there has been relatively little development for family-based designs although family data have been shown to be more powerful to detect rare variants. This study introduces a blocking approach that extends two popular family-based common variant association tests to rare variants association studies. Several options are considered to partition a genomic region (gene) into “independent” blocks by which information from SNVs is aggregated within a block and an overall test statistic for the entire genomic region is calculated by combining information across these blocks. The proposed methodology allows different variants to have different directions (risk or protective) and specification of minor allele frequency threshold is not needed. We carried out a simulation to verify the validity of the method by showing that type I error is well under control when the underlying null hypothesis and the assumption of independence across blocks are satisfied. Further, data from the Genetic Analysis Workshop are utilized to illustrate the feasibility and performance of the proposed methodology in a realistic setting.

Population-Based Association and Gene by Environment Interactions in Genetic Analysis Workshop 18

In the past decade, genome‐wide association studies have been successful in identifying genetic loci that play a role in many complex diseases. Despite this, it has become clear that for many traits, investigation of single common variants does not give a complete picture of the genetic contribution to the phenotype. Therefore a number of new approaches are currently being investigated to further the search for susceptibility loci or regions. We summarize the contributions to Genetic Analysis Workshop 18 (GAW18) that concern this search using methods for population‐based association analysis. Many of the members of our GAW18 working group made use of data types that have only recently become available through the use of next‐generation sequencing technologies, with many focusing on the investigation of rare variants instead of or in combination with common variants. Some contributors used a haplotype‐based approach, which to date has been used relatively infrequently but may become more important for analyzing rare variant association data. Others analyzed gene‐gene or gene‐environment interactions, where novel statistical approaches were needed to make the best use of the available information without requiring an excessive computational burden. GAW18 provided participants with the chance to make use of state‐of‐the‐art data, statistical techniques, and technology. We report here some of the experiences and conclusions that were reached by workshop participants who analyzed the GAW18 data as a population‐based association study.

The Effect of Outliers in Independent Component Analysis

SYNOPTIC ABSTRACT Independent Component Analysis (ICA) is a statistical and computational technique for decomposing a complex multivariate data into independent components. Several methods have been proposed to find the independent components and they all assume the homogeneity (free of outliers) of the data, which is almost never true in practice. In this study, we propose an algorithm to improve ICA performance in the presence of outliers by introducing an additional step in the data pre-processing. We also show, by using the simulated and real mixed data sets, that the proposed algorithm provides a significant improvement in finding more accurate independent components in the presence of outliers.

Outlier Resistant Estimation in Difference-Based Semiparametric Partially Linear Models

Partially linear models are extensions of linear models that include a nonparametric function of some covariate allowing an adequate and more flexible handling of explanatory variables than in linear models. The difference-based estimation in partially linear models is an approach designed to estimate parametric component by using the ordinary least squares estimator after removing the nonparametric component from the model by differencing. However, it is known that least squares estimates do not provide useful information for the majority of data when the error distribution is not normal, particularly when the errors are heavy-tailed and when outliers are present in the dataset. This paper aims to find an outlier-resistant fit that represents the information in the majority of the data by robustly estimating the parametric and the nonparametric components of the partially linear model. Simulations and a real data example are used to illustrate the feasibility of the proposed methodology and to compare it with the classical difference-based estimator when outliers exist.

Rank-based ridge estimation in multiple linear regression

Multicollinearity and model misspecification are frequently encountered problems in practice that produce undesirable effects on classical ordinary least squares (OLS) regression estimator. The ridge regression estimator is an important tool to reduce the effects of multicollinearity, but it is still sensitive to a model misspecification of error distribution. Although rank-based statistical inference has desirable robustness properties compared to the OLS procedures, it can be unstable in the presence of multicollinearity. This paper introduces a rank regression estimator for regression parameters and develops tests for general linear hypotheses in a multiple linear regression model. The proposed estimator and the tests have desirable robustness features against the multicollinearity and model misspecification of error distribution. Asymptotic behaviours of the proposed estimator and the test statistics are investigated. Real and simulated data sets are used to demonstrate the feasibility and the performance of the estimator and the tests.

Are rare variants really independent

Recent advances in genotyping with high‐density markers allow researchers access to genomic variants including rare ones. Linkage disequilibrium (LD) is widely used to provide insight into evolutionary history. It is also the basis for association mapping in humans and other species. Better understanding of the genomic LD structure may lead to better‐informed statistical tests that can improve the power of association studies. Although rare variant associations with common diseases (RVCD) have been extensively studied recently, there is very limited understanding, and even controversial view of LD structures among rare variants and between rare and common variants. In fact, many popular RVCD tests make the assumptions that rare variants are independent. In this report, we show that two commonly used LD measures are not capable of detecting LD when rare variants are involved. We present this argument from two perspectives, both the LD measures themselves and the computational issues associated with them. To address these issues, we propose an alternative LD measure, the polychoric correlation, that was originally designed for detecting associations among categorical variables. Using simulated as well as the 1000 Genomes data, we explore the performances of LD measures in detail and discuss their implications in association studies.

Identifying rare variant associations in population-based and family-based designs

For almost all complex traits studied in humans, the identified genetic variants discovered to date have accounted for only a small portion of the estimated trait heritability. Consequently, several methods have been developed to identify rare single-nucleotide variants associated with complex traits for population-based designs. Because rare disease variants tend to be enriched in families containing multiple affected individuals, family-based designs can play an important role in the identification of rare causal variants. In this study, we utilize Genetic Analysis Workshop 18 simulated data to examine the performance of some existing rare variant identification methods for unrelated individuals, including our recent method (rPLS). The simulated data is used to investigate whether there is an advantage to using family data compared to case-control data. The results indicate that population-based methods suffer from power loss, especially when the sample size is small. The family-based method employed in this paper results in higher power but fails to control type I error. Our study also highlights the importance of the phenotype choice, which can affect the power of detecting causal genes substantially.