Gene association detection via local linear regression method.

Genotype-phenotype (G-P) analyses for complex morphological traits typically utilize simple, predetermined anatomical measures or features derived via unsupervised dimension reduction techniques (e.g. principal component analysis (PCA) or eigen-shapes). Despite the popularity of these approaches, they do not necessarily reveal axes of phenotypic variation that are genetically relevant. Therefore, we introduce a framework to optimize phenotyping for G-P analyses, such as genome-wide association studies (GWAS) of common variants or rare variant association studies (RVAS) of rare variants. Our strategy is two-fold: (i) we construct a multidimensional feature space spanning a wide range of phenotypic variation, and (ii) within this feature space, we use an optimization algorithm to search for directions or feature combinations that are genetically enriched. To test our approach, we examine human facial shape in the context of GWAS and RVAS. In GWAS, we optimize for phenotypes exhibiting high heritability, estimated from either family data or genomic relatedness measured in unrelated individuals. In RVAS, we optimize for the skewness of phenotype distributions, aiming to detect commingled distributions that suggest single or few genomic loci with major effects. We compare our approach with eigen-shapes as baseline in GWAS involving 8246 individuals of European ancestry and in gene-based tests of rare variants with a subset of 1906 individuals. After applying linkage disequilibrium score regression to our GWAS results, heritability-enriched phenotypes yielded the highest SNP heritability, followed by eigen-shapes, while commingling-based traits displayed the lowest SNP heritability. Heritability-enriched phenotypes also exhibited higher discovery rates, identifying the same number of independent genomic loci as eigen-shapes with a smaller effective number of traits. For RVAS, commingling-based traits resulted in more genes passing the exome-wide significance threshold than eigen-shapes, while heritability-enriched phenotypes lead to only a few associations. Overall, our results demonstrate that optimized phenotyping allows for the extraction of genetically relevant traits that can specifically enhance discovery efforts of common and rare variants, as evidenced by their increased power in facial GWAS and RVAS.

Objective: The kernel machine (KM) test reportedly performs well in the set-based association test of rare variants. Many studies have been conducted to measure phenotypes at multiple time points, but the standard KM methodology has only been available for phenotypes at a single time point. In addition, family-based designs have been widely used in genetic association studies; therefore, the data analysis method used must appropriately handle familial relatedness. A rare-variant test does not currently exist for longitudinal data from family samples. Therefore, in this paper, we aim to introduce an association test for rare variants, which includes multiple longitudinal phenotype measurements for either population or family samples. Methods: This approach uses KM regression based on the linear mixed model framework and is applicable to longitudinal data from either population (L-KM) or family samples (LF-KM). Results: In our population-based simulation studies, L-KM has good control of Type I error rate and increased power in all the scenarios we considered compared with other competing methods. Conversely, in the family-based simulation studies, we found an inflated Type I error rate when L-KM was applied directly to the family samples, whereas LF-KM retained the desired Type I error rate and had the best power performance overall. Finally, we illustrate the utility of our proposed LF-KM approach by analyzing data from an association study between rare variants and blood pressure from the Genetic Analysis Workshop 18 (GAW18). Conclusion: We propose a method for rare-variant association testing in population and family samples using phenotypes measured at multiple time points for each subject. The proposed method has the best power performance compared to competing approaches in our simulation study.

In recent years, there has been an increasing interest in detecting disease-related rare variants in sequencing studies. Numerous studies have shown that common variants can only explain a small proportion of the phenotypic variance for complex diseases. More and more evidence suggests that some of this missing heritability can be explained by rare variants. Considering the importance of rare variants, researchers have proposed a considerable number of methods for identifying the rare variants associated with complex diseases. Extensive research has been carried out on testing the association between rare variants and dichotomous, continuous or ordinal traits. So far, however, there has been little discussion about the case in which both genotypes and phenotypes are ordinal variables. This paper introduces a method based on the γ-statistic, called OV-RV, for examining disease-related rare variants when both genotypes and phenotypes are ordinal. At present, little is known about the asymptotic distribution of the γ-statistic when conducting association analyses for rare variants. One advantage of OV-RV is that it provides a robust estimation of the distribution of the γ-statistic by employing the permutation approach proposed by Fisher. We also perform extensive simulations to investigate the numerical performance of OV-RV under various model settings. The simulation results reveal that OV-RV is valid and efficient; namely, it controls the type I error approximately at the pre-specified significance level and achieves greater power at the same significance level. We also apply OV-RV for rare variant association studies of diastolic blood pressure.

In human genome research, genetic association studies of rare variants have been widely studied since the advent of high-throughput DNA sequencing platforms. However, detection of outcome-related rare variants still remains a statistically challenging problem because the number of observed genetic mutations is extremely rare. Recently, a power set-based statistical selection procedure has been proposed to locate both risk and protective rare variants within the outcome-related genes or genetic regions. Although it can perform an individual selection of rare variants, the procedure has a limitation that it cannot measure the certainty of selected rare variants. In this article, we propose a selection probability of individual rare variants, where selection frequencies of rare variants are computed based on bootstrap resampling. Therefore, it can quantify the certainty of both selected and unselected rare variants. Also, a new selection approach using a threshold of selection probability is introduced and compared with some existing selection procedures from extensive simulation studies and real sequencing data analysis. We have demonstrated that the proposed approach outperforms the existing methods in terms of a selection power.

Many common human diseases are complex and are expected to be highly heterogeneous, with multiple causative loci and multiple rare and common variants at some of the causative loci contributing to the risk of these diseases. Data from the genome-wide association studies (GWAS) and metadata such as known gene functions and pathways provide the possibility of identifying genetic variants, genes and pathways that are associated with complex phenotypes. Single-marker-based tests have been very successful in identifying thousands of genetic variants for hundreds of complex phenotypes. However, these variants only explain very small percentages of the heritabilities. To account for the locus- and allelic-heterogeneity, gene-based and pathway-based tests can be very useful in the next stage of the analysis of GWAS data. U-statistics, which summarize the genomic similarity between pair of individuals and link the genomic similarity to phenotype similarity, have proved to be very useful for testing the associations between a set of single nucleotide polymorphisms and the phenotypes. Compared to single marker analysis, the advantages afforded by the U-statistics-based methods is large when the number of markers involved is large. We review several formulations of U-statistics in genetic association studies and point out the links of these statistics with other similarity-based tests of genetic association. Finally, potential application of U-statistics in analysis of the next-generation sequencing data and rare variants association studies are discussed.

Genome-wide association studies (GWAS) and rare variant association studies (RVAS) are applied across many areas of complex disease to analyze variation in whole genomes of thousands of unrelated patients. These approaches are able to identify variants and/or biological pathways which are associated with disease status and, in contrast to traditional linkage studies or candidate gene approaches, do so without requiring multigenerational affected families, prior hypotheses, or known genes of interest. However, the novel associations identified by these methods typically have lower effect sizes than those found in classical family studies. In the motor neuron disease amyotrophic lateral sclerosis (ALS), GWAS, and RVAS have been used to identify multiple disease-associated genes but have not yet resulted in novel therapeutic interventions. There is significant urgency within the ALS community to identify additional genetic markers of disease to uncover novel biological mechanisms, stratify genetic subgroups of disease, and drive drug development. Given the widespread and increasing application of genetic association studies of complex disease, it is important to recognize the strengths and limitations of these approaches. Here, we review ALS gene discovery via GWAS and RVAS.

Gene-environment interactions (G × E) have attracted considerable research interest in the past owing to their scientific and public health implications, but powerful statistical methods are required to successfully track down G × E, particularly at a genome-wide level. Previously, a case-only (CO) design has been proposed as a means to identify G × E with greater efficiency than traditional case-control or cohort studies. However, as with genotype-phenotype association studies themselves, hidden population stratification (PS) can impact the validity of G × E studies using a CO design. Since this problem has been subject to little research to date, we used comprehensive simulation to systematically assess the type I error rate, power and effect size bias of CO studies of G × E in the presence of PS. Three types of PS were considered, namely genetic-only (PSG), environment-only (PSE), and joint genetic and environmental stratification (PSGE). Our results reveal that the type I error rate of an unadjusted Wald test, appropriate for the CO design, would be close to its nominal level (0.05 in our study) as long as PS involves only one interaction partner (i.e., either PSG or PSE). In contrast, if the study population is stratified with respect to both G and E (i.e., if there is PSGE), then the type I error rate is seriously inflated and estimates of the underlying G × E interaction are biased. Comparison of CO to a family-based case-parents design confirmed that the latter is more robust against PSGE, as expected. However, case-parent trios may be particularly unsuitable for G × E studies in view of the fact that they require genotype data from parents and that many diseases with an environmental component are likely to be of late onset. An alternative approach to adjusting for PS is principal component analysis (PCA), which has been widely used for this very purpose in past genome-wide association studies (GWAS). However, resolving genetic PS properly by PCA requires genetic data at the population level, the availability of which would conflict with the basic idea of the CO design. Therefore, we explored three modified Wald test statistics, inspired by the genomic control (GC) approach to GWAS, as an alternative means to allow for PSGE. The modified statistics were benchmarked against a stratified Wald test assuming known population affiliation, which should provide maximum power under PS. Our results confirm that GC is capable of successfully and efficiently correcting the PS-induced inflation of the type I error rate in CO studies of G × E.

Case-control genetic association studies in admixed populations are known to be susceptible to genetic confounding due to population stratification. The transmission/disequilibrium test (TDT) approach can avoid this problem. However, the TDT is expensive and impractical for late-onset diseases. Case-control study designs, in which, cases and controls are matched by admixture, can be an appealing and a suitable alternative for genetic association studies in admixed populations. In this study, we applied this matching strategy when recruiting our African American participants in the Study of African American, Asthma, Genes and Environments. Group admixture in this cohort consists of 83% African ancestry and 17% European ancestry, which was consistent with reports from other studies. By carrying out several complementary analyses, our results show that there is a substructure in the cohort, but that the admixture distributions are almost identical in cases and controls, and also in cases only. We performed association tests for asthma-related traits with ancestry, and only found that FEV(1), a measure for baseline pulmonary function, was associated with ancestry after adjusting for socio-economic and environmental risk factors (P=0.01). We did not observe an excess of type I error rate in our association tests for ancestry informative markers and asthma-related phenotypes when ancestry was not adjusted in the analyses. Furthermore, using the association tests between genetic variants in a known asthma candidate gene, beta(2) adrenergic receptor (beta(2)AR) and DeltaFEF(25-75), an asthma-related phenotype, as an example, we demonstrated population stratification was not a confounder in our genetic association. Our present work demonstrates that admixture-matched case-control strategies can efficiently control population stratification confounding in admixed populations.

DNA methylation is an important epigenetic mechanism that has been linked to complex diseases and is of great interest to researchers as a potential link between genome, environment, and disease. As the scale of DNA methylation association studies approaches that of genome-wide association studies, issues such as population stratification will need to be addressed. It is well-documented that failure to adjust for population stratification can lead to false positives in genetic association studies, but population stratification is often unaccounted for in DNA methylation studies. Here, we propose several approaches to correct for population stratification using principal components (PCs) from different subsets of genome-wide methylation data. We first illustrate the potential for confounding due to population stratification by demonstrating widespread associations between DNA methylation and race in 388 individuals (365 African American and 23 Caucasian). We subsequently evaluate the performance of our PC-based approaches and other methods in adjusting for confounding due to population stratification. Our simulations show that (1) all of the methods considered are effective at removing inflation due to population stratification, and (2) maximum power can be obtained with single-nucleotide polymorphism (SNP)-based PCs, followed by methylation-based PCs, which outperform both surrogate variable analysis and genomic control. Among our different approaches to computing methylation-based PCs, we find that PCs based on CpG sites chosen for their potential to proxy nearby SNPs can provide a powerful and computationally efficient approach to adjust for population stratification in DNA methylation studies when genome-wide SNP data are unavailable.

The recent development of DNA sequencing technology has given rise to many statistical methods for Rare Variant Association Studies (RVASs), such as burden and sequence kernel association tests. However, these methods, which usually require large samples, can lose power in association studies with small samples. In this study, we propose two statistical approaches applicable for RVASs when the sample size is not large. Our approaches are based on the Hamming distance, which compares the dissimilarity of Single Nucleotide Polymorphisms (SNPs) components between cases and controls. Existing Hamming distance-based methods mainly analyse common variants. For rare variant data with a small sample size, we extended two existing methods by using the weight based on minor allele frequency. Through simulation studies, we show that our proposed approaches control type 1 error rates and are more powerful even when given very small sample sizes. They also work well regardless of the direction of causal SNP effects. Applying these methods to real data, we confirmed that they identified true causal genes well. Based on the results of this study, we firmly believe that our proposed methods are powerful for small sample data.

We summarize the work done by the contributors to Group 13 at Genetic Analysis Workshop 17 (GAW17) and provide a synthesis of their data analyses. The Group 13 contributors used a variety of approaches to test associations of both rare variants and common single-nucleotide polymorphisms (SNPs) with the GAW17 simulated traits, implementing analytic methods that incorporate multiallelic genotypes and haplotypes. In addition to using a wide variety of statistical methods and approaches, the contributors exhibited a remarkable amount of flexibility and creativity in coding the variants and their genes and in evaluating their proposed approaches and methods. We describe and contrast their methods along three dimensions: (1) selection and coding of genetic entities for analysis, (2) method of analysis, and (3) evaluation of the results. The contributors consistently presented a strong rationale for using multiallelic analytic approaches. They indicated that power was likely to be increased by capturing the signals of multiple markers within genetic entities defined by sliding windows, haplotypes, genes, functional pathways, and the entire set of SNPs and rare variants taken in aggregate. Despite this variability, the methods were fairly consistent in their ability to identify two associated genes for each simulated trait. The first gene was selected for the largest number of causal alleles and the second for a high-frequency causal SNP. The presumed model of inheritance and choice of genetic entities are likely to have a strong effect on the outcomes of the analyses.

Genetic association studies in practice often involve multiple traits resulting from a common disease mechanism, and samples for such studies are often stratified based on some trait outcomes. In such situations, statistical methods using only one of these traits may be inadequate and lead to under-powered tests for detecting genetic associations. We propose in this article an estimation and testing procedure for evaluating the shared-association of a genetic marker on the joint distribution of multiple traits of a common disease. Specifically, we assume that the disease mechanism involves both quantitative and qualitative traits, and our samples could be stratified based on the qualitative trait. Through a joint likelihood function, we derive a class of estimators and test statistics for evaluating the shared genetic association on both the quantitative and qualitative traits. Our simulation study shows that the joint likelihood test procedure is potentially more powerful than association tests based on separate traits. Application of our proposed procedure is demonstrated through the rheumatoid arthritis data provided by the Genetic Analysis Workshop 16 (GAW16).

Fast and cheaper next-generation sequencing technologies will generate unprecedentedly massive and highly dimensional genetic variation data that allow nearly complete evaluation of genetic variation including both common and rare variants. There are two types of association tests: variant-by-variant test and group test. The variant-by-variant test is designed to test the association of common variants, while the group test is suitable to collectively test the association of multiple rare variants. We propose here a smoothed functional principal component analysis (SFPCA) statistic as a general approach for testing association of the entire allelic spectrum of genetic variation (both common and rare variants), which utilizes the merits of both variant-by-variant analysis and group tests. By intensive simulations, we demonstrate that the SFPCA statistic has the correct type 1 error rates and much higher power than the existing methods to detect association of (1) common variants, (2) rare variants, (3) both common and rare variants and (4) variants with opposite directions of effects. To further evaluate its performance, the SFPCA statistic is applied to ANGPTL4 sequence and six continuous phenotypes data from the Dallas Heart Study as an example for testing association of rare variants and a GWAS of schizophrenia data as an example for testing association of common variants. The results show that the SFPCA statistic has much smaller P-values than many existing statistics in both real data analysis examples.

The HapMap project has given case-control association studies a unique opportunity to uncover the genetic basis of complex diseases. However, persistent issues in such studies remain the proper quantification of, testing for, and correction for population stratification (PS). In this paper, we present the first unified paradigm that addresses all three fundamental issues within one statistical framework. Our unified approach makes use of an omnibus quantity (δ), which can be estimated in a case-control study from suitable null loci. We show how this estimated value can be used to quantify PS, to statistically test for PS, and to correct for PS, all in the context of case-control studies. Moreover, we provide guidelines for interpreting values of δ in association studies (e.g., at α = 0.05, a δ of size 0.416 is small, a δ of size 0.653 is medium, and a δ of size 1.115 is large). A novel feature of our testing procedure is its ability to test for either strictly any PS or only ‘practically important’ PS. We also performed simulations to compare our correction procedure with Genomic Control (GC). Our results show that, unlike GC, it maintains good Type I error rates and power across all levels of PS.

With the completion of the HapMap project1 and the development of technology that allows the examination of ≥1 million genetic polymorphisms at once, genetic association studies are becoming more comprehensive. This article first provides a brief overview of the rationale for genetic association studies; it then discusses the primary features differentiating genetic from standard association studies and emphasizes these differences with an example. Finally, this article reviews methods for addressing 2 of the main pitfalls of genetic association studies: population stratification and multiple testing. The principal focus of this primer is population-based association studies using unrelated individuals. A future article will address family-based linkage and association studies. Traditional epidemiological studies focus on assessing the impact of specific risk factors on disease risk in populations. The goal of a genetic association study is to establish statistical associations between ≥1 genetic polymorphisms and phenotypes or disease states and thus to identify genetic risk factors that can later be studied in a more comprehensive manner using traditional epidemiological methods. Ideally, the statistical analyses brings us to the point where 1 or several genetic variants are identified as the potential functional variants within a gene, so that laboratory scientists can then use experimental methods to determine what functional purpose the variants have and how it might relate to the phenotype. Historically, the term polymorphism has been used to refer to genetic mutations that occur with a frequency ≥1% in the population. This article refers to genomic locations with multiple alleles interchangeably as genetic variants or polymorphisms. Pollex and Hegele2 describe many types of genetic variants found in the human genome and review the current state of knowledge concerning copy number variants and cardiovascular disease. This article focuses on single-nucleotide polymorphisms (SNPs), although much of what is presented is relevant to all types …