Development and Application of Genomic Control Methods for Genome-Wide Association Studies Using Non-Additive Models

Genome-wide association studies (GWAS) comprise a powerful tool for mapping genes of complex traits. However, an inflation of the test statistic can occur because of population substructure or cryptic relatedness, which could cause spurious associations. If information on a large number of genetic markers is available, adjusting the analysis results by using the method of genomic control (GC) is possible. GC was originally proposed to correct the Cochran-Armitage additive trend test. For non-additive models, correction has been shown to depend on allele frequencies. Therefore, usage of GC is limited to situations where allele frequencies of null markers and candidate markers are matched. In this work, we extended the capabilities of the GC method for non-additive models, which allows us to use null markers with arbitrary allele frequencies for GC. Analytical expressions for the inflation of a test statistic describing its dependency on allele frequency and several population parameters were obtained for recessive, dominant, and over-dominant models of inheritance. We proposed a method to estimate these required population parameters. Furthermore, we suggested a GC method based on approximation of the correction coefficient by a polynomial of allele frequency and described procedures to correct the genotypic (two degrees of freedom) test for cases when the model of inheritance is unknown. Statistical properties of the described methods were investigated using simulated and real data. We demonstrated that all considered methods were effective in controlling type 1 error in the presence of genetic substructure. The proposed GC methods can be applied to statistical tests for GWAS with various models of inheritance. All methods developed and tested in this work were implemented using R language as a part of the GenABEL package.     

Comparison of Methods to Account for Relatedness in Genome-Wide Association Studies with Family-Based Data

Approaches based on linear mixed models (LMMs) have recently gained popularity for modelling population substructure and relatedness in genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it is not always clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several LMM approaches (and software implementations, including EMMAX, GenABEL, FaST-LMM, Mendel, GEMMA and MMM) via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals (1972 genotyped). The implementations differ in precise details of methodology implemented and through various user-chosen options such as the method and number of SNPs used to estimate the kinship (relatedness) matrix. We investigate sensitivity to these choices and the success (or otherwise) of the approaches in controlling the overall genome-wide error-rate for both real and simulated phenotypes. We compare the LMM results to those obtained using traditional family-based association tests (based on transmission of alleles within pedigrees) and to alternative approaches implemented in the software packages MQLS, ROADTRIPS and MASTOR. We find strong concordance between the results from different LMM approaches, and all are successful in controlling the genome-wide error rate (except for some approaches when applied naively to longitudinal data with many repeated measures). We also find high correlation between LMMs and alternative approaches (apart from transmission-based approaches when applied to SNPs with small or non-existent effects). We conclude that LMM approaches perform well in comparison to competing approaches. Given their strong concordance, in most applications, the choice of precise LMM implementation cannot be based on power/type I error considerations but must instead be based on considerations such as speed and ease-of-use.     

On the Analysis of Genome-Wide Association Studies in Family-Based Designs: A Universal,Robust Analysis Approach and an Application to Four Genome-Wide Association Studies

For genome-wide association studies in family-based designs, we propose a new, universally applicable approach. The new test statistic exploits all available information about the association, while, by virtue of its design, it maintains the same robustness against population admixture as traditional family-based approaches that are based exclusively on the within-family information. The approach is suitable for the analysis of almost any trait type, e.g. binary, continuous, time-to-onset, multivariate, etc., and combinations of those. We use simulation studies to verify all theoretically derived properties of the approach, estimate its power, and compare it with other standard approaches. We illustrate the practical implications of the new analysis method by an application to a lung-function phenotype, forced expiratory volume in one second (FEV1) in 4 genome-wide association studies.     

Penalized Multimarker vs. Single-Marker Regression Methods for Genome-Wide Association Studies of Quantitative Traits

The data from genome-wide association studies (GWAS) in humans are still predominantly analyzed using single-marker association methods. As an alternative to single-marker analysis (SMA), all or subsets of markers can be tested simultaneously. This approach requires a form of penalized regression (PR) as the number of SNPs is much larger than the sample size. Here we review PR methods in the context of GWAS, extend them to perform penalty parameter and SNP selection by false discovery rate (FDR) control, and assess their performance in comparison with SMA. PR methods were compared with SMA, using realistically simulated GWAS data with a continuous phenotype and real data. Based on these comparisons our analytic FDR criterion may currently be the best approach to SNP selection using PR for GWAS. We found that PR with FDR control provides substantially more power than SMA with genome-wide type-I error control but somewhat less power than SMA with Benjamini–Hochberg FDR control (SMA-BH). PR with FDR-based penalty parameter selection controlled the FDR somewhat conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on SNP selection with FDR control. Incorporating linkage disequilibrium into the penalization by adapting penalties developed for covariates measured on graphs can improve power but also generate more false positives or wider regions for follow-up. We recommend the elastic net with a mixing weight for the Lasso penalty near 0.5 as the best method.     

On Quality Control Measures in Genome-Wide Association Studies: A Test to Assess the Genotyping Quality of Individual Probands in Family-Based Association Studies and an Application to the HapMap Data

Allele transmissions in pedigrees provide a natural way of evaluating the genotyping quality of a particular proband in a family-based, genome-wide association study. We propose a transmission test that is based on this feature and that can be used for quality control filtering of genome-wide genotype data for individual probands. The test has one degree of freedom and assesses the average genotyping error rate of the genotyped SNPs for a particular proband. As we show in simulation studies, the test is sufficiently powerful to identify probands with an unreliable genotyping quality that cannot be detected with standard quality control filters. This feature of the test is further exemplified by an application to the third release of the HapMap data. The test is ideally suited as the final layer of quality control filters in the cleaning process of genome-wide association studies. It identifies probands with insufficient genotyping quality that were not removed by standard quality control filtering.     

High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

We consider the problem of high-dimensional regression under non-constant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows non-constant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.     

Novel Genetic Analysis for Case-Control Genome-Wide Association Studies: Quantification of Power and Genomic Prediction Accuracy

Genome-wide association studies (GWAS) are routinely conducted for both quantitative and binary (disease) traits. We present two analytical tools for use in the experimental design of GWAS. Firstly, we present power calculations quantifying power in a unified framework for a range of scenarios. In this context we consider the utility of quantitative scores (e.g. endophenotypes) that may be available on cases only or both cases and controls. Secondly, we consider, the accuracy of prediction of genetic risk from genome-wide SNPs and derive an expression for genomic prediction accuracy using a liability threshold model for disease traits in a case-control design. The expected values based on our derived equations for both power and prediction accuracy agree well with observed estimates from simulations.     

Commercially Available Outbred Mice for Genome-Wide Association Studies

Genome-wide association studies using commercially available outbred mice can detect genes involved in phenotypes of biomedical interest. Useful populations need high-frequency alleles to ensure high power to detect quantitative trait loci (QTLs), low linkage disequilibrium between markers to obtain accurate mapping resolution, and an absence of population structure to prevent false positive associations. We surveyed 66 colonies for inbreeding, genetic diversity, and linkage disequilibrium, and we demonstrate that some have haplotype blocks of less than 100 Kb, enabling gene-level mapping resolution. The same alleles contribute to variation in different colonies, so that when mapping progress stalls in one, another can be used in its stead. Colonies are genetically diverse: 45% of the total genetic variation is attributable to differences between colonies. However, quantitative differences in allele frequencies, rather than the existence of private alleles, are responsible for these population differences. The colonies derive from a limited pool of ancestral haplotypes resembling those found in inbred strains: over 95% of sequence variants segregating in outbred populations are found in inbred strains. Consequently it is possible to impute the sequence of any mouse from a dense SNP map combined with inbred strain sequence data, which opens up the possibility of cataloguing and testing all variants for association, a situation that has so far eluded studies in completely outbred populations. We demonstrate the colonies'' potential by identifying a deletion in the promoter of H2-Ea as the molecular change that strongly contributes to setting the ratio of CD4+ and CD8+ lymphocytes.     

A Multiple Imputation Approach to Regression Analysis for Doubly Censored Data with Application to AIDS Studies

Sun, Liao, and Pagano (1999) proposed an interesting estimating equation approach to Cox regression with doubly censored data. Here we point out that a modification of their proposal leads to a multiple imputation approach, where the double censoring is reduced to single censoring by imputing for the censored initiating times. For each imputed data set one can take advantage of many existing techniques and software for singly censored data. Under the general framework of multiple imputation, the proposed method is simple to implement and can accommodate modeling issues such as model checking, which has not been adequately discussed previously in the literature for doubly censored data. Here we illustrate our method with an application to a formal goodness-of-fit test and a graphical check for the proportional hazards model for doubly censored data. We reanalyze a well-known AIDS data set.     

Genome-Wide Association Study for Incident Myocardial Infarction and Coronary Heart Disease in Prospective Cohort Studies: The CHARGE Consortium

Background

Data are limited on genome-wide association studies (GWAS) for incident coronary heart disease (CHD). Moreover, it is not known whether genetic variants identified to date also associate with risk of CHD in a prospective setting.

Methods

We performed a two-stage GWAS analysis of incident myocardial infarction (MI) and CHD in a total of 64,297 individuals (including 3898 MI cases, 5465 CHD cases). SNPs that passed an arbitrary threshold of 5×10⁻⁶ in Stage I were taken to Stage II for further discovery. Furthermore, in an analysis of prognosis, we studied whether known SNPs from former GWAS were associated with total mortality in individuals who experienced MI during follow-up.

Results

In Stage I 15 loci passed the threshold of 5×10⁻⁶; 8 loci for MI and 8 loci for CHD, for which one locus overlapped and none were reported in previous GWAS meta-analyses. We took 60 SNPs representing these 15 loci to Stage II of discovery. Four SNPs near QKI showed nominally significant association with MI (p-value<8.8×10⁻³) and three exceeded the genome-wide significance threshold when Stage I and Stage II results were combined (top SNP rs6941513: p = 6.2×10⁻⁹). Despite excellent power, the 9p21 locus SNP (rs1333049) was only modestly associated with MI (HR = 1.09, p-value = 0.02) and marginally with CHD (HR = 1.06, p-value = 0.08). Among an inception cohort of those who experienced MI during follow-up, the risk allele of rs1333049 was associated with a decreased risk of subsequent mortality (HR = 0.90, p-value = 3.2×10⁻³).

Conclusions

QKI represents a novel locus that may serve as a predictor of incident CHD in prospective studies. The association of the 9p21 locus both with increased risk of first myocardial infarction and longer survival after MI highlights the importance of study design in investigating genetic determinants of complex disorders.     

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

The prevailing method of analyzing GWAS data is still to test each marker individually, although from a statistical point of view it is quite obvious that in case of complex traits such single marker tests are not ideal. Recently several model selection approaches for GWAS have been suggested, most of them based on LASSO-type procedures. Here we will discuss an alternative model selection approach which is based on a modification of the Bayesian Information Criterion (mBIC2) which was previously shown to have certain asymptotic optimality properties in terms of minimizing the misclassification error. Heuristic search strategies are introduced which attempt to find the model which minimizes mBIC2, and which are efficient enough to allow the analysis of GWAS data. Our approach is implemented in a software package called MOSGWA. Its performance in case control GWAS is compared with the two algorithms HLASSO and d-GWASelect, as well as with single marker tests, where we performed a simulation study based on real SNP data from the POPRES sample. Our results show that MOSGWA performs slightly better than HLASSO, where specifically for more complex models MOSGWA is more powerful with only a slight increase in Type I error. On the other hand according to our simulations GWASelect does not at all control the type I error when used to automatically determine the number of important SNPs. We also reanalyze the GWAS data from the Wellcome Trust Case-Control Consortium and compare the findings of the different procedures, where MOSGWA detects for complex diseases a number of interesting SNPs which are not found by other methods.     

Exploiting Population Samples to Enhance Genome-Wide Association Studies of Disease

It is widely acknowledged that genome-wide association studies (GWAS) of complex human disease fail to explain a large portion of heritability, primarily due to lack of statistical power—a problem that is exacerbated when seeking detection of interactions of multiple genomic loci. An untapped source of information that is already widely available, and that is expected to grow in coming years, is population samples. Such samples contain genetic marker data for additional individuals, but not their relevant phenotypes. In this article we develop a highly efficient testing framework based on a constrained maximum-likelihood estimate in a case–control–population setting. We leverage the available population data and optional modeling assumptions, such as Hardy–Weinberg equilibrium (HWE) in the population and linkage equilibrium (LE) between distal loci, to substantially improve power of association and interaction tests. We demonstrate, via simulation and application to actual GWAS data sets, that our approach is substantially more powerful and robust than standard testing approaches that ignore or make naive use of the population sample. We report several novel and credible pairwise interactions, in bipolar disorder, coronary artery disease, Crohn’s disease, and rheumatoid arthritis.     

Analysis of Genome-Wide Association Studies with Multiple Outcomes Using Penalization

Genome-wide association studies have been extensively conducted, searching for markers for biologically meaningful outcomes and phenotypes. Penalization methods have been adopted in the analysis of the joint effects of a large number of SNPs (single nucleotide polymorphisms) and marker identification. This study is partly motivated by the analysis of heterogeneous stock mice dataset, in which multiple correlated phenotypes and a large number of SNPs are available. Existing penalization methods designed to analyze a single response variable cannot accommodate the correlation among multiple response variables. With multiple response variables sharing the same set of markers, joint modeling is first employed to accommodate the correlation. The group Lasso approach is adopted to select markers associated with all the outcome variables. An efficient computational algorithm is developed. Simulation study and analysis of the heterogeneous stock mice dataset show that the proposed method can outperform existing penalization methods.     

A Novel Test for Gene-Ancestry Interactions in Genome-Wide Association Data

Genome-wide association study (GWAS) data on a disease are increasingly available from multiple related populations. In this scenario, meta-analyses can improve power to detect homogeneous genetic associations, but if there exist ancestry-specific effects, via interactions on genetic background or with a causal effect that co-varies with genetic background, then these will typically be obscured. To address this issue, we have developed a robust statistical method for detecting susceptibility gene-ancestry interactions in multi-cohort GWAS based on closely-related populations. We use the leading principal components of the empirical genotype matrix to cluster individuals into “ancestry groups” and then look for evidence of heterogeneous genetic associations with disease or other trait across these clusters. Robustness is improved when there are multiple cohorts, as the signal from true gene-ancestry interactions can then be distinguished from gene-collection artefacts by comparing the observed interaction effect sizes in collection groups relative to ancestry groups. When applied to colorectal cancer, we identified a missense polymorphism in iron-absorption gene CYBRD1 that associated with disease in individuals of English, but not Scottish, ancestry. The association replicated in two additional, independently-collected data sets. Our method can be used to detect associations between genetic variants and disease that have been obscured by population genetic heterogeneity. It can be readily extended to the identification of genetic interactions on other covariates such as measured environmental exposures. We envisage our methodology being of particular interest to researchers with existing GWAS data, as ancestry groups can be easily defined and thus tested for interactions.     

Conditional Random Fields for Fast, Large-Scale Genome-Wide Association Studies

Understanding the role of genetic variation in human diseases remains an important problem to be solved in genomics. An important component of such variation consist of variations at single sites in DNA, or single nucleotide polymorphisms (SNPs). Typically, the problem of associating particular SNPs to phenotypes has been confounded by hidden factors such as the presence of population structure, family structure or cryptic relatedness in the sample of individuals being analyzed. Such confounding factors lead to a large number of spurious associations and missed associations. Various statistical methods have been proposed to account for such confounding factors such as linear mixed-effect models (LMMs) or methods that adjust data based on a principal components analysis (PCA), but these methods either suffer from low power or cease to be tractable for larger numbers of individuals in the sample. Here we present a statistical model for conducting genome-wide association studies (GWAS) that accounts for such confounding factors. Our method scales in runtime quadratic in the number of individuals being studied with only a modest loss in statistical power as compared to LMM-based and PCA-based methods when testing on synthetic data that was generated from a generalized LMM. Applying our method to both real and synthetic human genotype/phenotype data, we demonstrate the ability of our model to correct for confounding factors while requiring significantly less runtime relative to LMMs. We have implemented methods for fitting these models, which are available at http://www.microsoft.com/science.     

Statistical Power of Model Selection Strategies for Genome-Wide Association Studies

Genome-wide association studies (GWAS) aim to identify genetic variants related to diseases by examining the associations between phenotypes and hundreds of thousands of genotyped markers. Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level. Although a number of model selection methods have been proposed in the literature, including marginal search, exhaustive search, and forward search, their relative performance has only been evaluated through limited simulations due to the lack of an analytical approach to calculating the power of these methods. This article develops a novel statistical approach for power calculation, derives accurate formulas for the power of different model selection strategies, and then uses the formulas to evaluate and compare these strategies in genetic model spaces. In contrast to previous studies, our theoretical framework allows for random genotypes, correlations among test statistics, and a false-positive control based on GWAS practice. After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models. For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy. An example is provided for the application of our approach to empirical research. The statistical approach used in our derivations is general and can be employed to address the model selection problems in other random predictor settings. We have developed an R package markerSearchPower to implement our formulas, which can be downloaded from the Comprehensive R Archive Network (CRAN) or http://bioinformatics.med.yale.edu/group/.