Improved correction for population stratification in genome-wide association studies by identifying hidden population structures

Hidden population substructure can cause population stratification and lead to false-positive findings in population-based genome-wide association (GWA) studies. Given a large panel of markers scanned in a GWA study, it becomes increasingly feasible to uncover the hidden population substructure within the study sample based on measured genotypes across the genome. Recognizing that population substructure can be displayed as clustered and/or continuous patterns of genetic variation, we propose a method that aims at the detection and correction of the confounding effect resulting from both patterns of population substructure. The proposed method is an extension of the EIGENSTRAT method (Price et al. [2006] Nat Genet 38:904-909). This approach is computationally feasible and easily applied to large-scale GWA studies. We show through simulation studies that, compared with the EIGENSTRAT method, the new method requires a smaller number of markers and yields a more appropriate correction for population stratification.     

Testing for genetic association in the presence of population stratification in genome‐wide association studies

Genome‐wide case‐control association study is gaining popularity, thanks to the rapid development of modern genotyping technology. In such studies, population stratification is a potential concern especially when the number of study subjects is large as it can lead to seriously inflated false‐positive rates. Current methods addressing this issue are still not completely immune to excess false positives. A simple method that corrects for population stratification is proposed. This method modifies a test statistic such as the Armitage trend test by using an additive constant that measures the variation of the effect size confounded by population stratification across genomic control (GC) markers. As a result, the original statistic is deflated by a multiplying factor that is specific to the marker being tested for association. This deflating multiplying factor is guaranteed to be larger than 1. These properties are in contrast to the conventional GC method where the original statistic is deflated by a common factor regardless of the marker being tested and the deflation factor may turn out to be less than 1. The new method is introduced first for regular case‐control design and then for other situations such as quantitative traits and the presence of covariates. Extensive simulation study indicates that this new method provides an appealing alternative for genetic association analysis in the presence of population stratification. Genet. Epidemiol. 33:637–645, 2009. © 2009 Wiley‐Liss, Inc.     

Using ancestry matching to combine family‐based and unrelated samples for genome‐wide association studies

We propose a method to analyze family‐based samples together with unrelated cases and controls. The method builds on the idea of matched case–control analysis using conditional logistic regression (CLR). For each trio within the family, a case (the proband) and matched pseudo‐controls are constructed, based upon the transmitted and untransmitted alleles. Unrelated controls, matched by genetic ancestry, supplement the sample of pseudo‐controls; likewise unrelated cases are also paired with genetically matched controls. Within each matched stratum, the case genotype is contrasted with control/pseudo‐control genotypes via CLR, using a method we call matched‐CLR (mCLR). Eigenanalysis of numerous SNP genotypes provides a tool for mapping genetic ancestry. The result of such an analysis can be thought of as a multidimensional map, or eigenmap, in which the relative genetic similarities and differences amongst individuals is encoded in the map. Once constructed, new individuals can be projected onto the ancestry map based on their genotypes. Successful differentiation of individuals of distinct ancestry depends on having a diverse, yet representative sample from which to construct the ancestry map. Once samples are well‐matched, mCLR yields comparable power to competing methods while ensuring excellent control over Type I error. Copyright © 2010 John Wiley & Sons, Ltd.     

Stratification-score matching improves correction for confounding by population stratification in case-control association studies

Proper control of confounding due to population stratification is crucial for valid analysis of case-control association studies. Fine matching of cases and controls based on genetic ancestry is an increasingly popular strategy to correct for such confounding, both in genome-wide association studies (GWASs) as well as studies that employ next-generation sequencing, where matching can be used when selecting a subset of participants from a GWAS for rare-variant analysis. Existing matching methods match on measures of genetic ancestry that combine multiple components of ancestry into a scalar quantity. However, we show that including nonconfounding ancestry components in a matching criterion can lead to inaccurate matches, and hence to an improper control of confounding. To resolve this issue, we propose a novel method that assigns cases and controls to matched strata based on the stratification score (Epstein et al. [2007] Am J Hum Genet 80:921-930), which is the probability of disease given genomic variables. Matching on the stratification score leads to more accurate matches because case participants are matched to control participants who have a similar risk of disease given ancestry information. We illustrate our matching method using the African-American arm of the GAIN GWAS of schizophrenia. In this study, we observe that confounding due to stratification can be resolved by our matching approach but not by other existing matching procedures. We also use simulated data to show our novel matching approach can provide a more appropriate correction for population stratification than existing matching approaches.     

A propensity score approach to correction for bias due to population stratification using genetic and non‐genetic factors

Confounding due to population stratification (PS) arises when differences in both allele and disease frequencies exist in a population of mixed racial/ethnic subpopulations. Genomic control, structured association, principal components analysis (PCA), and multidimensional scaling (MDS) approaches have been proposed to address this bias using genetic markers. However, confounding due to PS can also be due to non‐genetic factors. Propensity scores are widely used to address confounding in observational studies but have not been adapted to deal with PS in genetic association studies. We propose a genomic propensity score (GPS) approach to correct for bias due to PS that considers both genetic and non‐genetic factors. We compare the GPS method with PCA and MDS using simulation studies. Our results show that GPS can adequately adjust and consistently correct for bias due to PS. Under no/mild, moderate, and severe PS, GPS yielded estimated with bias close to 0 (mean=?0.0044, standard error=0.0087). Under moderate or severe PS, the GPS method consistently outperforms the PCA method in terms of bias, coverage probability (CP), and type I error. Under moderate PS, the GPS method consistently outperforms the MDS method in terms of CP. PCA maintains relatively high power compared to both MDS and GPS methods under the simulated situations. GPS and MDS are comparable in terms of statistical properties such as bias, type I error, and power. The GPS method provides a novel and robust tool for obtaining less‐biased estimates of genetic associations that can consider both genetic and non‐genetic factors. Genet. Epidemiol. 33:679–690, 2009. © 2009 Wiley‐Liss, Inc.     

On testing for genetic association in case‐control studies when population allele frequencies are known

With the emergence of Biobanks alongside large‐scale genome‐wide association studies (GWAS) we will soon be in the enviable situation of obtaining precise estimates of population allele frequencies for SNPs which make up the panels in standard genotyping arrays, such as those produced from Illumina and Affymetrix. For disease association studies it is well known that for rare diseases with known population minor allele frequencies (pMAFs) a case‐only design is most powerful. That is, for a fixed budget the optimal procedure is to genotype only cases (affecteds). In such tests experimenters look for a divergence from allele distribution in cases from that of the known population pMAF; in order to test the null hypothesis of no association between the disease status and the allele frequency. However, what has not been previously characterized is the utility of controls (known unaffecteds) when available. In this study we consider frequentist and Bayesian statistical methods for testing for SNP genotype association when population MAFs are known and when both cases and controls are available. We demonstrate that for rare diseases the most powerful frequentist design is, somewhat counterintuitively, to actively discard the controls even though they contain information on the association. In contrast we develop a Bayesian test which uses all available information (cases and controls) and appears to exhibit uniformaly greater power than all frequentist methods we considered. Genet. Epidemiol. 33:371–378, 2009. © 2009 Wiley Liss, Inc.     

Robust analysis of secondary phenotypes in case‐control genetic association studies

The case‐control study is a common design for assessing the association between genetic exposures and a disease phenotype. Though association with a given (case‐control) phenotype is always of primary interest, there is often considerable interest in assessing relationships between genetic exposures and other (secondary) phenotypes. However, the case‐control sample represents a biased sample from the general population. As a result, if this sampling framework is not correctly taken into account, analyses estimating the effect of exposures on secondary phenotypes can be biased leading to incorrect inference. In this paper, we address this problem and propose a general approach for estimating and testing the population effect of a genetic variant on a secondary phenotype. Our approach is based on inverse probability weighted estimating equations, where the weights depend on genotype and the secondary phenotype. We show that, though slightly less efficient than a full likelihood‐based analysis when the likelihood is correctly specified, it is substantially more robust to model misspecification, and can out‐perform likelihood‐based analysis, both in terms of validity and power, when the model is misspecified. We illustrate our approach with an application to a case‐control study extracted from the Framingham Heart Study. Copyright © 2016 John Wiley & Sons, Ltd.     

Validity of using ad hoc methods to analyze secondary traits in case‐control association studies

Case‐control association studies often collect from their subjects information on secondary phenotypes. Reusing the data and studying the association between genes and secondary phenotypes provide an attractive and cost‐effective approach that can lead to discovery of new genetic associations. A number of approaches have been proposed, including simple and computationally efficient ad hoc methods that ignore ascertainment or stratify on case‐control status. Justification for these approaches relies on the assumption of no covariates and the correct specification of the primary disease model as a logistic model. Both might not be true in practice, for example, in the presence of population stratification or the primary disease model following a probit model. In this paper, we investigate the validity of ad hoc methods in the presence of covariates and possible disease model misspecification. We show that in taking an ad hoc approach, it may be desirable to include covariates that affect the primary disease in the secondary phenotype model, even though these covariates are not necessarily associated with the secondary phenotype. We also show that when the disease is rare, ad hoc methods can lead to severely biased estimation and inference if the true disease model follows a probit model instead of a logistic model. Our results are justified theoretically and via simulations. Applied to real data analysis of genetic associations with cigarette smoking, ad hoc methods collectively identified as highly significant () single nucleotide polymorphisms from over 10 genes, genes that were identified in previous studies of smoking cessation.     

A unified genetic association test robust to latent population structure for a count phenotype

Confounding caused by latent population structure in genome‐wide association studies has been a big concern despite the success of genome‐wide association studies at identifying genetic variants associated with complex diseases. In particular, because of the growing interest in association mapping using count phenotype data, it would be interesting to develop a testing framework for genetic associations that is immune to population structure when phenotype data consist of count measurements. Here, I propose a solution for testing associations between single nucleotide polymorphisms and a count phenotype in the presence of an arbitrary population structure. I consider a classical range of models for count phenotype data. Under these models, a unified test for genetic associations that protects against confounding was derived. An algorithm was developed to efficiently estimate the parameters that are required to fit the proposed model. I illustrate the proposed approach using simulation studies and an empirical study. Both simulated and real‐data examples suggest that the proposed method successfully corrects population structure.     

A powerful approach to sub‐phenotype analysis in population‐based genetic association studies

The ultimate goal of genome‐wide association (GWA) studies is to identify genetic variants contributing effects to complex phenotypes in order to improve our understanding of the biological architecture underlying the trait. One approach to allow us to meet this challenge is to consider more refined sub‐phenotypes of disease, defined by pattern of symptoms, for example, which may be physiologically distinct, and thus may have different underlying genetic causes. The disadvantage of sub‐phenotype analysis is that large disease cohorts are sub‐divided into smaller case categories, thus reducing power to detect association. To address this issue, we have developed a novel test of association within a multinomial regression modeling framework, allowing for heterogeneity of genetic effects between sub‐phenotypes. The modeling framework is extremely flexible, and can be generalized to any number of distinct sub‐phenotypes. Simulations demonstrate the power of the multinomial regression‐based analysis over existing methods when genetic effects differ between sub‐phenotypes, with minimal loss of power when these effects are homogenous for the unified phenotype. Application of the multinomial regression analysis to a genome‐wide association study of type 2 diabetes, with cases categorized according to body mass index, highlights previously recognized differential mechanisms underlying obese and non‐obese forms of the disease, and provides evidence of a potential novel association that warrants follow‐up in independent replication cohorts. Genet. Epidemiol. 34: 335–343, 2010. © 2009 Wiley‐Liss, Inc.     

A novel haplotype‐sharing approach for genome‐wide case‐control association studies implicates the calpastatin gene in Parkinson's disease

The large number of markers considered in a genome‐wide association study (GWAS) has resulted in a simplification of analyses conducted. Most studies are analyzed one marker at a time using simple tests like the trend test. Methods that account for the special features of genetic association studies, yet remain computationally feasible for genome‐wide analysis, are desirable as they may lead to increased power to detect associations. Haplotype sharing attempts to translate between population genetics and genetic epidemiology. Near a recent mutation that increases disease risk, haplotypes of case participants should be more similar to each other than haplotypes of control participants; conversely, the opposite pattern may be found near a recent mutation that lowers disease risk. We give computationally simple association tests based on haplotype sharing that can be easily applied to GWASs while allowing use of fast (but not likelihood‐based) haplotyping algorithms and properly accounting for the uncertainty introduced by using inferred haplotypes. We also give haplotype‐sharing analyses that adjust for population stratification. Applying our methods to a GWAS of Parkinson's disease, we find a genome‐wide significant signal in the CAST gene that is not found by single‐SNP methods. Further, a missing‐data artifact that causes a spurious single‐SNP association on chromosome 9 does not impact our test. Genet. Epidemiol. 33:657–667, 2009. Published 2009 Wiley‐Liss, Inc.     

Efficient unified rare variant association test by modeling the population genetic distribution in case‐control studies

Recent advancements in next‐generation DNA sequencing technologies have made it plausible to study the association of rare variants with complex diseases. Due to the low frequency, rare variants need to be aggregated in association tests to achieve adequate power with reasonable sample sizes. Hierarchical modeling/kernel machine methods have gained popularity among many available methods for testing a set of rare variants collectively. Here, we propose a new score statistic based on a hierarchical model by additionally modeling the distribution of rare variants under the case‐control study design. Results from extensive simulation studies show that the proposed method strikes a balance between robustness and power and outperforms several popular rare‐variant association tests. We demonstrate the performance of our method using the Dallas Heart Study.     

Avoiding the high Bonferroni penalty in genome‐wide association studies

A major challenge in genome‐wide association studies (GWASs) is to derive the multiple testing threshold when hypothesis tests are conducted using a large number of single nucleotide polymorphisms. Permutation tests are considered the gold standard in multiple testing adjustment in genetic association studies. However, it is computationally intensive, especially for GWASs, and can be impractical if a large number of random shuffles are used to ensure accuracy. Many researchers have developed approximation algorithms to relieve the computing burden imposed by permutation. One particularly attractive alternative to permutation is to calculate the effective number of independent tests, M_eff, which has been shown to be promising in genetic association studies. In this study, we compare recently developed M_eff methods and validate them by the permutation test with 10,000 random shuffles using two real GWAS data sets: an Illumina 1M BeadChip and an Affymetrix GeneChip^® Human Mapping 500K Array Set. Our results show that the simpleM method produces the best approximation of the permutation threshold, and it does so in the shortest amount of time. We also show that M_eff is indeed valid on a genome‐wide scale in these data sets based on statistical theory and significance tests. The significance thresholds derived can provide practical guidelines for other studies using similar population samples and genotyping platforms. Genet. Epidemiol. 34:100–105, 2010. © 2009 Wiley‐Liss, Inc.     

locStra: Fast analysis of regional/global stratification in whole‐genome sequencing studies

locStra is an ‐package for the analysis of regional and global population stratification in whole‐genome sequencing (WGS) studies, where regional stratification refers to the substructure defined by the loci in a particular region on the genome. Population substructure can be assessed based on the genetic covariance matrix, the genomic relationship matrix, and the unweighted/weighted genetic Jaccard similarity matrix. Using a sliding window approach, the regional similarity matrices are compared with the global ones, based on user‐defined window sizes and metrics, for example, the correlation between regional and global eigenvectors. An algorithm for the specification of the window size is provided. As the implementation fully exploits sparse matrix algebra and is written in C++, the analysis is highly efficient. Even on single cores, for realistic study sizes (several thousand subjects, several million rare variants per subject), the runtime for the genome‐wide computation of all regional similarity matrices does typically not exceed one hour, enabling an unprecedented investigation of regional stratification across the entire genome. The package is applied to three WGS studies, illustrating the varying patterns of regional substructure across the genome and its beneficial effects on association testing.     

Genome‐wide association scans for secondary traits using case‐control samples

Genome‐wide association studies (GWAS) require considerable investment, so researchers often study multiple traits collected on the same set of subjects to maximize return. However, many GWAS have adopted a case‐control design; improperly accounting for case‐control ascertainment can lead to biased estimates of association between markers and secondary traits. We show that under the null hypothesis of no marker‐secondary trait association, naïve analyses that ignore ascertainment or stratify on case‐control status have proper Type I error rates except when both the marker and secondary trait are independently associated with disease risk. Under the alternative hypothesis, these methods are unbiased when the secondary trait is not associated with disease risk. We also show that inverse‐probability‐of‐sampling‐weighted (IPW) regression provides unbiased estimates of marker‐secondary trait association. We use simulation to quantify the Type I error, power and bias of naïve and IPW methods. IPW regression has appropriate Type I error in all situations we consider, but has lower power than naïve analyses. The bias for naïve analyses is small provided the marker is independent of disease risk. Considering the majority of tested markers in a GWAS are not associated with disease risk, naïve analyses provide valid tests of and nearly unbiased estimates of marker‐secondary trait association. Care must be taken when there is evidence that both the secondary trait and tested marker are associated with the primary disease, a situation we illustrate using an analysis of the relationship between a marker in FGFR2 and mammographic density in a breast cancer case‐control sample. Genet. Epidemiol. 33:717–728, 2009. © 2009 Wiley‐Liss, Inc.     

Pathway‐based analysis for genome‐wide association studies using supervised principal components

Many complex diseases are influenced by genetic variations in multiple genes, each with only a small marginal effect on disease susceptibility. Pathway analysis, which identifies biological pathways associated with disease outcome, has become increasingly popular for genome‐wide association studies (GWAS). In addition to combining weak signals from a number of SNPs in the same pathway, results from pathway analysis also shed light on the biological processes underlying disease. We propose a new pathway‐based analysis method for GWAS, the supervised principal component analysis (SPCA) model. In the proposed SPCA model, a selected subset of SNPs most associated with disease outcome is used to estimate the latent variable for a pathway. The estimated latent variable for each pathway is an optimal linear combination of a selected subset of SNPs; therefore, the proposed SPCA model provides the ability to borrow strength across the SNPs in a pathway. In addition to identifying pathways associated with disease outcome, SPCA also carries out additional within‐category selection to identify the most important SNPs within each gene set. The proposed model operates in a well‐established statistical framework and can handle design information such as covariate adjustment and matching information in GWAS. We compare the proposed method with currently available methods using data with realistic linkage disequilibrium structures, and we illustrate the SPCA method using the Wellcome Trust Case‐Control Consortium Crohn Disease (CD) data set. Genet. Epidemiol. 34: 716‐724, 2010. © 2010 Wiley‐Liss, Inc.     

An improved score test for genetic association studies

Large-scale genome-wide association studies (GWAS) have become feasible recently because of the development of bead and chip technology. However, the success of GWAS partially depends on the statistical methods that are able to manage and analyze this sort of large-scale data. Currently, the commonly used tests for GWAS include the Cochran-Armitage trend test, the allelic χ(2) test, the genotypic χ(2) test, the haplotypic χ(2) test, and the multi-marker genotypic χ(2) test among others. From a methodological point of view, it is a great challenge to improve the power of commonly used tests, since these tests are commonly used precisely because they are already among the most powerful tests. In this article, we propose an improved score test that is uniformly more powerful than the score test based on the generalized linear model. Since the score test based on the generalized linear model includes the aforementioned commonly used tests as its special cases, our proposed improved score test is thus uniformly more powerful than these commonly used tests. We evaluate the performance of the improved score test by simulation studies and application to a real data set. Our results show that the power increases of the improved score test over the score test cannot be neglected in most cases.     

Evaluating bias due to population stratification in case-control association studies of admixed populations

The potential for bias from population stratification (PS) has raised concerns about case-control studies involving admixed ethnicities. We evaluated the potential bias due to PS in relating a binary outcome with a candidate gene under simulated settings where study populations consist of multiple ethnicities. Disease risks were assigned within the range of prostate cancer rates of African Americans reported in SEER registries assuming k=2, 5, or 10 admixed ethnicities. Genotype frequencies were considered in the range of 5-95%. Under a model assuming no genotype effect on disease (odds ratio (OR)=1), the range of observed OR estimates ignoring ethnicity was 0.64-1.55 for k=2, 0.72-1.33 for k=5, and 0.81-1.22 for k=10. When genotype effect on disease was modeled to be OR=2, the ranges of observed OR estimates were 1.28-3.09, 1.43-2.65, and 1.62-2.42 for k=2, 5, and 10 ethnicities, respectively. Our results indicate that the magnitude of bias is small unless extreme differences exist in genotype frequency. Bias due to PS decreases as the number of admixed ethnicities increases. The biases are bounded by the minimum and maximum of all pairwise baseline disease odds ratios across ethnicities. Therefore, bias due to PS alone may be small when baseline risk differences are small within major categories of admixed ethnicity, such as African Americans.     

An evaluation of statistical approaches to rare variant analysis in genetic association studies

Genome‐wide association (GWA) studies have proved to be extremely successful in identifying novel common polymorphisms contributing effects to the genetic component underlying complex traits. Nevertheless, one source of, as yet, undiscovered genetic determinants of complex traits are those mediated through the effects of rare variants. With the increasing availability of large‐scale re‐sequencing data for rare variant discovery, we have developed a novel statistical method for the detection of complex trait associations with these loci, based on searching for accumulations of minor alleles within the same functional unit. We have undertaken simulations to evaluate strategies for the identification of rare variant associations in population‐based genetic studies when data are available from re‐sequencing discovery efforts or from commercially available GWA chips. Our results demonstrate that methods based on accumulations of rare variants discovered through re‐sequencing offer substantially greater power than conventional analysis of GWA data, and thus provide an exciting opportunity for future discovery of genetic determinants of complex traits. Genet. Epidemiol. 34: 188–193, 2010. © 2009 Wiley‐Liss, Inc.