On the meta-analysis of genome-wide association studies: a robust and efficient approach to combine population and family-based studies

For the meta-analysis of genome-wide association studies, we propose a new method to adjust for the population stratification and a linear mixed approach that combines family-based and unrelated samples. The proposed approach achieves similar power levels as a standard meta-analysis which combines the different test statistics or p values across studies. However, by virtue of its design, the proposed approach is robust against population admixture and stratification, and no adjustments for population admixture and stratification, even in unrelated samples, are required. Using simulation studies, we examine the power of the proposed method and compare it to standard approaches in the meta-analysis of genome-wide association studies. The practical features of the approach are illustrated with a meta-analysis of three genome-wide association studies for Alzheimer's disease. We identify three single nucleotide polymorphisms showing significant genome-wide association with affection status. Two single nucleotide polymorphisms are novel and will be verified in other populations in our follow-up study.     

Comparison of biometrical models for joint linkage association mapping

Joint linkage association mapping (JLAM) combines the advantages of linkage mapping and association mapping, and is a powerful tool to dissect the genetic architecture of complex traits. The main goal of this study was to use a cross-validation strategy, resample model averaging and empirical data analyses to compare seven different biometrical models for JLAM with regard to the correction for population structure and the quantitative trait loci (QTL) detection power. Three linear models and four linear mixed models with different approaches to control for population stratification were evaluated. Models A, B and C were linear models with either cofactors (Model-A), or cofactors and a population effect (Model-B), or a model in which the cofactors and the single-nucleotide polymorphism effect were modeled as nested within population (Model-C). The mixed models, D, E, F and G, included a random population effect (Model-D), or a random population effect with defined variance structure (Model-E), a kinship matrix defining the degree of relatedness among the genotypes (Model-F), or a kinship matrix and principal coordinates (Model-G). The tested models were conceptually different and were also found to differ in terms of power to detect QTL. Model-B with the cofactors and a population effect, effectively controlled population structure and possessed a high predictive power. The varying allele substitution effects in different populations suggest as a promising strategy for JLAM to use Model-B for the detection of QTL and then to estimate their effects by applying Model-C.     

Case-control association studies in mixed populations: correcting using genomic control

OBJECTIVE: Case-control association studies in mixed populations can result in spurious disease-marker associations if subpopulation disease prevalence and marker frequencies both differ. Genomic control (GC) uses neutral loci to correct for spurious association (due to population stratification), but how well this works remains undetermined. METHODS: We simulated and mixed populations with different disease and marker frequencies but without marker-disease association. We generated case-control datasets, calculated the chi2 for disease association with each marker, and applied two GC procedures, dividing by the mean chi2 or median-chi2/0.456. RESULTS: Corrections became conservative (false positive rate [FPR] <5%) with increasing subpopulation prevalence and marker differences. The mean correction resulted in FPRs close to 5% at average subpopulation allele frequency differences <0.26, but inclusion of just a few markers with large frequency differences resulted in conservative FPRs. FPRs from the median correction were mostly conservative but became anticonservative when a few markers with large frequency differences were included. CONCLUSION: GC can both lead to a notable loss of power to detect a true association (conservative) in many circumstances or may fail to eliminate the spurious associations (anticonservative). The mean correction factor is useful in certain situations to correct population stratification, but it is difficult to know when those situations exist.     

Linear parameter haplotype models with stratification

OBJECTIVES: The question of interest is estimating the relationship between haplotypes and an outcome measure, based upon unphased genotypes. The outcome of interest might be predicting the presence of disease in a logistic model, predicting a numeric drug response in a linear model, or predicting survival time in a parametric survival model with censoring. Explanatory variables may include phased haplotype design variables, environmental variables, or interactions between them. METHODS: We extend existing generalized linear haplotype models to parametric survival outcomes. To improve the stability of model variance estimates, a profile likelihood solution is proposed. An adjustment for population stratification is also considered. Here we investigate data sampled from known 'strata' (e.g., gender or ethnicity) that influence haplotype prior probabilities and thus the regression model weights. Differing linear model variance estimates, and the effect of stratification and departures from Hardy-Weinberg Equilibrium (HWE) on parameter estimates, are compared and contrasted via simulation. RESULTS: From simulations, we observed an improvement in statistical power when using a solution to profile likelihood equations. We also saw that stratification had little impact on estimates. Haplotypes that are not in HWE had a negative impact on power to test hypotheses. Finally, profile likelihood solutions for haplotypes deviating from HWE had improved power and confidence interval coverage of regression model coefficients.     

Candidate gene analysis for quantitative traits using the transmission disequilibrium test: the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal or in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.     

Accounting for population stratification in practice: a comparison of the main strategies dedicated to genome-wide association studies

Genome-Wide Association Studies are powerful tools to detect genetic variants associated with diseases. Their results have, however, been questioned, in part because of the bias induced by population stratification. This is a consequence of systematic differences in allele frequencies due to the difference in sample ancestries that can lead to both false positive or false negative findings. Many strategies are available to account for stratification but their performances differ, for instance according to the type of population structure, the disease susceptibility locus minor allele frequency, the degree of sampling imbalanced, or the sample size. We focus on the type of population structure and propose a comparison of the most commonly used methods to deal with stratification that are the Genomic Control, Principal Component based methods such as implemented in Eigenstrat, adjusted Regressions and Meta-Analyses strategies. Our assessment of the methods is based on a large simulation study, involving several scenarios corresponding to many types of population structures. We focused on both false positive rate and power to determine which methods perform the best. Our analysis showed that if there is no population structure, none of the tests led to a bias nor decreased the power except for the Meta-Analyses. When the population is stratified, adjusted Logistic Regressions and Eigenstrat are the best solutions to account for stratification even though only the Logistic Regressions are able to constantly maintain correct false positive rates. This study provides more details about these methods. Their advantages and limitations in different stratification scenarios are highlighted in order to propose practical guidelines to account for population stratification in Genome-Wide Association Studies.     

Utilizing Population Controls in Rare-Variant Case-Parent Association Tests

There is great interest in detecting associations between human traits and rare genetic variation. To address the low power implicit in single-locus tests of rare genetic variants, many rare-variant association approaches attempt to accumulate information across a gene, often by taking linear combinations of single-locus contributions to a statistic. Using the right linear combination is key—an optimal test will up-weight true causal variants, down-weight neutral variants, and correctly assign the direction of effect for causal variants. Here, we propose a procedure that exploits data from population controls to estimate the linear combination to be used in an case-parent trio rare-variant association test. Specifically, we estimate the linear combination by comparing population control allele frequencies with allele frequencies in the parents of affected offspring. These estimates are then used to construct a rare-variant transmission disequilibrium test (rvTDT) in the case-parent data. Because the rvTDT is conditional on the parents’ data, using parental data in estimating the linear combination does not affect the validity or asymptotic distribution of the rvTDT. By using simulation, we show that our new population-control-based rvTDT can dramatically improve power over rvTDTs that do not use population control information across a wide variety of genetic architectures. It also remains valid under population stratification. We apply the approach to a cohort of epileptic encephalopathy (EE) trios and find that dominant (or additive) inherited rare variants are unlikely to play a substantial role within EE genes previously identified through de novo mutation studies.     

Comparison of tests for association and linkage in incomplete families

To analyze incomplete families, the following statistical tests can be used: LRAT-a simple likelihood-based association test, TRANSMIT, SIBASSOC/STDT, and RCTDT. We compared these four tests, for the diallelic case, on simulated data sets. The comparisons focused on the power to detect linkage and association when different familial structures, resistance to population stratification, resistance to misclassification of the disease status of the healthy sib, and the effect of nonpaternity were considered. The simulations lead to the following conclusions. The type I errors of TRANSMIT, SIBASSOC/STDT, and RCTDT were not affected by population stratification. LRAT showed bias under strong population stratification. High nonpaternity rates can lead to inflated type I errors, highlighting the importance of identification of half sibs. Under different homogeneous models, the power of TRANSMIT was very similar to that of LRAT, and, similarly, no difference in power was observed between SIBASSOC/STDT and RCTDT. Under various recessive and additive models, TRANSMIT was slightly more powerful than SIBASSOC/STDT when monoparental families with one affected and one unaffected sib were analyzed. Under various dominant models, SIBASSOC/STDT was slightly more powerful than TRANSMIT. Misclassification of the disease status of healthy sibs, as well as the discarding of incomplete families, resulted in a consistent loss of power.     

Testing quantitative traits for association and linkage in the presence or absence of parental data

Zhu and Elston developed a transmission disequilibrium test for quantitative traits by defining a linear transformation to condition out founder information. The method tests the null hypothesis of no linkage or association and can be applied to general pedigree structures. However, this method requires both genotype and phenotype parental information, which may be difficult to obtain. In this paper, we describe parametric and non-parametric methods to relax this requirement when only nuclear families are sampled. We show that neither method is affected by population stratification in the absence of linkage. The statistical power and validity of the tests are investigated by simulation. A simple simulation method to calculate the power of the nonparametric method is also discussed. In practice, the data may have some families with parental phenotype and genotype information available and some without. We briefly discuss how all the data may be analyzed jointly.     

A randomization test for controlling population stratification in whole-genome association studies

Population stratification can be a serious obstacle in the analysis of genomewide association studies. We propose a method for evaluating the significance of association scores in whole-genome cohorts with stratification. Our approach is a randomization test akin to a standard permutation test. It conditions on the genotype matrix and thus takes into account not only the population structure but also the complex linkage disequilibrium structure of the genome. As we show in simulation experiments, our method achieves higher power and significantly better control over false-positive rates than do existing methods. In addition, it can be easily applied to whole-genome association studies.     

Comparison of population-based association study methods correcting for population stratification

Population stratification can cause spurious associations in population-based association studies. Several statistical methods have been proposed to reduce the impact of population stratification on population-based association studies. We simulated a set of stratified populations based on the real haplotype data from the HapMap ENCODE project, and compared the relative power, type I error rates, accuracy and positive prediction value of four prevailing population-based association study methods: traditional case-control tests, structured association (SA), genomic control (GC) and principal components analysis (PCA) under various population stratification levels. Additionally, we evaluated the effects of sample sizes and frequencies of disease susceptible allele on the performance of the four analytical methods in the presence of population stratification. We found that the performance of PCA was very stable under various scenarios. Our comparison results suggest that SA and PCA have comparable performance, if sufficient ancestral informative markers are used in SA analysis. GC appeared to be strongly conservative in significantly stratified populations. It may be better to apply GC in the stratified populations with low stratification level. Our study intends to provide a practical guideline for researchers to select proper study methods and make appropriate inference of the results in population-based association studies.     

Simultaneously correcting for population stratification and for genotyping error in case-control association studies

In population-based case-control association studies, the regular chi (2) test is often used to investigate association between a candidate locus and disease. However, it is well known that this test may be biased in the presence of population stratification and/or genotyping error. Unlike some other biases, this bias will not go away with increasing sample size. On the contrary, the false-positive rate will be much larger when the sample size is increased. The usual family-based designs are robust against population stratification, but they are sensitive to genotype error. In this article, we propose a novel method of simultaneously correcting for the bias arising from population stratification and/or for the genotyping error in case-control studies. The appropriate corrections depend on sample odds ratios of the standard 2x3 tables of genotype by case and control from null loci. Therefore, the test is simple to apply. The corrected test is robust against misspecification of the genetic model. If the null hypothesis of no association is rejected, the corrections can be further used to estimate the effect of the genetic factor. We considered a simulation study to investigate the performance of the new method, using parameter values similar to those found in real-data examples. The results show that the corrected test approximately maintains the expected type I error rate under various simulation conditions. It also improves the power of the association test in the presence of population stratification and/or genotyping error. The discrepancy in power between the tests with correction and those without correction tends to be more extreme as the magnitude of the bias becomes larger. Therefore, the bias-correction method proposed in this article should be useful for the genetic analysis of complex traits.     

Non-linear heart rate variability and risk stratification in cardiovascular disease

Traditional time and frequency domain heart rate variability (HRV) have cardiac patients at risk of mortality post-myocardial infarction. More recently, non linear HRV has been applied to risk stratification of cardiac patients. In this review we describe studies of non linear HRV and outcome in cardiac patients. We have included studies that used the three most common non-linear indices: power law slope, the short term fractal scaling exponent and measures based on Poincare plots. We suggest that a combination of traditional and non-linear HRV may be optimal for risk stratification. Considerations in using non linear HRV in a clinical setting are described.     

Retrospective Binary-Trait Association Test Elucidates Genetic Architecture of Crohn Disease

In genetic association testing, failure to properly control for population structure can lead to severely inflated type 1 error and power loss. Meanwhile, adjustment for relevant covariates is often desirable and sometimes necessary to protect against spurious association and to improve power. Many recent methods to account for population structure and covariates are based on linear mixed models (LMMs), which are primarily designed for quantitative traits. For binary traits, however, LMM is a misspecified model and can lead to deteriorated performance. We propose CARAT, a binary-trait association testing approach based on a mixed-effects quasi-likelihood framework, which exploits the dichotomous nature of the trait and achieves computational efficiency through estimating equations. We show in simulation studies that CARAT consistently outperforms existing methods and maintains high power in a wide range of population structure settings and trait models. Furthermore, CARAT is based on a retrospective approach, which is robust to misspecification of the phenotype model. We apply our approach to a genome-wide analysis of Crohn disease, in which we replicate association with 17 previously identified regions. Moreover, our analysis on 5p13.1, an extensively reported region of association, shows evidence for the presence of multiple independent association signals in the region. This example shows how CARAT can leverage known disease risk factors to shed light on the genetic architecture of complex traits.     

Quantitative similarity-based association tests using population samples

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification, such as family-based association designs, may be less powerful. Furthermore, it is often more feasible and less expensive to collect unrelated individuals. Recently, several statistical methods have been proposed for case-control association tests in a structured population; these methods may be robust to population stratification. In the present study, we propose a quantitative similarity-based association test (QSAT) to identify association between a candidate marker and a quantitative trait of interest, through use of unrelated individuals. For the QSAT, we first determine whether two individuals are from the same subpopulation or from different subpopulations, using genotype data at a set of independent markers. We then perform an association test between the candidate marker and the quantitative trait, through incorporation of such information. Simulation results based on either coalescent models or empirical population genetics data show that the QSAT has a correct type I error rate in the presence of population stratification and that the power of the QSAT is higher than that of family-based association designs.     

Family-Based Bivariate Association Tests for Quantitative Traits

The availability of a large number of dense SNPs, high-throughput genotyping and computation methods promotes the application of family-based association tests. While most of the current family-based analyses focus only on individual traits, joint analyses of correlated traits can extract more information and potentially improve the statistical power. However, current TDT-based methods are low-powered. Here, we develop a method for tests of association for bivariate quantitative traits in families. In particular, we correct for population stratification by the use of an integration of principal component analysis and TDT. A score test statistic in the variance-components model is proposed. Extensive simulation studies indicate that the proposed method not only outperforms approaches limited to individual traits when pleiotropic effect is present, but also surpasses the power of two popular bivariate association tests termed FBAT-GEE and FBAT-PC, respectively, while correcting for population stratification. When applied to the GAW16 datasets, the proposed method successfully identifies at the genome-wide level the two SNPs that present pleiotropic effects to HDL and TG traits.     

Genome-wide association mapping of agronomic and morphologic traits in highly structured populations of barley cultivars

Genome-wide association study (GWAS) has become an obvious general approach for studying traits of agricultural importance in higher plants, especially crops. Here, we present a GWAS of 32 morphologic and 10 agronomic traits in a collection of 615 barley cultivars genotyped by genome-wide polymorphisms from a recently developed barley oligonucleotide pool assay. Strong population structure effect related to mixed sampling based on seasonal growth habit and ear row number is present in this barley collection. Comparison of seven statistical approaches in a genome-wide scan for significant associations with or without correction for confounding by population structure, revealed that in reducing false positive rates while maintaining statistical power, a mixed linear model solution outperforms genomic control, structured association, stepwise regression control and principal components adjustment. The present study reports significant associations for sixteen morphologic and nine agronomic traits and demonstrates the power and feasibility of applying GWAS to explore complex traits in highly structured plant samples.     

A semiparametric test to detect associations between quantitative traits and candidate genes in structured populations

MOTIVATION: Although population-based association mapping may be subject to the bias caused by population stratification, alternative methods that are robust to population stratification such as family-based linkage analysis have lower mapping resolution. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate genes and traits of interest. The association between a candidate gene and a quantitative trait is often evaluated via a regression model with inferred population structure variables as covariates, where the residual distribution is customarily assumed to be from a symmetric and unimodal parametric family, such as a Gaussian, although this may be inappropriate for the analysis of many real-life datasets. RESULTS: In this article, we proposed a new structured association (SA) test. Our method corrects for continuous population stratification by first deriving population structure and kinship matrices through a set of random genetic markers and then modeling the relationship between trait values, genotypic scores at a candidate marker and genetic background variables through a semiparametric model, where the error distribution is modeled as a mixture of Polya trees centered around a normal family of distributions. We compared our model to the existing SA tests in terms of model fit, type I error rate, power, precision and accuracy by application to a real dataset as well as simulated datasets.     

Testing for association in the presence of population stratification: a simulation study comparing the S-TDT, STRAT and the GC

A novel approach for association testing in the presence of population stratification has been introduced by Pritchard et al. (2000a) and Pritchard et al. (2000b). The structured association approach is a two-tiered procedure that first estimates the population structure and then tests the null hypothesis H0: 'no association within subpopulations' in the second step. A power comparison of the stratified test for association (STRAT) (Pritchard et al., 2000b) and the Transmission-Disequilibrium-Test (TDT) (Spielman and Ewens, 1993a) in a simulation framework showed superiority of STRAT if allele frequencies or associations between allele and disease differ strongly in subpopulations. In more homogeneous situations, the TDT had greater power than STRAT. However, the TDT, based on family trios,that uses population controls, needs 50% more genotyping compared to STRAT. The Sib-Transmission-Disequilibrium-Test (S-TDT) needs the same amount of genotyping since it relays in its minimal configuration on pairs of siblings. This raises the question how the S-TDT (Spielman and Ewens, 1998a) performs compared to the population based methods STRAT and Genomic Controls (GC). In this paper, we present a simulation study accounting for two different models of population stratification in different settings of allele frequencies and under different risk models. The results showed that under a discrete as well as under an admixed population model, STRAT strongly outperformed the S-TDT and the GC when different alleles were associated in different subpopulations. In contrast, the S-TDT had greater power than STRAT when the same allele was associated in both subpopulations. Here, the GC was sometimes even more powerful than the S-TDT, depending on the population model and the allele frequency differences. A general recommendation for the use of one of the tests can therefore not be given.     

SHEsis PCA: A GPU-Based Software to Correct for Population Stratification that Efficiently Accelerates the Process for Handling Genome-Wide Datasets

Population stratification is a problem in genetic association studies because it is likely to highlight loci that underlie the population structure rather than disease-related loci. At present, principal component analysis(PCA) has been proven to be an effective way to correct for population stratification. However, the conventional PCA algorithm is time-consuming when dealing with large datasets. We developed a Graphic processing unit(GPU)-based PCA software named SHEsis PCA(http://analysis.bio-x.cn/SHEsis Main.htm) that is highly parallel with a highest speedup greater than 100 compared with its CPU version. A cluster algorithm based on X-means was also implemented as a way to detect population subgroups and to obtain matched cases and controls in order to reduce the genomic inflation and increase the power. A study of both simulated and real datasets showed that SHEsis PCA ran at an extremely high speed while the accuracy was hardly reduced. Therefore, SHEsis PCA can help correct for population stratification much more efficiently than the conventional CPU-based algorithms.