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.     

Joint analysis for genome-wide association studies in family-based designs

In family-based data, association information can be partitioned into the between-family information and the within-family information. Based on this observation, Steen et al. (Nature Genetics. 2005, 683-691) proposed an interesting two-stage test for genome-wide association (GWA) studies under family-based designs which performs genomic screening and replication using the same data set. In the first stage, a screening test based on the between-family information is used to select markers. In the second stage, an association test based on the within-family information is used to test association at the selected markers. However, we learn from the results of case-control studies (Skol et al. Nature Genetics. 2006, 209-213) that this two-stage approach may be not optimal. In this article, we propose a novel two-stage joint analysis for GWA studies under family-based designs. For this joint analysis, we first propose a new screening test that is based on the between-family information and is robust to population stratification. This new screening test is used in the first stage to select markers. Then, a joint test that combines the between-family information and within-family information is used in the second stage to test association at the selected markers. By extensive simulation studies, we demonstrate that the joint analysis always results in increased power to detect genetic association and is robust to population stratification.     

Family-based designs in the age of large-scale gene-association studies

Both population-based and family-based designs are commonly used in genetic association studies to locate genes that underlie complex diseases. The simplest version of the family-based design--the transmission disequilibrium test--is well known, but the numerous extensions that broaden its scope and power are less widely appreciated. Family-based designs have unique advantages over population-based designs, as they are robust against population admixture and stratification, allow both linkage and association to be tested for and offer a solution to the problem of model building. Furthermore, the fact that family-based designs contain both within- and between-family information has substantial benefits in terms of multiple-hypothesis testing, especially in the context of whole-genome association studies.     

A unified association analysis approach for family and unrelated samples correcting for stratification

There are two common designs for association mapping of complex diseases: case-control and family-based designs. A case-control sample is more powerful to detect genetic effects than a family-based sample that contains the same numbers of affected and unaffected persons, although additional markers may be required to control for spurious association. When family and unrelated samples are available, statistical analyses are often performed in the family and unrelated samples separately, conditioning on parental information for the former, thus resulting in reduced power. In this report, we propose a unified approach that can incorporate both family and case-control samples and, provided the additional markers are available, at the same time corrects for population stratification. We apply the principal components of a marker matrix to adjust for the effect of population stratification. This unified approach makes it unnecessary to perform a conditional analysis of the family data and is more powerful than the separate analyses of unrelated and family samples, or a meta-analysis performed by combining the results of the usual separate analyses. This property is demonstrated in both a variety of simulation models and empirical data. The proposed approach can be equally applied to the analysis of both qualitative and quantitative traits.     

The bias introduced by population stratification in IBD based linkage analysis

The lack of replication of model-free linkage analyses performed on complex diseases raises questions about the robustness of these methods to various biases. The confounding effect of population stratification on a genetic association study has long been recognized in the genetic epidemiology community. Because the estimation of the number of alleles shared identical by descent (IBD) does not depend on the marker allele frequency when founders of families are observed, model-free linkage analysis is usually thought to be robust to population stratification. However, for common complex diseases, the genotypes of founders are often unobserved and therefore population stratification has the potential to impair model-free linkage analysis. Here, we demonstrate that, when some or all of the founder genotypes are missing, population stratification can introduce deleterious effects on various model-free linkage methods or designs. For an affected sib pair design, it can cause excess false-positive discoveries even when the trait distribution is homogeneous among subpopulations. After incorporating a control group of discordant sib pairs or for a quantitative trait, two circumstances must be met for population stratification to be a confounder: the distributions for both the marker and the trait must be heterogeneous among subpopulations. When this occurs, the bias can result in either a liberal, and hence invalid, test or a conservative test. Bias can be eliminated or alleviated by inclusion of founders' or other family members' genotype data. When this is not possible, new methods need to be developed to be robust to population stratification.     

Control of confounding of genetic associations in stratified populations

To control for hidden population stratification in genetic-association studies, statistical methods that use marker genotype data to infer population structure have been proposed as a possible alternative to family-based designs. In principle, it is possible to infer population structure from associations between marker loci and from associations of markers with the trait, even when no information about the demographic background of the population is available. In a model in which the total population is formed by admixture between two or more subpopulations, confounding can be estimated and controlled. Current implementations of this approach have limitations, the most serious of which is that they do not allow for uncertainty in estimations of individual admixture proportions or for lack of identifiability of subpopulations in the model. We describe methods that overcome these limitations by a combination of Bayesian and classical approaches, and we demonstrate the methods by using data from three admixed populations--African American, African Caribbean, and Hispanic American--in which there is extreme confounding of trait-genotype associations because the trait under study (skin pigmentation) varies with admixture proportions. In these data sets, as many as one-third of marker loci show crude associations with the trait. Control for confounding by population stratification eliminates these associations, except at loci that are linked to candidate genes for the trait. With only 32 markers informative for ancestry, the efficiency of the analysis is 70%. These methods can deal with both confounding and selection bias in genetic-association studies, making family-based designs unnecessary.     

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.     

Statistical equivalent of the classical TDT for quantitative traits and multivariate phenotypes

Clinical end-point traits are usually governed by quantitative precursors. Hence, there is active research interest in developing statistical methods for association mapping of quantitative traits. Unlike population-based tests for association, family-based tests for transmission disequilibrium are protected against population stratification. In this study, we propose a logistic regression model to test the association for quantitative traits based on a trio design. We show that the method can be viewed as a direct extension of the classical transmission diequilibrium test for binary traits to quantitative traits. We evaluate the performance of our method using extensive simulations and compare it with an existing method, family-based association test. We found that the two methods yield comparable powers if all families are considered. However, unlike FBAT, which yields an inflated rate of false positives when noninformative trios with all three individuals’ heterozygous are removed, our method maintains the correct size without compromising too much on power. We show that our method can be easily modified to incorporate multivariate phenotypes. Here, we applied this method to analyse a quantitative endophenotype associated with alcoholism.     

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.     

Use of unlinked genetic markers to detect population stratification in association studies.

We examine the issue of population stratification in association-mapping studies. In case-control studies of association, population subdivision or recent admixture of populations can lead to spurious associations between a phenotype and unlinked candidate loci. Using a model of sampling from a structured population, we show that if population stratification exists, it can be detected by use of unlinked marker loci. We show that the case-control-study design, using unrelated control individuals, is a valid approach for association mapping, provided that marker loci unlinked to the candidate locus are included in the study, to test for stratification. We suggest guidelines as to the number of unlinked marker loci to use.     

A general framework for two-stage analysis of genome-wide association studies and its application to case-control studies

Two-stage analyses of genome-wide association studies have been proposed as a means to improving power for designs including family-based association and gene-environment interaction testing. In these analyses, all markers are first screened via a statistic that may not be robust to an underlying assumption, and the markers thus selected are then analyzed in a second stage with a test that is independent from the first stage and is robust to the assumption in question. We give a general formulation of two-stage designs and show how one can use this formulation both to derive existing methods and to improve upon them, opening up a range of possible further applications. We show how using simple regression models in conjunction with external data such as average trait values can improve the power of genome-wide association studies. We focus on case-control studies and show how it is possible to use allele frequencies derived from an external reference to derive a powerful two-stage analysis. An illustration involving the Wellcome Trust Case-Control Consortium data shows several genome-wide-significant associations, subsequently validated, that were not significant in the standard analysis. We give some analytic properties of the methods and discuss some underlying principles.     

The power of genomic control

Although association analysis is a useful tool for uncovering the genetic underpinnings of complex traits, its utility is diminished by population substructure, which can produce spurious association between phenotype and genotype within population-based samples. Because family-based designs are robust against substructure, they have risen to the fore of association analysis. Yet, if population substructure could be ignored, this robustness can come at the price of power. Unfortunately it is rarely evident when population substructure can be ignored. Devlin and Roeder recently have proposed a method, termed "genomic control" (GC), which has the robustness of family-based designs even though it uses population-based data. GC uses the genome itself to determine appropriate corrections for population-based association tests. Using the GC method, we contrast the power of two study designs, family trios (i.e., father, mother, and affected progeny) versus case-control. For analysis of trios, we use the TDT test. When population substructure is absent, we find GC is always more powerful than TDT; furthermore, contrary to previous results, we show that as a disease becomes more prevalent the discrepancy in power becomes more extreme. When population substructure is present, however, the results are more complex: TDT is more powerful when population substructure is substantial, and GC is more powerful otherwise. We also explore general issues of power and implementation of GC within the case-control setting and find that, economically, GC is at least comparable to and often less expensive than family-based methods. Therefore, GC methods should prove a useful complement to family-based methods for the genetic analysis of complex traits.     

The association of a SNP upstream of INSIG2 with body mass index is reproduced in several but not all cohorts

A SNP upstream of the INSIG2 gene, rs7566605, was recently found to be associated with obesity as measured by body mass index (BMI) by Herbert and colleagues. The association between increased BMI and homozygosity for the minor allele was first observed in data from a genome-wide association scan of 86,604 SNPs in 923 related individuals from the Framingham Heart Study offspring cohort. The association was reproduced in four additional cohorts, but was not seen in a fifth cohort. To further assess the general reproducibility of this association, we genotyped rs7566605 in nine large cohorts from eight populations across multiple ethnicities (total n = 16,969). We tested this variant for association with BMI in each sample under a recessive model using family-based, population-based, and case-control designs. We observed a significant (p < 0.05) association in five cohorts but saw no association in three other cohorts. There was variability in the strength of association evidence across examination cycles in longitudinal data from unrelated individuals in the Framingham Heart Study Offspring cohort. A combined analysis revealed significant independent validation of this association in both unrelated (p = 0.046) and family-based (p = 0.004) samples. The estimated risk conferred by this allele is small, and could easily be masked by small sample size, population stratification, or other confounders. These validation studies suggest that the original association is less likely to be spurious, but the failure to observe an association in every data set suggests that the effect of SNP rs7566605 on BMI may be heterogeneous across population samples.     

Family-based versus unrelated case-control designs for genetic associations

The most simple and commonly used approach for genetic associations is the case-control study design of unrelated people. This design is susceptible to population stratification. This problem is obviated in family-based studies, but it is usually difficult to accumulate large enough samples of well-characterized families. We addressed empirically whether the two designs give similar estimates of association in 93 investigations where both unrelated case-control and family-based designs had been employed. Estimated odds ratios differed beyond chance between the two designs in only four instances (4%). The summary relative odds ratio (ROR) (the ratio of odds ratios obtained from unrelated case-control and family-based studies) was close to unity (0.96 [95% confidence interval, 0.91-1.01]). There was no heterogeneity in the ROR across studies (amount of heterogeneity beyond chance I(2) = 0%). Differences on whether results were nominally statistically significant (p < 0.05) or not with the two designs were common (opposite classification rates 14% and 17%); this reflected largely differences in power. Conclusions were largely similar in diverse subgroup analyses. Unrelated case-control and family-based designs give overall similar estimates of association. We cannot rule out rare large biases or common small biases.     

Genetic association studies: design,analysis and interpretation

This paper provides a review of the design and analysis of genetic association studies. In case control studies, the different contingency tables and their relationships to the underlying genetic model are defined. Population stratification is discussed, with suggested methods to identify and correct for the effect. The transmission disequilibrium test is provided as an alternative family-based test, which is robust to population stratification. The relative benefits of each analysis are summarised.     

A new powerful non-parametric two-stage approach for testing multiple phenotypes in family-based association studies

We introduce a new powerful nonparametric testing strategy for family-based association studies in which multiple quantitative traits are recorded and the phenotype with the strongest genetic component is not known prior to the analysis. In the first stage, using a population-based test based on the generalized estimating equation approach, we test all recorded phenotypes for association with the marker locus without biasing the nominal significance level of the later family-based analysis. In the second stage the phenotype with the smallest p value is selected and tested by a family-based association test for association with the marker locus. This strategy is robust against population admixture and stratification and does not require any adjustment for multiple testing. We demonstrate the advantages of this testing strategy over standard methodology in a simulation study. The practical importance of our testing strategy is illustrated by applications to the Childhood Asthma Management Program asthma data sets.     

A robust statistical method for association-based eQTL analysis

Background

It has been well established that theoretical kernel for recently surging genome-wide association study (GWAS) is statistical inference of linkage disequilibrium (LD) between a tested genetic marker and a putative locus affecting a disease trait. However, LD analysis is vulnerable to several confounding factors of which population stratification is the most prominent. Whilst many methods have been proposed to correct for the influence either through predicting the structure parameters or correcting inflation in the test statistic due to the stratification, these may not be feasible or may impose further statistical problems in practical implementation.

Methodology

We propose here a novel statistical method to control spurious LD in GWAS from population structure by incorporating a control marker into testing for significance of genetic association of a polymorphic marker with phenotypic variation of a complex trait. The method avoids the need of structure prediction which may be infeasible or inadequate in practice and accounts properly for a varying effect of population stratification on different regions of the genome under study. Utility and statistical properties of the new method were tested through an intensive computer simulation study and an association-based genome-wide mapping of expression quantitative trait loci in genetically divergent human populations.

Results/Conclusions

The analyses show that the new method confers an improved statistical power for detecting genuine genetic association in subpopulations and an effective control of spurious associations stemmed from population structure when compared with other two popularly implemented methods in the literature of GWAS.     

The quantitative trait linkage disequilibrium test: a more powerful alternative to the quantitative transmission disequilibrium test for use in the absence of population stratification

Linkage analysis based on identity-by-descent allele-sharing can be used to identify a chromosomal region harboring a quantitative trait locus (QTL), but lacks the resolution required for gene identification. Consequently, linkage disequilibrium (association) analysis is often employed for fine-mapping. Variance-components based combined linkage and association analysis for quantitative traits in sib pairs, in which association is modeled as a mean effect and linkage is modeled in the covariance structure has been extended to general pedigrees (quantitative transmission disequilibrium test, QTDT). The QTDT approach accommodates data not only from parents and siblings, but also from all available relatives. QTDT is also robust to population stratification. However, when population stratification is absent, it is possible to utilize even more information, namely the additional information contained in the founder genotypes. In this paper, we introduce a simple modification of the allelic transmission scoring method used in the QTDT that results in a more powerful test of linkage disequilibrium, but is only applicable in the absence of population stratification. This test, the quantitative trait linkage disequilibrium (QTLD) test, has been incorporated into a new procedure in the statistical genetics computer package SOLAR. We apply this procedure in a linkage/association analysis of an electrophysiological measurement previously shown to be related to alcoholism. We also demonstrate by simulation the increase in power obtained with the QTLD test, relative to the QTDT, when a true association exists between a marker and a QTL.     

Association between the CHRM2 gene and intelligence in a sample of 304 Dutch families

The CHRM2 gene is thought to be involved in neuronal excitability, synaptic plasticity and feedback regulation of acetylcholine release and has previously been implicated in higher cognitive processing. In a sample of 667 individuals from 304 families, we genotyped three single-nucleotide polymorphisms (SNPs) in the CHRM2 gene on 7q31-35. From all individuals, standardized intelligence measures were available. Using a test of within-family association, which controls for the possible effects of population stratification, a highly significant association was found between the CHRM2 gene and intelligence. The strongest association was between rs324650 and performance IQ (PIQ), where the T allele was associated with an increase of 4.6 PIQ points. In parallel with a large family-based association, we observed an attenuated - although still significant - population-based association, illustrating that population stratification may decrease our chances of detecting allele-trait associations. Such a mechanism has been predicted earlier, and this article is one of the first to empirically show that family-based association methods are not only needed to guard against false positives, but are also invaluable in guarding against false negatives.