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.     

Using the noninformative families in family-based association tests: a powerful new testing strategy

For genetic association studies with multiple phenotypes, we propose a new strategy for multiple testing with family-based association tests (FBATs). The strategy increases the power by both using all available family data and reducing the number of hypotheses tested while being robust against population admixture and stratification. By use of conditional power calculations, the approach screens all possible null hypotheses without biasing the nominal significance level, and it identifies the subset of phenotypes that has optimal power when tested for association by either univariate or multivariate FBATs. An application of our strategy to an asthma study shows the practical relevance of the proposed methodology. In simulation studies, we compare our testing strategy with standard methodology for family studies. Furthermore, the proposed principle of using all data without biasing the nominal significance in an analysis prior to the computation of the test statistic has broad and powerful applications in many areas of family-based association studies.     

Genetic association analysis using data from triads and unrelated subjects

The selection of an appropriate control sample for use in association mapping requires serious deliberation. Unrelated controls are generally easy to collect, but the resulting analyses are susceptible to spurious association arising from population stratification. Parental controls are popular, since triads comprising a case and two parents can be used in analyses that are robust to this stratification. However, parental controls are often expensive and difficult to collect. In some situations, studies may have both parental and unrelated controls available for analysis. For example, a candidate-gene study may analyze triads but may have an additional sample of unrelated controls for examination of background linkage disequilibrium in genomic regions. Also, studies may collect a sample of triads to confirm results initially found using a traditional case-control study. Initial association studies also may collect each type of control, to provide insurance against the weaknesses of the other type. In these situations, resulting samples will consist of some triads, some unrelated controls, and, possibly, some unrelated cases. Rather than analyze the triads and unrelated subjects separately, we present a likelihood-based approach for combining their information in a single combined association analysis. Our approach allows for joint analysis of data from both triad and case-control study designs. Simulations indicate that our proposed approach is more powerful than association tests that are based on each separate sample. Our approach also allows for flexible modeling and estimation of allele effects, as well as for missing parental data. We illustrate the usefulness of our approach using SNP data from a candidate-gene study of psoriasis.     

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.     

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.     

Likelihood-based association analysis for nuclear families and unrelated subjects with missing genotype data

Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.     

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.     

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.     

Control of population stratification by correlation-selected principal components

In genome-wide association studies, population stratification is recognized as producing inflated type I error due to the inflation of test statistics. Principal component-based methods applied to genotypes provide information about population structure, and have been widely used to control for stratification. Here we explore the precise relationship between genotype principal components and inflation of association test statistics, thereby drawing a connection between principal component-based stratification control and the alternative approach of genomic control. Our results provide an inherent justification for the use of principal components, but call into question the popular practice of selecting principal components based on significance of eigenvalues alone. We propose a new approach, called EigenCorr, which selects principal components based on both their eigenvalues and their correlation with the (disease) phenotype. Our approach tends to select fewer principal components for stratification control than does testing of eigenvalues alone, providing substantial computational savings and improvements in power. Analyses of simulated and real data demonstrate the usefulness of the proposed approach.     

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.     

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 unified GMDR method for detecting gene–gene interactions in family and unrelated samples with application to nicotine dependence

Gene–gene and gene–environment interactions govern a substantial portion of the variation in complex traits and diseases. In convention, a set of either unrelated or family samples are used in detection of such interactions; even when both kinds of data are available, the unrelated and the family samples are analyzed separately, potentially leading to loss in statistical power. In this report, to detect gene–gene interactions we propose a generalized multifactor dimensionality reduction method that unifies analyses of nuclear families and unrelated subjects within the same statistical framework. We used principal components as genetic background controls against population stratification, and when sibling data are included, within-family control were used to correct for potential spurious association at the tested loci. Through comprehensive simulations, we demonstrate that the proposed method can remarkably increase power by pooling unrelated and offspring’s samples together as compared with individual analysis strategies and the Fisher’s combining p value method while it retains a controlled type I error rate in the presence of population structure. In application to a real dataset, we detected one significant tetragenic interaction among CHRNA4, CHRNB2, BDNF, and NTRK2 associated with nicotine dependence in the Study of Addiction: Genetics and Environment sample, suggesting the biological role of these genes in nicotine dependence development.     

Parental phenotypes in family-based association analysis

Family-based association designs are popular, because they offer inherent control of population stratification based on age, sex, ethnicity, and environmental exposure. However, the efficiency of these designs is hampered by current analytic strategies that consider only offspring phenotypes. Here, we describe the incorporation of parental phenotypes and, specifically, the inclusion of parental genotype-phenotype correlation terms in association tests, providing a series of tests that effectively span an efficiency-robustness spectrum. The model is based on the between-within-sibship association model presented in 1999 by Fulker and colleagues for quantitative traits and extended here to nuclear families. By use of a liability-threshold-model approach, standard dichotomous and/or qualitative disease phenotypes can be analyzed (and can include appropriate corrections for phenotypically ascertained samples), which allows for the application of this model to analysis of the commonly used affected-proband trio design. We show that the incorporation of parental phenotypes can considerably increase power, as compared with the standard transmission/disequilibrium test and equivalent quantitative tests, while providing both significant protection against stratification and a means of evaluating the contribution of stratification to positive results. This methodology enables the extraction of more information from existing family-based collections that are currently being genotyped and analyzed by use of standard approaches.     

A powerful and flexible multilocus association test for quantitative traits

Association mapping of complex traits typically employs tagSNP genotype data to identify a trait locus within a region of interest. However, considerable debate exists regarding the most powerful strategy for utilizing such tagSNP data for inference. A popular approach tests each tagSNP within the region individually, but such tests could lose power as a result of incomplete linkage disequilibrium between the genotyped tagSNP and the trait locus. Alternatively, one can jointly test all tagSNPs simultaneously within the region (by using genotypes or haplotypes), but such multivariate tests have large degrees of freedom that can also compromise power. Here, we consider a semiparametric model for quantitative-trait mapping that uses genetic information from multiple tagSNPs simultaneously in analysis but produces a test statistic with reduced degrees of freedom compared to existing multivariate approaches. We fit this model by using a dimension-reducing technique called least-squares kernel machines, which we show is identical to analysis using a specific linear mixed model (which we can fit by using standard software packages like SAS and R). Using simulated SNP data based on real data from the International HapMap Project, we demonstrate that our approach often has superior performance for association mapping of quantitative traits compared to the popular approach of single-tagSNP testing. Our approach is also flexible, because it allows easy modeling of covariates and, if interest exists, high-dimensional interactions among tagSNPs and environmental predictors.     

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H(0) and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.     

复杂疾病全基因组关联研究进展——遗传统计分析

2005年, Science杂志首次报道了有关人类年龄相关性黄斑变性的全基因组关联研究, 此后有关肥胖、2型糖尿病、冠心病、阿尔茨海默病等一系列复杂疾病的全基因组关联研究被陆续报道, 这一阶段被称为人类全基因组关联研究的第一次浪潮。文章分别介绍了全基因组关联研究统计分析的方法、软件和应用实例; 比较了关联分析中多重检验的P值调整方法, 包括Bonferroni、递减的Bonferroni校正法、模拟运算法和控制错误发现率的方法; 还讨论了人群混杂对关联分析结果可能产生的影响及原理, 以及全基因组关联研究中控制人群混杂的方法的研究进展和应用实例。在全基因组关联研究的第一次浪潮中, 应用经典的遗传统计方法发现了许多基因-表型之间的关联并且能够对这些关联做出解释, 其中包括许多基因组中的未知基因和染色体区域。然而, 全基因组关联研究的继续发展需要进一步阐述基因组内基因之间相互作用、基因-基因之间的复杂作用网络与环境因素的相互作用在复杂疾病发生中的作用, 现有的统计分析方法肯定不能满足需要, 开发更为高级的统计分析方法势在必行。最后, 文章还给出了全基因组关联研究统计分析软件的相关网站信息。     

UGMDR: a unified conceptual framework for detection of multifactor interactions underlying complex traits

Biological outcomes are governed by multiple genetic and environmental factors that act in concert. Determining multifactor interactions is the primary topic of interest in recent genetics studies but presents enormous statistical and mathematical challenges. The computationally efficient multifactor dimensionality reduction (MDR) approach has emerged as a promising tool for meeting these challenges. On the other hand, complex traits are expressed in various forms and have different data generation mechanisms that cannot be appropriately modeled by a dichotomous model; the subjects in a study may be recruited according to its own analytical goals, research strategies and resources available, not only consisting of homogeneous unrelated individuals. Although several modifications and extensions of MDR have in part addressed the practical problems, they are still limited in statistical analyses of diverse phenotypes, multivariate phenotypes and correlated observations, correcting for potential population stratification and unifying both unrelated and family samples into a more powerful analysis. I propose a comprehensive statistical framework, referred as to unified generalized MDR (UGMDR), for systematic extension of MDR. The proposed approach is quite versatile, not only allowing for covariate adjustment, being suitable for analyzing almost any trait type, for example, binary, count, continuous, polytomous, ordinal, time-to-onset, multivariate and others, as well as combinations of those, but also being applicable to various study designs, including homogeneous and admixed unrelated-subject and family as well as mixtures of them. The proposed UGMDR offers an important addition to the arsenal of analytical tools for identifying nonlinear multifactor interactions and unraveling the genetic architecture of complex traits.     

Analysis of family- and population-based samples in cohort genome-wide association studies

Cohort studies typically sample unrelated individuals from a population, although family members of index cases may also be recruited to investigate shared familial risk factors. Recruitment of family members may be incomplete or ancillary to the main cohort, resulting in a mixed sample of independent family units, including unrelated singletons and multiplex families. Multiple methods are available to perform genome-wide association (GWA) analysis of binary or continuous traits in families, but it is unclear whether methods known to perform well on ascertained pedigrees, sibships, or trios are appropriate in analysis of a mixed unrelated cohort and family sample. We present simulation studies based on Multi-Ethnic Study of Atherosclerosis (MESA) pedigree structures to compare the performance of several popular methods of GWA analysis for both quantitative and dichotomous traits in cohort studies. We evaluate approaches suitable for analysis of families, and combined the best performing methods with population-based samples either by meta-analysis, or by pooled analysis of family- and population-based samples (mega-analysis), comparing type 1 error and power. We further assess practical considerations, such as availability of software and ability to incorporate covariates in statistical modeling, and demonstrate our recommended approaches through quantitative and binary trait analysis of HDL cholesterol (HDL-C) in 2,553 MESA family- and population-based African-American samples. Our results suggest linear modeling approaches that accommodate family-induced phenotypic correlation (e.g., variance-component model for quantitative traits or generalized estimating equations for dichotomous traits) perform best in the context of combined family- and population-based cohort GWAS.     

Linkage and association studies of QTL for nuclear families by mixed models

The transmission disequilibrium test (TDT) has been utilized to test the linkage and association between a genetic trait locus and a marker. Spielman et al. (1993) introduced TDT to test linkage between a qualitative trait and a marker in the presence of association. In the presence of linkage, TDT can be applied to test for association for fine mapping (Martin et al., 1997; Spielman and Ewens, 1996). In recent years, extensive research has been carried out on the TDT between a quantitative trait and a marker locus (Allison, 1997; Fan et al., 2002; George et al., 1999; Rabinowitz, 1997; Xiong et al., 1998; Zhu and Elston, 2000, 2001). The original TDT for both qualitative and quantitative traits requires unrelated offspring of heterozygous parents for analysis, and much research has been carried out to extend it to fit for different settings. For nuclear families with multiple offspring, one approach is to treat each child independently for analysis. Obviously, this may not be a valid method since offspring of one family are related to each other. Another approach is to select one offspring randomly from each family for analysis. However, with this method much information may be lost. Martin et al. (1997, 2000) constructed useful statistical tests to analyse the data for qualitative traits. In this paper, we propose to use mixed models to analyse sample data of nuclear families with multiple offspring for quantitative traits according to the models in Amos (1994). The method uses data of all offspring by taking into account their trait mean and variance-covariance structures, which contain all the effects of major gene locus, polygenic loci and environment. A test statistic based on mixed models is shown to be more powerful than the test statistic proposed by George et al. (1999) under moderate disequilibrium for nuclear families. Moreover, it has higher power than the TDT statistic which is constructed by randomly choosing a single offspring from each nuclear family.