A Powerful Nonparametric Statistical Framework for Family-Based Association Analyses

Family-based study design is commonly used in genetic research. It has many ideal features, including being robust to population stratification (PS). With the advance of high-throughput technologies and ever-decreasing genotyping cost, it has become common for family studies to examine a large number of variants for their associations with disease phenotypes. The yield from the analysis of these family-based genetic data can be enhanced by adopting computationally efficient and powerful statistical methods. We propose a general framework of a family-based U-statistic, referred to as family-U, for family-based association studies. Unlike existing parametric-based methods, the proposed method makes no assumption of the underlying disease models and can be applied to various phenotypes (e.g., binary and quantitative phenotypes) and pedigree structures (e.g., nuclear families and extended pedigrees). By using only within-family information, it can offer robust protection against PS. In the absence of PS, it can also utilize additional information (i.e., between-family information) for power improvement. Through simulations, we demonstrated that family-U attained higher power over a commonly used method, family-based association tests, under various disease scenarios. We further illustrated the new method with an application to large-scale family data from the Framingham Heart Study. By utilizing additional information (i.e., between-family information), family-U confirmed a previous association of CHRNA5 with nicotine dependence.     

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.     

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.     

Genomewide weighted hypothesis testing in family-based association studies, with an application to a 100K scan

For genomewide association (GWA) studies in family-based designs, we propose a novel two-stage strategy that weighs the association P values with the use of independently estimated weights. The association information contained in the family sample is partitioned into two orthogonal components--namely, the between-family information and the within-family information. The between-family component is used in the first (i.e., screening) stage to obtain a relative ranking of all the markers. The within-family component is used in the second (i.e., testing) stage in the framework of the standard family-based association test, and the resulting P values are weighted using the estimated marker ranking from the screening step. The approach is appealing, in that it ensures that all the markers are tested in the testing step and, at the same time, also uses information from the screening step. Through simulation studies, we show that testing all the markers is more powerful than testing only the most promising ones from the screening step, which was the method suggested by Van Steen et al. A comparison with a population-based approach shows that the approach achieves comparable power. In the presence of a reasonable level of population stratification, our approach is only slightly affected in terms of power and, since it is a family-based method, is completely robust to spurious effects. An application to a 100K scan in the Framingham Heart Study illustrates the practical advantages of our approach. The proposed method is of general applicability; it extends to any setting in which prior, independent ranking of hypotheses is available.     

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.     

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.     

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.     

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.     

Allowing for missing data at highly polymorphic genes when testing for maternal, offspring and maternal-fetal genotype incompatibility effects

Genes can be associated with disease through an individual's inherited genotype, the maternal genotype or the interaction between these two. When the gene is highly polymorphic, it is more difficult to identify the gene's functional role than for less polymorphic loci, because different alleles at the locus may be associated with the disease through separate and joint effects from maternal and offspring genotypes. Family-based studies are used to test genetic associations because of their robustness to population stratification. However, parental genotype data are often missing, and omitting incompletely genotyped families is inefficient. Methods have been proposed to accommodate incomplete families in family-based association studies. They are not easily generalized to allow simultaneous examination of offspring allelic, maternal allelic and maternal-fetal genotype (MFG) incompatibility effects. Since many MFG incompatibility effects occur through matching between maternal and offspring's genotypes, we present an identity-by-state (IBS) framework to incorporate incomplete families in the MFG test when modeling genetic effects produced by a polymorphic gene. Using simulations, we examine the MFG test's performance with incomplete parental genotype data and an IBS framework. The MFG test using the IBS framework is immune to population stratification and efficiently uses information from incomplete families.     

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.     

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.     

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.     

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.     

TrioMDR: Detecting SNP interactions in trio families with model-based multifactor dimensionality reduction

Single nucleotide polymorphism (SNP) interactions can explain the missing heritability of common complex diseases. Many interaction detection methods have been proposed in genome-wide association studies, and they can be divided into two types: population-based and family-based. Compared with population-based methods, family-based methods are robust vs. population stratification. Several family-based methods have been proposed, among which Multifactor Dimensionality Reduction (MDR)-based methods are popular and powerful. However, current MDR-based methods suffer from heavy computational burden. Furthermore, they do not allow for main effect adjustment. In this work we develop a two-stage model-based MDR approach (TrioMDR) to detect multi-locus interaction in trio families (i.e., two parents and one affected child). TrioMDR combines the MDR framework with logistic regression models to check interactions, so TrioMDR can adjust main effects. In addition, unlike consuming permutation procedures used in traditional MDR-based methods, TrioMDR utilizes a simple semi-parameter P-values correction procedure to control type I error rate, this procedure only uses a few permutations to achieve the significance of a multi-locus model and significantly speeds up TrioMDR. We performed extensive experiments on simulated data to compare the type I error and power of TrioMDR under different scenarios. The results demonstrate that TrioMDR is fast and more powerful in general than some recently proposed methods for interaction detection in trios. The R codes of TrioMDR are available at: https://github.com/TrioMDR/TrioMDR.     

Transmission/disequilibrium tests using multiple tightly linked markers

Transmission/disequilibrium tests have attracted much attention in genetic studies of complex traits because (a) their power to detect genes having small to moderate effects may be greater than that of other linkage methods and (b) they are robust against population stratification. Highly polymorphic markers have become available throughout the human genome, and many such markers can be studied within short physical distances. Studies using multiple tightly linked markers are more informative than those using single markers. However, such information has not been fully utilized by existing statistical methods, resulting in possibly substantial loss of information in the identification of genes underlying complex traits. In this article, we propose novel statistical methods to analyze multiple tightly linked markers. Simulation studies comparing our methods versus existing methods suggest that our methods are more powerful. Finally, we apply the proposed methods to study genetic linkage between the dopamine D2 receptor locus and alcoholism.     

A Generalized Family-Based Association Test for Dichotomous Traits

Recent advances in genotyping technology make it possible to utilize large-scale association analysis for disease-gene mapping. Powerful and robust family-based association methods are crucial for successful gene mapping. We propose a family-based association method, the generalized disequilibrium test (GDT), in which the genotype differences of all discordant relative pairs are utilized in assessing association within a family. The improvement of the GDT over existing methods is threefold: (1) information beyond first-degree relatives is incorporated efficiently, yielding substantial gains in power in comparison to existing tests; (2) the GDT statistic is implemented via a robust technique that does not rely on large sample theory, resulting in further power gains, especially at high levels of significance; and (3) covariates and weights based on family size are incorporated. Advantages of the GDT over existing methods are demonstrated by extensive computer simulations and by application to recently published large-scale genome-wide linkage data from the Type 1 Diabetes Genetics Consortium (T1DGC). In our simulations, the GDT consistently outperforms other tests for a common disease and frequently outperforms other tests for a rare disease; the power improvement is > 13% in 6 out of 8 extended pedigree scenarios. All of the six strongest associations identified by the GDT have been reported by other studies, whereas only three or four of these associations can be identified by existing methods. For the T1D association at gene UBASH3A, the GDT resulted in a genome-wide significance (p = 4.3 × 10⁻⁶), much stronger than the published significance (p = 10⁻⁴).     

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.     

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.     

人类复杂疾病关联研究中群体分层的检出和校正

病例对照研究是鉴定多基因疾病易感位点重要的遗传流行病学方法, 而群体分层是导致病例对照研究关联研究结果出现偏倚甚至是假关联的重要原因之一。文章对人群分层的检出及校正的方法和原理进行了阐述, 包括基于核心家系的传递/不平衡检验(TDT)以及基于不相关基因组遗传标记的基因组对照(GC)和结构化关联(SA)等, 并且对这几种方法进行了比较。     

Genomewide rapid association using mixed model and regression: a fast and simple method for genomewide pedigree-based quantitative trait loci association analysis

For pedigree-based quantitative trait loci (QTL) association analysis, a range of methods utilizing within-family variation such as transmission-disequilibrium test (TDT)-based methods have been developed. In scenarios where stratification is not a concern, methods exploiting between-family variation in addition to within-family variation, such as the measured genotype (MG) approach, have greater power. Application of MG methods can be computationally demanding (especially for large pedigrees), making genomewide scans practically infeasible. Here we suggest a novel approach for genomewide pedigree-based quantitative trait loci (QTL) association analysis: genomewide rapid association using mixed model and regression (GRAMMAR). The method first obtains residuals adjusted for family effects and subsequently analyzes the association between these residuals and genetic polymorphisms using rapid least-squares methods. At the final step, the selected polymorphisms may be followed up with the full measured genotype (MG) analysis. In a simulation study, we compared type 1 error, power, and operational characteristics of the proposed method with those of MG and TDT-based approaches. For moderately heritable (30%) traits in human pedigrees the power of the GRAMMAR and the MG approaches is similar and is much higher than that of TDT-based approaches. When using tabulated thresholds, the proposed method is less powerful than MG for very high heritabilities and pedigrees including large sibships like those observed in livestock pedigrees. However, there is little or no difference in empirical power of MG and the proposed method. In any scenario, GRAMMAR is much faster than MG and enables rapid analysis of hundreds of thousands of markers.