An improved score test for genetic association studies

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

A new association test using haplotype similarity

Association tests based on multi-marker haplotypes may be more powerful than those based on single markers. The existing association tests based on multi-marker haplotypes include Pearson's chi2 test which tests for the difference of haplotype distributions in cases and controls, and haplotype-similarity based methods which compare the average similarity among cases with that of the controls. In this article, we propose new association tests based on haplotype similarities. These new tests compare the average similarities within cases and controls with the average similarity between cases and controls. These methods can be applied to either phase-known or phase-unknown data. We compare the performance of the proposed methods with Pearson's chi2 test and the existing similarity-based tests by simulation studies under a variety of scenarios and by analyzing a real data set. The simulation results show that, in most cases, the new proposed methods are more powerful than both Pearson's chi2 test and the existing similarity-based tests. In one extreme case where the disease mutant induced at a very rare haplotype (相似文献   

An efficient family-based association test using multiple markers

In genetic association studies, multiple markers are usually employed to cover a genomic region of interest for localizing a trait locus. In this report, we propose a novel multi-marker family-based association test (T(LC)) that linearly combines the single-marker test statistics using data-driven weights. We examine the type-I error rate in a numerical study and compare its power to identify a common trait locus using tag single nucleotide polymorphisms (SNPs) within the same haplotype block that the trait locus resides with three competing tests including a global haplotype test (T(H)), a multi-marker test similar to the Hotelling-T(2) test for the population-based data (T(MM)), and a single-marker test with Bonferroni's correction for multiple testing (T(B)). The type-I error rate of T(LC) is well maintained in our numeric study. In all the scenarios we examined, T(LC) is the most powerful, followed by T(B). T(MM) and T(H) are the poorest. T(H) and T(MM) have essentially the same power when parents are available. However, when both parents are missing, T(MM) is substantially more powerful than T(H). We also apply this new test on a data set from a previous association study on nicotine dependence.     

Gene-based sequential burden association test

Detecting the association between a set of variants and a phenotype of interest is the first and important step in genetic and genomic studies. Although it attracted a large amount of attention in the scientific community and several related statistical approaches have been proposed in the literature, powerful and robust statistical tests are still highly desired and yet to be developed in this area. In this paper, we propose a powerful and robust association test, which combines information from each individual single-nucleotide polymorphisms based on sequential independent burden tests. We compare the proposed approach with some popular tests through a comprehensive simulation study and real data application. Our results show that, in general, the new test is more powerful; the gain in detecting power can be substantial in many situations, compared to other methods.     

Resampling-based multiple hypothesis testing procedures for genetic case-control association studies

In case-control studies of unrelated subjects, gene-based hypothesis tests consider whether any tested feature in a candidate gene--single nucleotide polymorphisms (SNPs), haplotypes, or both--are associated with disease. Standard statistical tests are available that control the false-positive rate at the nominal level over all polymorphisms considered. However, more powerful tests can be constructed that use permutation resampling to account for correlations between polymorphisms and test statistics. A key question is whether the gain in power is large enough to justify the computational burden. We compared the computationally simple Simes Global Test to the min P test, which considers the permutation distribution of the minimum p-value from marginal tests of each SNP. In simulation studies incorporating empirical haplotype structures in 15 genes, the min P test controlled the type I error, and was modestly more powerful than the Simes test, by 2.1 percentage points on average. When disease susceptibility was conferred by a haplotype, the min P test sometimes, but not always, under-performed haplotype analysis. A resampling-based omnibus test combining the min P and haplotype frequency test controlled the type I error, and closely tracked the more powerful of the two component tests. This test achieved consistent gains in power (5.7 percentage points on average), compared to a simple Bonferroni test of Simes and haplotype analysis. Using data from the Shanghai Biliary Tract Cancer Study, the advantages of the newly proposed omnibus test were apparent in a population-based study of bile duct cancer and polymorphisms in the prostaglandin-endoperoxide synthase 2 (PTGS2) gene.     

Genotype-based association test for general pedigrees: the genotype-PDT

Many family-based tests of linkage disequilibrium (LD) are based on counts of alleles rather than genotypes. However, allele-based tests may not detect interactions among alleles at a single locus that are apparent when examining associations with genotypes. Family-based tests of LD based on genotypes have been developed, but they are typically valid as tests of association only in families with a single affected individual. To take advantage of families with multiple affected individuals, we propose the genotype-pedigree disequilibrium test (geno-PDT) to test for LD between marker locus genotypes and disease. Unlike previous tests for genotypic association, the geno-PDT is valid in general pedigrees. Simulations to compare the power of the allele-based PDT and geno-PDT reveal that under an additive model, the allele-based PDT is more powerful, but that the geno-PDT can have greater power when the genetic model is recessive or dominant. Perhaps the most important property of the geno-PDT is the ability to test for association with particular genotypes, which can reveal underlying patterns of association at the genotypic level. These genotype-specific tests can be used to suggest possible underlying genetic models that are consistent with the pattern of genotypic association. This is illustrated through an application to a candidate gene analysis of the MLLT3 gene in families with Alzheimer disease. The geno-PDT approach for testing genotypes in general family data provides a useful tool for identifying genes in complex disease, and partitioning individual genotype contributions will help to dissect the influence of genotype on risk.     

Multiple hypothesis testing strategies for genetic case-control association studies

The genetic case-control association study of unrelated subjects is a leading method to identify single nucleotide polymorphisms (SNPs) and SNP haplotypes that modulate the risk of complex diseases. Association studies often genotype several SNPs in a number of candidate genes; we propose a two-stage approach to address the inherent statistical multiple comparisons problem. In the first stage, each gene's association with disease is summarized by a single p-value that controls a familywise error rate. In the second stage, summary p-values are adjusted for multiplicity using a false discovery rate (FDR) controlling procedure. For the first stage, we consider marginal and joint tests of SNPs and haplotypes within genes, and we construct an omnibus test that combines SNP and haplotype analysis. Simulation studies show that when disease susceptibility is conferred by a SNP, and all common SNPs in a gene are genotyped, marginal analysis of SNPs using the Simes test has similar or higher power than marginal or joint haplotype analysis. Conversely, haplotype analysis can be more powerful when disease susceptibility is conferred by a haplotype. The omnibus test tracks the more powerful of the two approaches, which is generally unknown. Multiple testing balances the desire for statistical power against the implicit costs of false positive results, which up to now appear to be common in the literature.     

Omnibus permutation tests of the association of an ensemble of genetic markers with disease in case-control studies

An omnibus permutation test of the overall null hypothesis can be used to assess the association of an entire ensemble of genetic markers with disease in case-control studies. In this approach, p-values for univariate marker-specific Armitage trend tests are combined to form a scalar statistic, which is then used in a permutation test to determine an overall p-value. Two previously described competing methods utilize either a standard two-sample Hotelling's T2 statistic or a global U statistic that is a weighted sum of univariate U statistics. In contrast to Hotelling's test, omnibus tests are much less sensitive to missing data, and utilize all available data. In contrast to the global U test, omnibus tests do not require that the direction of the effects of the individual markers on the risk of disease be correctly specified in advance; in fact, any combination of one- and two-sided univariate tests can be used. Simulations show that, even under circumstances favoring the competing tests (no missing data; direction of effects known), omnibus permutation tests based on Fisher's combining function or the Anderson-Darling statistic typically have power comparable to or greater than Hotelling's and the global U tests.     

Simultaneously testing for marginal genetic association and gene-environment interaction

In this article, the authors propose to simultaneously test for marginal genetic association and gene-environment interaction to discover single nucleotide polymorphisms that may be involved in gene-environment or gene-treatment interaction. The asymptotic independence of the marginal association estimator and various interaction estimators leads to a simple and flexible way of combining the 2 tests, allowing for exploitation of gene-environment independence in estimating gene-environment interaction. The proposed test differs from the 2-df test proposed by Kraft et al. (Hum Hered. 2007;63(2):111-119) in two respects. First, for the genetic association component, it tests for marginal association, which is often the primary objective in inference, rather than the main effect in a model with gene-environment interaction. Second, the gene-environment testing component can easily exploit putative gene-environment independence using either the case-only estimator or the empirical Bayes estimator, depending on whether the goal is gene-treatment interaction in a randomized trial or gene-environment interaction in an observational study. The use of the proposed joint test is illustrated through simulations and a genetic study (1993-2005) from the Women's Health Initiative.     

A Nonparametric Test to Detect Quantitative Trait Loci Where the Phenotypic Distribution Differs by Genotypes

Searching for genetic variants involved in gene‐gene and gene‐environment interactions in large‐scale data raises multiple methodological issues. Many existing methods have focused on the problem of dimensionality, trying to explore the largest number of combinations between risk factors while considering simple interaction models. Despite evidence demonstrating the efficacy of these methods in simulated data, their application in real data has been unsuccessful so far. The classical test of a linear marginal genetic effect has been widely used for agnostic genome‐wide association studies, with the underlying idea that most variants involved in interactions might display marginal effect on the phenotypic mean. Although this approach may allow for the identification of genetic variants involved in interactions in many scenarios, the linear marginal effects of some causal alleles on the phenotypic mean might not be always detectable at genome‐wide significance level. We introduce in this study a general association test for quantitative trait loci that compare the distributions of phenotypic values by genotypic classes as opposed to most standard tests that compare phenotypic means by genotypic classes. Using simulations we show that in presence of interactions, this approach can be more powerful than the standard test of the linear marginal effect, with a gain of power increasing with increasing interaction effect and decreasing frequencies of the interacting exposures. We demonstrate the potential utility of our method on real data by analyzing mammographic density genome‐wide data from the Nurses’ Health Study.     

Powerful and robust cross‐phenotype association test for case‐parent trios

There has been increasing interest in identifying genes within the human genome that influence multiple diverse phenotypes. In the presence of pleiotropy, joint testing of these phenotypes is not only biologically meaningful but also statistically more powerful than univariate analysis of each separate phenotype accounting for multiple testing. Although many cross‐phenotype association tests exist, the majority of such methods assume samples composed of unrelated subjects and therefore are not applicable to family‐based designs, including the valuable case‐parent trio design. In this paper, we describe a robust gene‐based association test of multiple phenotypes collected in a case‐parent trio study. Our method is based on the kernel distance covariance (KDC) method, where we first construct a similarity matrix for multiple phenotypes and a similarity matrix for genetic variants in a gene; we then test the dependency between the two similarity matrices. The method is applicable to either common variants or rare variants in a gene, and resulting tests from the method are by design robust to confounding due to population stratification. We evaluated our method through simulation studies and observed that the method is substantially more powerful than standard univariate testing of each separate phenotype. We also applied our method to phenotypic and genotypic data collected in case‐parent trios as part of the Genetics of Kidneys in Diabetes (GoKinD) study and identified a genome‐wide significant gene demonstrating cross‐phenotype effects that was not identified using standard univariate approaches.     

Genotype‐based matching to correct for population stratification in large‐scale case‐control genetic association studies

Genome‐wide association studies are helping to dissect the etiology of complex diseases. Although case‐control association tests are generally more powerful than family‐based association tests, population stratification can lead to spurious disease‐marker association or mask a true association. Several methods have been proposed to match cases and controls prior to genotyping, using family information or epidemiological data, or using genotype data for a modest number of genetic markers. Here, we describe a genetic similarity score matching (GSM) method for efficient matched analysis of cases and controls in a genome‐wide or large‐scale candidate gene association study. GSM comprises three steps: (1) calculating similarity scores for pairs of individuals using the genotype data; (2) matching sets of cases and controls based on the similarity scores so that matched cases and controls have similar genetic background; and (3) using conditional logistic regression to perform association tests. Through computer simulation we show that GSM correctly controls false‐positive rates and improves power to detect true disease predisposing variants. We compare GSM to genomic control using computer simulations, and find improved power using GSM. We suggest that initial matching of cases and controls prior to genotyping combined with careful re‐matching after genotyping is a method of choice for genome‐wide association studies. Genet. Epidemiol. 33:508–517, 2009. © 2009 Wiley‐Liss, Inc.     

Recommended Joint and Meta‐Analysis Strategies for Case‐Control Association Testing of Single Low‐Count Variants

In genome‐wide association studies of binary traits, investigators typically use logistic regression to test common variants for disease association within studies, and combine association results across studies using meta‐analysis. For common variants, logistic regression tests are well calibrated, and meta‐analysis of study‐specific association results is only slightly less powerful than joint analysis of the combined individual‐level data. In recent sequencing and dense chip based association studies, investigators increasingly test low‐frequency variants for disease association. In this paper, we seek to (1) identify the association test with maximal power among tests with well controlled type I error rate and (2) compare the relative power of joint and meta‐analysis tests. We use analytic calculation and simulation to compare the empirical type I error rate and power of four logistic regression based tests: Wald, score, likelihood ratio, and Firth bias‐corrected. We demonstrate for low‐count variants (roughly minor allele count [MAC] < 400) that: (1) for joint analysis, the Firth test has the best combination of type I error and power; (2) for meta‐analysis of balanced studies (equal numbers of cases and controls), the score test is best, but is less powerful than Firth test based joint analysis; and (3) for meta‐analysis of sufficiently unbalanced studies, all four tests can be anti‐conservative, particularly the score test. We also establish MAC as the key parameter determining test calibration for joint and meta‐analysis.     

Testing for genetic association: a powerful score test

To study the association between a candidate gene and a complex genetic disease, Pearson's chi(2) statistic can be applied to an m x 2 contingency table, where the m categories correspond to m haplotypes or marker alleles. For m>2, two alternative approaches for Pearson's chi(2) can be followed, which are more powerful if one haplotype or marker allele is associated. For the first approach, various 2 x 2 tables are formed by combining various categories and the maximum of the corresponding chi-square statistics is considered as the final statistic. The second approach takes the average over the possible associated categories by writing down an overall likelihood. For the latter approach, we propose a new score statistic, which gives more weight to haplotypes or marker alleles that are common. Since the disease allele is often not observed, the power of the various statistics depends on both the linkage disequilibrium pattern and the frequencies of the associated haplotype or marker allele in the cases and the controls. We heuristically compare various statistics within the two approaches and present the results of a simulation that compares the performance of all considered statistics. Finally, we apply the statistics to a case-control study on the association between COL2A1 gene and radiographic osteoarthritis. Our conclusion is that overall the new proposed score statistic has good power. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Combined haplotype relative risk (CHRR): a general and simple genetic association test that combines trios and unrelated case-controls

In some genetic association studies, samples contain both parental and unrelated controls. Under such scenarios, instead of analyzing only trios using family-based association tests or only unrelated subjects using a case-control study design, Nagelkerke et al. ([2004] Eur. J. Hum. Genet. 12:964-970) and Epstein et al. ([2005] Am. J. Hum. Genet. 76:592-608) proposed methods that implemented a likelihood ratio test to combine the two different types of data. In this article, we put forward a more powerful and simplified strategy to combine trios with unrelated subjects based on the haplotype relative risk (HRR) (Falk and Rubinstein [1987] Ann. Hum. Genet. 51:227-233). The HRR compares parental marker alleles transmitted to an affected offspring to those not transmitted as a test for association, a strategy that is similar to a case-control study that compares allele frequencies in diseased cases to those of unrelated controls. We prove that affected offspring can be pooled with diseased cases and that parental controls can be treated as unrelated controls when the trios and unrelated subjects are randomly sampled from the same population. Therefore, unrelated subjects can be incorporated into the HRR intuitively and effortlessly. For trios without complete parental genotypes, we adopted the strategy proposed by (Guo et al. [2005a] BMC Genet. 6:S90; [2005b] Hum. Hered. 59: 125-135), which is more feasible than the one proposed by Weinberg ([1999] Am. J. Hum. Genet. 64:1186-1193). In addition, simulation results suggest that the combined haplotype relative risk is more powerful than Epstein et al.'s method regardless of the disease prevalence in a homogeneous population.     

A prevalence-based association test for case-control studies

Genetic association is often determined in case-control studies by the differential distribution of alleles or genotypes. Recent work has demonstrated that association can also be assessed by deviations from the expected distributions of alleles or genotypes. Specifically, multiple methods motivated by the principles of Hardy-Weinberg equilibrium (HWE) have been developed. However, these methods do not take into account many of the assumptions of HWE. Therefore, we have developed a prevalence-based association test (PRAT) as an alternative method for detecting association in case-control studies. This method, also motivated by the principles of HWE, uses an estimated population allele frequency to generate expected genotype frequencies instead of using the case and control frequencies separately. Our method often has greater power, under a wide variety of genetic models, to detect association than genotypic, allelic or Cochran-Armitage trend association tests. Therefore, we propose PRAT as a powerful alternative method of testing for association.     

Efficient multilocus association testing for whole genome association studies using localized haplotype clustering

Whole genome association studies are generating data sets with hundreds of thousands of markers genotyped on thousands of cases and controls. We show that whole genome haplotypic association testing with permutation to account for multiple testing is statistically powerful and computationally feasible on such data, using an efficient software implementation of a recently proposed method. We use realistic simulations to explore the statistical properties of the method, and show that for ungenotyped disease-susceptibility variants with population frequencies of 5% or less the haplotypic tests have markedly better power than single-marker tests. We propose a combined single-marker and haplotypic strategy, in which both single-marker and haplotypic tests are applied, with the minimum P-value adjusted for multiple testing by permutation which results in a test that is powerful for detecting both low-and high-frequency disease-susceptibility variants.     

The admixture maximum likelihood test: a novel experiment-wise test of association between disease and multiple SNPs

Disease association studies often test large numbers of markers, and various methods have been proposed to correct for multiple testing. In this paper, we propose an admixture maximum likelihood approach that estimates both the proportion of associated single nucleotide polymorphisms (SNPs) and their typical effect size. We assessed this method and compared it with several previously proposed approaches by simulation. The maximum likelihood approach performed similarly to or better than all other tests across a wide range of alternative hypotheses. The rank truncated product method also had good power, though somewhat inferior to the maximum likelihood approach in most cases. A simple Bonferroni correction performed best only when the number of associated SNPs was small.     

An ensemble learning approach jointly modeling main and interaction effects in genetic association studies

Complex diseases are presumed to be the results of interactions of several genes and environmental factors, with each gene only having a small effect on the disease. Thus, the methods that can account for gene-gene interactions to search for a set of marker loci in different genes or across genome and to analyze these loci jointly are critical. In this article, we propose an ensemble learning approach (ELA) to detect a set of loci whose main and interaction effects jointly have a significant association with the trait. In the ELA, we first search for "base learners" and then combine the effects of the base learners by a linear model. Each base learner represents a main effect or an interaction effect. The result of the ELA is easy to interpret. When the ELA is applied to analyze a data set, we can get a final model, an overall P-value of the association test between the set of loci involved in the final model and the trait, and an importance measure for each base learner and each marker involved in the final model. The final model is a linear combination of some base learners. We know which base learner represents a main effect and which one represents an interaction effect. The importance measure of each base learner or marker can tell us the relative importance of the base learner or marker in the final model. We used intensive simulation studies as well as a real data set to evaluate the performance of the ELA. Our simulation studies demonstrated that the ELA is more powerful than the single-marker test in all the simulation scenarios. The ELA also outperformed the other three existing multi-locus methods in almost all cases. In an application to a large-scale case-control study for Type 2 diabetes, the ELA identified 11 single nucleotide polymorphisms that have a significant multi-locus effect (P-value=0.01), while none of the single nucleotide polymorphisms showed significant marginal effects and none of the two-locus combinations showed significant two-locus interaction effects.     

Equivalence of three score tests for association mapping of quantitative trait loci under selective genotyping

Huang and Lin ([2007] Am J Hum Genet 80:567–572) proposed a conditional‐likelihood approach for mapping quantitative trait loci (QTL) under selective genotyping, and demonstrated via simulation that their model tends to be more powerful than the prospective linear regression. However, we show that the three score tests based on the conditional, prospective and retrospective likelihoods are numerically identical in testing association between a quantitative trait and a candidate locus. Two approximations are derived for calculating power and sample size for the score test. Compared to the random sampling, a single‐tail selection generally reduces the power of the score test in mapping small effect QTLs. A two‐tail selection generally enhances the QTL heritability; however, in small samples, the power of the test may actually decrease if the sample sizes are highly unbalanced in the upper and lower tails of the trait distribution. Genet. Epidemiol. 34: 522–527, 2010. © 2010 Wiley‐Liss, Inc.