A Family‐Based Joint Test for Mean and Variance Heterogeneity for Quantitative Traits

Traditional quantitative trait locus (QTL) analysis focuses on identifying loci associated with mean heterogeneity. Recent research has discovered loci associated with phenotype variance heterogeneity (vQTL), which is important in studying genetic association with complex traits, especially for identifying gene–gene and gene–environment interactions. While several tests have been proposed to detect vQTL for unrelated individuals, there are no tests for related individuals, commonly seen in family‐based genetic studies. Here we introduce a likelihood ratio test (LRT) for identifying mean and variance heterogeneity simultaneously or for either effect alone, adjusting for covariates and family relatedness using a linear mixed effect model approach. The LRT test statistic for normally distributed quantitative traits approximately follows χ²‐distributions. To correct for inflated Type I error for non‐normally distributed quantitative traits, we propose a parametric bootstrap‐based LRT that removes the best linear unbiased prediction (BLUP) of family random effect. Simulation studies show that our family‐based test controls Type I error and has good power, while Type I error inflation is observed when family relatedness is ignored. We demonstrate the utility and efficiency gains of the proposed method using data from the Framingham Heart Study to detect loci associated with body mass index (BMI) variability.     

Binomial Mixture Model-based Association Tests under Genetic Heterogeneity

Most of the existing association tests for population-based case-control studies are based on comparing the mean genotype scores between the case and control groups, which may not be efficient under genetic heterogeneity. Given that most common diseases are genetically heterogeneous, caused by mutations in multiple loci, it may be beneficial to fully account for genetic heterogeneity in an association test. Here we first propose a binomial mixture model for such a purpose and develop a corresponding mixture likelihood ratio test (MLRT) for a single locus. We also consider two methods to combine single-locus-based MLRTs across multiple loci in linkage disequilibrium to boost power when causal SNPs are not genotyped. We show with a wide spectrum of numerical examples that under genetic heterogeneity the proposed tests are more powerful than some commonly used association tests.     

A Marginal Likelihood Model for Family-Based Data

This paper presents a marginal likelihood model for family‐based data based upon the transmission of marker alleles from each heterozygous parent to his/her affected children. The proposed model, extending the maximum‐likelihood‐binomial (MLB) method and the disequilibrium maximum‐likelihood‐binomial (DMLB) method ( Abel et al. 1998 ; Abel & Müller‐Myhsok, 1998 ; Huang & Jiang, 1999 ), is adaptive to linkage disequilibrium (LD) and linkage heterogeneity. Compared with other procedures, the likelihood ratio test (LRT) derived from the proposed model enjoys superior qualities. First, simulations indicate that the power of the LRT is greater than that of the TDT or DMLB in all of our studied scenarios. Second, when we applied the LRT and other tests to a Tourette Syndrome data, the result was data favorable to the use of the LRT. Therefore, we recommend the use of the LRT as an additional linkage test wherever applicable, especially when the amount of LD is uncertain.     

Likelihood Ratio Tests in Rare Variant Detection for Continuous Phenotypes

It is believed that rare variants play an important role in human phenotypes; however, the detection of rare variants is extremely challenging due to their very low minor allele frequency. In this paper, the likelihood ratio test (LRT) and restricted likelihood ratio test (ReLRT) are proposed to test the association of rare variants based on the linear mixed effects model, where a group of rare variants are treated as random effects. Like the sequence kernel association test (SKAT), a state‐of‐the‐art method for rare variant detection, LRT and ReLRT can effectively overcome the problem of directionality of effect inherent in the burden test in practice. By taking full advantage of the spectral decomposition, exact finite sample null distributions for LRT and ReLRT are obtained by simulation. We perform extensive numerical studies to evaluate the performance of LRT and ReLRT, and compare to the burden test, SKAT and SKAT‐O. The simulations have shown that LRT and ReLRT can correctly control the type I error, and the controls are robust to the weights chosen and the number of rare variants under study. LRT and ReLRT behave similarly to the burden test when all the causal rare variants share the same direction of effect, and outperform SKAT across various situations. When both positive and negative effects exist, LRT and ReLRT suffer from few power reductions compared to the other two competing methods; under this case, an additional finding from our simulations is that SKAT‐O is no longer the optimal test, and its power is even lower than that of SKAT. The exome sequencing SNP data from Genetic Analysis Workshop 17 were employed to illustrate the proposed methods, and interesting results are described.     

A Comparison of the Likelihood Ratio Test and the Variance‐Stabilising Transformation‐Based Tests for Detecting Association of Rare Variants

In a recent paper in this journal, the use of variance‐stabilising transformation techniques was proposed to overcome the problem of inadequacy in normality approximation when testing association for a low‐frequency variant in a case‐control study. It was shown that tests based on the variance‐stabilising transformations are more powerful than Fisher's exact test while controlling for type I error rate. Earlier in the journal, another study had shown that the likelihood ratio test (LRT) is superior to Fisher's exact test, Wald's test, and Pearson's χ² test in testing association for low‐frequency variants. Thus, it is of interest to make a direct comparison between the LRT and the tests based on the variance‐stabilising transformations. In this commentary, we show that the LRT and the variance‐stabilising transformation‐based tests have comparable power greater than Fisher's exact test, Wald's test, and Pearson's χ² test.     

High Resolution T2 Association Tests of Complex Diseases Based on Family Data

This paper proposes family based Hotelling's T² tests for high resolution linkage disequilibrium (LD) mapping or association studies of complex diseases. Assume that genotype data of multiple markers or haplotype blocks are available for a sample of nuclear families, in which some offspring are affected. Paired Hotelling's T² test statistics are proposed for a high resolution association study using parents as controls for affected offspring, based on two coding methods: haplotype/allele coding and genotype coding. The paired Hotelling's T² tests take not only the correlation between the haplotype blocks or markers into account, but also take the correlation within each parent‐offspring pair into account. The method extends two sample Hotelling's T² test statistics for population case control association studies, which are not valid for family data due to correlation of genetic data among family members. The validity of the proposed method is justified by rigorous mathematical and statistical proof under the large sample theory. The non‐centrality parameter approximations of the test statistics are calculated for power and sample size calculations. From power comparison and type I error calculations, it is shown that the test statistic based on haplotype/allele coding is advantageous over the test statistic of genotype coding. Analysis using multiple markers may provide higher power than single marker analysis. If only one marker is utilized the power of the test statistic based on haplotype/allele coding is nearly identical to that of 1‐TDT. Moreover, a permutation procedure is provided for data analysis. The method is applied to data from a German asthma family study. The results based on the paired Hotelling's T² statistic tests confirm the previous findings. However, the paired Hotelling's T² tests produce much smaller P‐values than those of the previous study. The permutation tests produce similar results to those of the previous study; moreover, additional marker combinations are shown to be significant by permutation tests. The proposed paired Hotelling's T² statistic tests are potentially powerful in mapping complex diseases. A SAS Macro, Hotel_fam.sas, has been written to implement the method for data analysis.     

Tests for Candidate-Gene Association Using Case-Parents Design

In the case‐parents design for testing candidate‐gene association, the conditional likelihood method based on genotype relative risks has been developed recently. A specific relation of the genotype relative risks is referred to as a genetic model. The efficient score tests have been used when the genetic model is correctly specified under the alternative hypothesis. In practice, however, it is usually not able to specify the genetic model correctly. In the latter situation, tests such as the likelihood ratio test (LRT) and the MAX3 (the maximum of the three score statistics for dominant, additive, and recessive models) have been used. In this paper, we consider the restricted likelihood ratio test (RLRT). For a specific genetic model, simulation results demonstrate that RLRT is asymptotically equivalent to the score test, and both are more powerful than the LRT. When the genetic model cannot be correctly specified, the simulation results show that RLRT is most robust and powerful in the situations we studied. MAX3 is the next most robust and powerful test. The TDT is the easiest statistic to compute, compared to MAX3 and RLRT. When the recessive model can be eliminated, it is also as robust and powerful as RLRT for other genetic models.     

Failure of replicating the association between hippocampal volume and 3 single-nucleotide polymorphisms identified from the European genome-wide association study in Asian populations

Hippocampal volume is a key brain structure for learning ability and memory process, and hippocampal atrophy is a recognized biological marker of Alzheimer's disease. However, the genetic bases of hippocampal volume are still unclear although it is a heritable trait. Genome-wide association studies (GWASs) on hippocampal volume have implicated several significantly associated genetic variants in Europeans. Here, to test the contributions of these GWASs identified genetic variants to hippocampal volume in different ethnic populations, we screened the GWAS-identified candidate single-nucleotide polymorphisms in 3 independent healthy Asian brain imaging samples (a total of 990 subjects). The results showed that none of these single-nucleotide polymorphisms were associated with hippocampal volume in either individual or combined Asian samples. The replication results suggested a complexity of genetic architecture for hippocampal volume and potential genetic heterogeneity between different ethnic populations.     

The challenges,advantages and future of phenome‐wide association studies

Over the last decade, significant technological breakthroughs have revolutionized human genomic research in the form of genome‐wide association studies (GWASs). GWASs have identified thousands of statistically significant genetic variants associated with hundreds of human conditions including many with immunological aetiologies (e.g. multiple sclerosis, ankylosing spondylitis and rheumatoid arthritis). Unfortunately, most GWASs fail to identify clinically significant associations. Identifying biologically significant variants by GWAS also presents a challenge. The GWAS is a phenotype‐to‐genotype approach. As a complementary/alternative approach to the GWAS, investigators have begun to exploit extensive electronic medical record systems to conduct a genotype‐to‐phenotype approach when studying human disease – specifically, the phenome‐wide association study (PheWAS). Although the PheWAS approach is in its infancy, this method has already demonstrated its capacity to rediscover important genetic associations related to immunological diseases/conditions. Furthermore, PheWAS has the advantage of identifying genetic variants with pleiotropic properties. This is particularly relevant for HLA variants. For example, PheWAS results have demonstrated that the HLA‐DRB1 variant associated with multiple sclerosis may also be associated with erythematous conditions including rosacea. Likewise, PheWAS has demonstrated that the HLA‐B genotype is not only associated with spondylopathies, uveitis, and variability in platelet count, but may also play an important role in other conditions, such as mastoiditis. This review will discuss and compare general PheWAS methodologies, describe both the challenges and advantages of the PheWAS, and provide insight into the potential directions in which PheWAS may lead.     

Fast permutation tests and related methods,for association between rare variants and binary outcomes

In large‐scale genetic studies, a primary aim is to test for an association between genetic variants and a disease outcome. The variants of interest are often rare and appear with low frequency among subjects. In this situation, statistical tests based on standard asymptotic results do not adequately control the type I error rate, especially if the case : control ratio is unbalanced. In this article, we propose the use of permutation and approximate unconditional tests for testing association with rare variants. We use novel analytical calculations to efficiently approximate the true type I error rate under common study designs, and in numerical studies show that the proposed classes of tests significantly improve upon standard testing methods. We also illustrate our methods in data from a recent case–control study for genetic causes of a severe side effect of a common drug treatment.     

Further Investigation of Linkage Disequilibrium SNPs and their Ability to Identify Associated Susceptibility Loci

There is currently considerable interest in the use of single‐nucleotide polymorphisms (SNPs) to map disease susceptibility genes. The success of this method will depend on a number of factors including the strength of linkage disequilibrium (LD) between marker and disease loci. We used a data set of SNP genotypings in the region of the APOE disease susceptibility locus to investigate the likely usefulness of SNPs in case‐control studies. Using the estimated haplotype structure surrounding and including the APOE locus, and assuming a codominant disease model, we treated each SNP in turn as if it were a disease susceptibility locus and obtained, for each disease locus and markers, the expected likelihood ratio test (LRT) to assess disease association.We were particularly interested in the power to detect association with the susceptibility polymorphism itself, the power of nearby markers to detect association, and the ability to distinguish between the susceptibility polymorphism and marker loci also showing association. We found that the expected LRT depended critically on disease allele frequencies. For disease loci with a reasonably common allele we were usually able to detect association. However, for only a subset of markers in the close neighbourhood of the disease locus was association detectable. In these cases we were usually, but not always, able to distinguish the disease locus from nearby associated marker loci. For some disease loci, no other loci demonstrated detectable association with the disease phenotype. We conclude that one may need to use very dense SNP maps in order to avoid overlooking polymorphisms affecting susceptibility to a common phenotype.     

Association of ANK3 with bipolar disorder confirmed in East Asia

Results of genome‐wide association studies (GWASs) for bipolar disorder (BD) have indicated ANK3 as one of the most promising candidates for a susceptibility gene. In this study, we performed genetic association analysis of two single‐nucleotide polymorphisms (SNPs) in ANK3 (rs1938526 and rs10994336), whose genome‐wide significant associations were reported in a previous meta‐analysis of GWASs, using genotyping data of Korean and Japanese case–control samples and a part of data from a GWAS in Han‐Chinese from Taiwan. The total number of participants was 2,212 cases (352 from Korea, 860 from Japan, and 1,000 from Taiwan) and 2,244 controls (349 from Korea, 895 from Japan, and 1,000 from Taiwan). We could not detect any significant difference of allele frequency in individual analyses using each of the three populations. However, when we combined the three data sets and performed a meta‐analysis, rs1938526 showed nominally significant association (P = 0.048, odds ratio = 1.09). The over‐represented allele in BD was same as that reported in Caucasian GWASs. On the other hand, any significant association was not detected in rs10994336. This discrepancy between two SNPs may be explained by the different degree of linkage disequilibrium between Asian and Caucasian. These findings further supported the association between ANK3 and BD, and also suggested the genomic region around rs1938526 as a common risk locus across ethnicities. © 2011 Wiley‐Liss, Inc.     

Examining the stability of genetic risk effect as evidence accumulates in the context of meta-analysis

The recursive cumulative meta-analysis (RCM) of genetic association studies explores the relative change of the cumulative risk effect (e.g. OR) in time, indicating the stability of risk effect as evidence accumulates. However, the stability in risk effect is currently evaluated empirically with a graphical approach. A Monte Carlo permutation test for examining the instability in RCM is proposed. The statistic used is a function of the difference between the observed change in risk effect and the expected change, and is expressed (stepwise) cumulatively from the last published GAS to the first one. The permutation method is based on the individual studies and the number of studies in each time step. The test was demonstrated using data from two large scale meta-analyses of GAS. The performance of the test was also explored by simulating data from meta-analyses with different settings in terms of heterogeneity and significance. Significance instability was detected when wide oscillations in risk effect were presented and vice versa. The proposed test for assessing stability may provide the framework for claiming or denying the existence of an association as evidence accumulates.     

Efficient Calculation of P‐value and Power for Quadratic Form Statistics in Multilocus Association Testing

We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest take the general form D=X^TA X , where A is a general similarity matrix which may or may not be positive semi‐definite, and X follows the multivariate normal distribution with mean μ and variance matrix Σ, where Σ may or may not be singular. We show that D can be written as a linear combination of independent χ² random variables with a shift. Furthermore, its distribution can be approximated by a χ² or the difference of two χ² distributions. In the setting of association testing, our methods are especially useful in two situations. First, when the required significance level is much smaller than 0.05 such as in a genome scan, the estimation of p‐values using permutation procedures can be challenging. Second, when an EM algorithm is required to infer haplotype frequencies from un‐phased genotype data, the computation can be intensive for a permutation procedure. In either situation, an efficient and accurate estimation procedure would be useful. Our method can be applied to any quadratic form statistic and therefore should be of general interest.     

Replication of past candidate loci for common diseases and phenotypes in 100 genome-wide association studies

Genome-wide association studies (GWASs) have created a paradigm shift in discovering genetic associations for common diseases and phenotypes, but it is unclear whether the thousands of candidate genetic association studies performed in the pre-GWAS era had found any reliable associations for common diseases and phenotypes. We aimed to systematically evaluate whether loci proposed to harbor candidate associations before the advent of GWASs are replicated in GWASs. The GWAS data published through August, 2008 and included in the NHGRI catalog were screened and variants in candidate loci were selected on the basis of statistical significance (P<0.05) to create a list of independent, non-redundant associations. Altogether, 159 articles on GWASs were evaluated, 100 of which addressed past proposed candidate loci. A total of 291 independent, nominally significant (P<0.05) candidate gene associations were assembled after keeping only the SNP with lowest P-value for each locus and each phenotype; 108 of those had P<10⁻³ for association and 41 had P<10⁻⁷. A total of 22 of these 41 candidate gene associations pertained to binary phenotypes with a median odds ratio=2.91 (IQR: 1.82–4.6) and median minor allele frequency=0.17 (IQR: 0.12–0.29) in Caucasians; for comparison, 60 new associations of binary outcomes with P<10⁻⁷ discovered in the same GWASs had much smaller effects (median odds ratio 1.30, IQR: 1.18–1.58) and modestly larger minor allele frequencies (median 0.27, IQR: 0.15–0.43). Overall, few of the numerous genetic associations proposed in the candidate gene era have been replicated in GWASs, but those that have been conclusively replicated have large genetic effects that should not be discarded.     

Association of Monocyte Chemoattractant Protein‐1 (MCP‐1)‐2518A>G Polymorphism with Susceptibility to Coronary Artery Disease: A Meta‐Analysis

We attempted to systematically elucidate the association between monocyte chemoattractant protein‐1 (MCP‐1) ‐2518A>G polymorphism and risk of coronary artery disease (CAD). Eligible studies were identified through PubMed, EBSCO, and Web of Science Databases. The magnitude of MCP‐1 polymorphism effect and its possible mode of action on CAD were estimated. The odds ratio (OR) with 95% confidence intervals (CI) were pooled in a specific genetic model to assess the association. A total of 21 studies were involved. There was significant gene effect on CAD risk in the overall population (likelihood ratio test: p < 0.0001). Patients with GG and AG genotypes had 1.435 (95% CI: 1.183–1.740) and 1.087 (95% CI: 1.008–1.172) times higher risk of CAD than those with AA genotype. These gene effects suggested a recessive model to be appropriate. The pooled OR was 1.362 (95% CI: 1.137–1.631; p_uncorrected = 0.001, p_FDR = 0.005) in the recessive model. In the ethnicity‐stratified analysis, significant association was observed in the Caucasian population (OR = 1.492; 95% CI: 1.106–2.014; p_uncorrected = 0.009, p_FDR = 0.015), whereas no statistical significant association was detected in the Asian population (adjusted p = 0.124). The results suggested that MCP‐1 ‐2518A>G polymorphism may be associated with susceptibility to CAD, especially in Caucasians.     

Permutation and Parametric Bootstrap Tests for Gene–Gene and Gene–Environment Interactions

Permutation tests are widely used in genomic research as a straightforward way to obtain reliable statistical inference without making strong distributional assumptions. However, in this paper we show that in genetic association studies it is not typically possible to construct exact permutation tests of gene‐gene or gene‐environment interaction hypotheses. We describe an alternative to the permutation approach in testing for interaction, a parametric bootstrap approach. Using simulations, we compare the finite‐sample properties of a few often‐used permutation tests and the parametric bootstrap. We consider interactions of an exposure with single and multiple polymorphisms. Finally, we address when permutation tests of interaction will be approximately valid in large samples for specific test statistics.     

Genome‐wide analyses of psychological resilience in U.S. Army soldiers

Though a growing body of preclinical and translational research is illuminating a biological basis for resilience to stress, little is known about the genetic basis of psychological resilience in humans. We conducted genome‐wide association studies (GWASs) of self‐assessed (by questionnaire) and outcome‐based (incident mental disorders from predeployment to postdeployment) resilience among European (EUR) ancestry soldiers in the Army study to assess risk and resilience in servicemembers. Self‐assessed resilience (N = 11,492) was found to have significant common‐variant heritability (h² = 0.162, se = 0.050, p = 5.37 × 10^?4), and to be significantly negatively genetically correlated with neuroticism (r_g = ?0.388, p = .0092). GWAS results from the EUR soldiers revealed a genome‐wide significant locus on an intergenic region on Chr 4 upstream from doublecortin‐like kinase 2 (DCLK2) (four single nucleotide polymorphisms (SNPs) in LD; top SNP: rs4260523 [p = 5.65 × 10^?9] is an eQTL in frontal cortex), a member of the doublecortin family of kinases that promote survival and regeneration of injured neurons. A second gene, kelch‐like family member 36 (KLHL36) was detected at gene‐wise genome‐wide significance [p = 1.89 × 10^?6]. A polygenic risk score derived from the self‐assessed resilience GWAS was not significantly associated with outcome‐based resilience. In very preliminary results, genome‐wide significant association with outcome‐based resilience was found for one locus (top SNP: rs12580015 [p = 2.37 × 10^?8]) on Chr 12 downstream from solute carrier family 15 member 5 (SLC15A5) in subjects (N = 581) exposed to the highest level of deployment stress. The further study of genetic determinants of resilience has the potential to illuminate the molecular bases of stress‐related psychopathology and point to new avenues for therapeutic intervention.     

On Efficient and Accurate Calculation of Significance P‐Values for Sequence Kernel Association Testing of Variant Set

The objective of this paper is to discuss and develop alternative computational methods to accurately and efficiently calculate significance P‐values for the commonly used sequence kernel association test (SKAT) and adaptive sum of SKAT and burden test (SKAT‐O) for variant set association. We show that the existing software can lead to either conservative or inflated type I errors. We develop alternative and efficient computational algorithms that quickly compute the SKAT P‐value and have well‐controlled type I errors. In addition, we derive an alternative and simplified formula for calculating the significance P‐value of SKAT‐O, which sheds light on the development of efficient and accurate numerical algorithms. We implement the proposed methods in the publicly available R package that can be readily used or adapted to large‐scale sequencing studies. Given that more and more large‐scale exome and whole genome sequencing or re‐sequencing studies are being conducted, the proposed methods are practically very important. We conduct extensive numerical studies to investigate the performance of the proposed methods. We further illustrate their usefulness with application to associations between rare exonic variants and fasting glucose levels in the Atherosclerosis Risk in Communities (ARIC) study.     

Allele‐Sharing Statistics Using Information on Family History

When conducting genetic studies for complex traits, large samples are commonly required to detect new genetic factors. A possible strategy to decrease the sample size is to reduce heterogeneity using available information. In this paper we propose a new class of model‐free linkage analysis statistics which takes into account the information given by the ungenotyped affected relatives (positive family history). This information is included into the scoring function of classical allele‐sharing statistics. We studied pedigrees of affected sibling pairs with one ungenotyped affected relative. We show that, for rare allele common complex diseases, the proposed method increases the expected power to detect linkage. Allele‐sharing methods were applied to the symptomatic osteoarthritis GARP study where taking into account the family‐history increased considerably the evidence of linkage in the region of the DIO2 susceptibility locus.