Removing phenotypic distribution assumptions from tests of linkage disequilibrium for quantitative traits

The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.     

Semiparametric Allelic Tests for Mapping Multiple Phenotypes: Binomial Regression and Mahalanobis Distance

Binary phenotypes commonly arise due to multiple underlying quantitative precursors and genetic variants may impact multiple traits in a pleiotropic manner. Hence, simultaneously analyzing such correlated traits may be more powerful than analyzing individual traits. Various genotype‐level methods, e.g., MultiPhen (O'Reilly et al. [ 2012 ]), have been developed to identify genetic factors underlying a multivariate phenotype. For univariate phenotypes, the usefulness and applicability of allele‐level tests have been investigated. The test of allele frequency difference among cases and controls is commonly used for mapping case‐control association. However, allelic methods for multivariate association mapping have not been studied much. In this article, we explore two allelic tests of multivariate association: one using a Binomial regression model based on inverted regression of genotype on phenotype (Binomial regression‐based Association of Multivariate Phenotypes [BAMP]), and the other employing the Mahalanobis distance between two sample means of the multivariate phenotype vector for two alleles at a single‐nucleotide polymorphism (Distance‐based Association of Multivariate Phenotypes [DAMP]). These methods can incorporate both discrete and continuous phenotypes. Some theoretical properties for BAMP are studied. Using simulations, the power of the methods for detecting multivariate association is compared with the genotype‐level test MultiPhen's. The allelic tests yield marginally higher power than MultiPhen for multivariate phenotypes. For one/two binary traits under recessive mode of inheritance, allelic tests are found to be substantially more powerful. All three tests are applied to two different real data and the results offer some support for the simulation study. We propose a hybrid approach for testing multivariate association that implements MultiPhen when Hardy‐Weinberg Equilibrium (HWE) is violated and BAMP otherwise, because the allelic approaches assume HWE.     

The impact of marker allele frequency misspecification in variance components quantitative trait locus analysis using sibship data

In cases where sibship data are collected for a quantitative trait locus (QTL) linkage study without access to parental genotypes, the proportion of genes shared identical by descent must be estimated using the marker allele frequencies. No systematic study has been conducted to date to evaluate the effect of misspecification of these frequencies on a test of quantitative trait linkage. Analysis of both simulated and actual data on quantitative traits was carried out under various sets of allele frequency estimates. While correctly specifying the allele frequency distribution led to a slightly more powerful test and higher lod scores, the differences were small and would not likely alter the conclusion of a study. These results suggest that, at least for QTL analysis, there is a great deal of tolerance for misspecifying marker allele frequencies with little, if any, appreciable effect on the linkage test. However, the observed variations may be sufficiently large to alter the priority on might give to a positive finding for follow up.     

Use of Variable Marker Density,Principal Components,and Neural Networks in the Dissection of Disease Etiology

Several approaches were taken to identify the loci contributing to the quantitative and qualitative phenotypes in the Genetic Analysis Workshop 12 simulated data set. To identify possible quantitative trait loci (QTL), the quantitative traits were analyzed using SOLAR. The four replicates identified as the “best replicates” by the simulators, 42, 25, 33, and 38, were analyzed separately. Each of the five quantitative phenotypes was analyzed individually in the four replicates. To increase the power to detect QTL with pleiotropic effects, principal component analysis was performed and one new multivariate phenotype was estimated. In each instance, after performing a 10‐cM genome screen, fine mapping was completed in the initially identified linked regions to further evaluate the evidence for linkage. This approach of initially performing a coarse marker screen followed by analyses using much higher marker density successfully identified all the QTL playing a role in the quantitative phenotypes. The principal component phenotype did not substantially improve the power of QTL detection or localization. A neural network approach was utilized to identify loci contributing to disease status. The neural network technique identified the strongest gene influencing disease status as well as a locus contributing to quantitative traits 3 and 4; however, the inputs that contributed the greatest information were markers not in QTL regions. © 2001 Wiley‐Liss, Inc.     

Population Based Linkage Disequilibrium Mapping of QTL: An Application to Simulated Data in an Isolated Population

Despite successes in mapping and cloning genes involved in rare Mendelian diseases, genetic dissection of quantitative traits into single Mendelian factors still remains a challenging task. As the dense map of single nucleotide polymorphism (SNP) markers becomes available in the near future, linkage disequilibrium (LD) mapping will become one of major tools for mapping and identifying quantitative trait loci (QTL). In this report, we present a population‐based linkage disequilibrium mapping of QTL. This method unifies the analysis of mapping QTL in humans and in model organisms and can be used for randomly sampled individuals. The proposed method is applied to search for polymorphism sites within the candidate genes 2 and 6, which influence quantitative traits Q1 and Q2 or Q5, in a simulated data set in an isolated population. © 2001 Wiley‐Liss, Inc.     

Combining Multiple Phenotypic Traits Optimally for Detecting Linkage with Sib‐Pair Observations

A number of investigators have proposed regression methods for testing linkage between a phenotypic trait and a genetic marker with sib‐pair observations. Xu et al. [Am J Hum Genet 67:1025–8, 2000] studied a unified method for testing linkage, which tends to be more powerful than existing procedures. Often there are multiple traits, which are linked to a common set of genetic markers. In this paper, we present a simple generalization of the unified test to combine information from multiple traits optimally. We use the simulated Genetic Analysis Workshop 12 data to illustrate this methodology and show the advantage of using the combined tests over the single‐trait tests. For the four quantitative traits (Q1,...,Q4) studied, our linkage results suggest that major loci affecting Q1 and Q2 localize at or near markers D02G172, D19G032, and D09G122, while loci affecting Q3 and Q4 localize at or near markers D09G122 and D17G051. © 2001 Wiley‐Liss, Inc.     

On the use of phylogeny‐based tests to detect association between quantitative traits and haplotypes

With the increasing availability of genetic data, several SNPs in a candidate gene can be combined into haplotypes to test for association with a quantitative trait. When the number of SNPs increases, the number of haplotypes can become very large and there is a need to group them together. The use of the phylogenetic relationships between haplotypes provides a natural and efficient way of grouping. Moreover, it allows us to identify disease or quantitative trait‐related loci. In this article, we describe ALTree‐q , a phylogeny‐based approach to test for association between quantitative traits and haplotypes and to identify putative quantitative trait nucleotides (QTN). This study focuses on ALTree‐q association test which is based on one‐way analyses of variance (ANOVA) performed at the different levels of the tree. The statistical properties (type‐one error and power rates) were estimated through simulations under different genetic models and were compared to another phylogeny‐based test, TreeScan, (Templeton, 2005) and to a haplotypic omnibus test consisting in a one‐way ANOVA between all haplotypes. For dominant and additive models ALTree‐q is usually the most powerful test whereas TreeScan performs better under a recessive model. However, power depends strongly on the recurrence rate of the QTN, on the QTN allele frequency, and on the linkage disequilibrium between the QTN and other markers. An application of the method on Thrombin Activatable Fibronolysis Inhibitor Antigen levels in European and African samples confirms a possible association with polymorphisms of the CPB2 gene and identifies several QTNs. Genet. Epidemiol. 33:729–739, 2009. © 2009 Wiley‐Liss, Inc.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.     

Power comparison of regression methods to test quantitative traits for association and linkage

George et al. [1999 Am J Hum Genet 65:236-245] proposed a regression-based TDT method for quantitative traits consisting of regressing the trait on the parental transmission of a marker allele. Zhu and Elston [2000] also developed a TDT method for quantitative traits by defining a linear transformation to condition out founder information. Both methods test the null hypothesis of no linkage or association and can be applied to general pedigree structures. In this paper, we compare the power of these two methods through simulation, sampling those nuclear families with at least one heterozygous parent. Overall, we find that a variant of Zhu and Elston's method with 2 d.f. is more powerful. However, if the mode of inheritance is known, then a most powerful test with 1 d.f. can be found. All these regression TDT tests require linkage to detect association, but a test that does not require linkage will be more powerful.     

Replication of Linkage to Quantitative Trait Loci: Variation in Location and Magnitude of the Lod Score

Replication of linkage signals from independent samples is considered an important step toward verifying the significance of linkage signals in studies of complex traits. The purpose of this empirical investigation was to examine the variability in the precision of localizing a quantitative trait locus (QTL) by analyzing multiple replicates of a simulated data set with the use of variance components‐based methods. Specifically, we evaluated across replicates the variation in both the magnitude and the location of the peak lod scores. We analyzed QTLs whose effects accounted for 10–37% of the phenotypic variance in the quantitative traits. Our analyses revealed that the precision of QTL localization was directly related to the magnitude of the QTL effect. For a QTL with effect accounting for > 20% of total phenotypic variation, > 90% of the linkage peaks fall within 10 cM from the true gene location. We found no evidence that, for a given magnitude of the lod score, the presence of interaction influenced the precision of QTL localization. © 2001 Wiley‐Liss, Inc.     

Sibship analysis of associations between SNP haplotypes and a continuous trait with application to mammographic density

Haplotype‐based association studies have been proposed as a powerful comprehensive approach to identify causal genetic variation underlying complex diseases. Data comparisons within families offer the additional advantage of dealing naturally with complex sources of noise, confounding and population stratification. Two problems encountered when investigating associations between haplotypes and a continuous trait using data from sibships are (i) the need to define within‐sibship comparisons for sibships of size greater than two and (ii) the difficulty of resolving the joint distribution of haplotype pairs within sibships in the absence of parental genotypes. We therefore propose first a method of orthogonal transformation of both outcomes and exposures that allow the decomposition of between‐ and within‐sibship regression effects when sibship size is greater than two. We conducted a simulation study, which confirmed analysis using all members of a sibship is statistically more powerful than methods based on cross‐sectional analysis or using subsets of sib‐pairs. Second, we propose a simple permutation approach to avoid errors of inference due to the within‐sibship correlation of any errors in haplotype assignment. These methods were applied to investigate the association between mammographic density (MD), a continuously distributed and heritable risk factor for breast cancer, and single nucleotide polymorphisms (SNPs) and haplotypes from the VDR gene using data from a study of 430 twins and sisters. We found evidence of association between MD and a 4‐SNP VDR haplotype. In conclusion, our proposed method retains the benefits of the between‐ and within‐pair analysis for pairs of siblings and can be implemented in standard software. Genet. Epidemiol. 34: 309–318, 2010. © 2009 Wiley‐Liss, Inc.     

A Fast and Noise‐Resilient Approach to Detect Rare‐Variant Associations With Deep Sequencing Data for Complex Disorders

Next generation sequencing technology has enabled the paradigm shift in genetic association studies from the common disease/common variant to common disease/rare‐variant hypothesis. Analyzing individual rare variants is known to be underpowered; therefore association methods have been developed that aggregate variants across a genetic region, which for exome sequencing is usually a gene. The foreseeable widespread use of whole genome sequencing poses new challenges in statistical analysis. It calls for new rare‐variant association methods that are statistically powerful, robust against high levels of noise due to inclusion of noncausal variants, and yet computationally efficient. We propose a simple and powerful statistic that combines the disease‐associated P‐values of individual variants using a weight that is the inverse of the expected standard deviation of the allele frequencies under the null. This approach, dubbed as Sigma‐P method, is extremely robust to the inclusion of a high proportion of noncausal variants and is also powerful when both detrimental and protective variants are present within a genetic region. The performance of the Sigma‐P method was tested using simulated data based on realistic population demographic and disease models and its power was compared to several previously published methods. The results demonstrate that this method generally outperforms other rare‐variant association methods over a wide range of models. Additionally, sequence data on the ANGPTL family of genes from the Dallas Heart Study were tested for associations with nine metabolic traits and both known and novel putative associations were uncovered using the Sigma‐P method.     

Comparison of four sib-pair linkage methods for analyzing sibships with more than two affecteds: Interest of the binomial maximum likelihood approach

Family samples collected for sib-pair linkage studies usually include some sibships with more than two affecteds (multiplex sibships). Several methods have been proposed to take into account these multiplex sibships, and four of them are discussed in this work. Two methods, which are the most widely used, are based on the number of alleles shared by the sib-pairs constitutive of the multiplex sibship, with the first using the total number of these shared alleles (“all possible pairs” method) and the second considering a weighted number of these alleles (weighted method). The two other approaches considered the sibship as a whole, with in particular a likelihood method based on a binomial distribution of parental alleles among affected offspring. We theoretically show that, in the analysis of sibships with two affecteds, this likelihood method is expected to be more powerful than the classical mean test when a common asymptotic type I error is used. The variation of the sibship informativeness (assessed by the proportion of heterozygous parents) according to the number of affected sibs is investigated under various genetic models. Simulations under the null hypothesis of no linkage indicate that the “all possible pairs” is anticonservative, especially for type I errors ≤ 0.001, whereas the weighted method generally provides satisfactory results. The likelihood method shows very consistent results in terms of type I errors, whatever the sample size, and provides power levels similar to those of the other methods. This binomial likelihood approach, which accounts in a natural way for multiplex sibships and provides a simple likelihood-ratio test for linkage involving a single parameter, appears to be a quite interesting alternative to analyze sib-pair studies. Genet. Epidemiol. 15:371–390,1998. © 1998 Wiley-Liss, Inc.     

A General Efficient and Flexible Approach for Genome‐Wide Association Analyses of Imputed Genotypes in Family‐Based Designs

Genotype imputation is a critical technique for following up genome‐wide association studies. Efficient methods are available for dealing with the probabilistic nature of imputed single nucleotide polymorphisms (SNPs) in population‐based designs, but not for family‐based studies. We have developed a new analytical approach (FBATdosage), using imputed allele dosage in the general framework of family‐based association tests to bridge this gap. Simulation studies showed that FBATdosage yielded highly consistent type I error rates, whatever the level of genotype uncertainty, and a much higher power than the best‐guess genotype approach. FBATdosage allows fast linkage and association testing of several million of imputed variants with binary or quantitative phenotypes in nuclear families of arbitrary size with arbitrary missing data for the parents. The application of this approach to a family‐based association study of leprosy susceptibility successfully refined the association signal at two candidate loci, C1orf141‐IL23R on chromosome 1 and RAB32‐C6orf103 on chromosome 6.     

Model-based linkage analysis with imprinting for quantitative traits: ignoring imprinting effects can severely jeopardize detection of linkage

Genes with imprinting (parent-of-origin) effects express differently when inheriting from the mother or from the father. Some genes for development and behavior in mammals are known to be imprinted. We developed parametric linkage analysis that accounts for imprinting effects for continuous traits, implementing it in MORGAN. To study misspecification of imprinting on linkage analysis, we simulated eight markers over a 35 cM region with phenotypes where imprinting contributes 0, 25, 50, and 75% of the variance of a quantitative trait locus (QTL) effect and analyzed them under all four models. Multipoint lod scores were computed and maximized over the same 35 cM region. Our most important finding is the dramatic lod score improvement under the correct imprinting model over the no-imprinting model. For data with minor QTL allele frequency 0.05, the correct model provided the highest lod scores with maximum expected lod scores over 4 in all settings. Ignoring imprinting provided the lowest lod scores with maximum expected lod scores between -9.9 and 2.4. In the extreme scenario, cases with max lod > or =3 from the correct imprinting model and max lod < or =-2 from the no-imprinting model occurred in 86% of replications. Models with misspecified imprinting produced lod scores intermediate between those with correct imprinting and with no imprinting. The effects of model misspecification were less pronounced for singlepoint analysis. Our multipoint results illustrate that ignoring true imprinting severely impairs detection of linkage and erroneously excludes genomic regions (with max lod <-2), whereas accounting for it can substantially improve linkage detection.     

A note on permutation tests for genetic association analysis of quantitative traits when variances are heterogeneous

The genetic dissection of quantitative traits, or endophenotypes, usually involves genetic linkage or association analysis in pedigrees and subsequent fine mapping association analysis in the population. The ascertainment procedure for quantitative traits often results in unequal variance of observations. For example, some phenotypes may be clinically measured whilst others are from self‐reports, or phenotypes may be the average of multiple measures but with the number of measurements varying. The resulting heterogeneity of variance poses no real problem for analysis, as long as it is properly modelled and thereby taken into account. However, if statistical significance is determined using an empirical permutation procedure, it is not obvious what the units of sampling are. We investigated a number of permutation approaches in a simulation study of an association analysis between a quantitative trait and a single nucleotide polymorphism. Our simulations were designed such that we knew the true p‐value of the test statistics. A number of permutation methods were compared from the regression of true on empirical p‐values and the precision of the empirical p‐values. We show that the best procedure involves an implicit adjustment of the original data for the effects in the model before permutation, and that other methods, some of which seemed appropriate a priori, are relatively biased. Genet. Epidemiol. 33:710–716, 2009. © 2009 Wiley‐Liss, Inc.     

Comparing apples and oranges: equating the power of case‐control and quantitative trait association studies

Genome‐wide association studies have achieved unprecedented success in the identification of novel genes and pathways implicated in complex traits. Typically, studies for disease use a case‐control (CC) design and studies for quantitative traits (QT) are population based. The question that we address is what is the equivalence between CC and QT association studies in terms of detection power and sample size? We compare the binary and continuous traits by assuming a threshold model for disease and assuming that the effect size on disease liability has similar feature as on QT. We derive the approximate ratio of the non‐centrality parameter (NCP) between CC and QT association studies, which is determined by sample size, disease prevalence (K) and the proportion of cases (v) in the CC study. For disease with prevalence <0.1, CC association study with equal numbers of cases and controls (v=0.5) needs smaller sample size than QT association study to achieve equivalent power, e.g. a CC association study of schizophrenia (K=0.01) needs only ～55% sample size required for association study of height. So a planned meta‐analysis for height on ～120,000 individuals has power equivalent to a CC study on 33,100 schizophrenia cases and 33,100 controls, a size not yet achievable for this disease. With equal sample size, when v=K, the power of CC association study is much less than that of QT association study because of the information lost by transforming a quantitative continuous trait to a binary trait. Genet. Epidemiol. 34: 254–257, 2010. © 2009 Wiley‐Liss, Inc.     

Adaptive testing for multiple traits in a proportional odds model with applications to detect SNP‐brain network associations

There has been increasing interest in developing more powerful and flexible statistical tests to detect genetic associations with multiple traits, as arising from neuroimaging genetic studies. Most of existing methods treat a single trait or multiple traits as response while treating an SNP as a predictor coded under an additive inheritance mode. In this paper, we follow an earlier approach in treating an SNP as an ordinal response while treating traits as predictors in a proportional odds model (POM). In this way, it is not only easier to handle mixed types of traits, e.g., some quantitative and some binary, but it is also potentially more robust to the commonly adopted additive inheritance mode. More importantly, we develop an adaptive test in a POM so that it can maintain high power across many possible situations. Compared to the existing methods treating multiple traits as responses, e.g., in a generalized estimating equation (GEE) approach, the proposed method can be applied to a high dimensional setting where the number of phenotypes (p) can be larger than the sample size (n), in addition to a usual small P setting. The promising performance of the proposed method was demonstrated with applications to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, in which either structural MRI driven phenotypes or resting‐state functional MRI (rs‐fMRI) derived brain functional connectivity measures were used as phenotypes. The applications led to the identification of several top SNPs of biological interest. Furthermore, simulation studies showed competitive performance of the new method, especially for .     

A Versatile Omnibus Test for Detecting Mean and Variance Heterogeneity

Recent research has revealed loci that display variance heterogeneity through various means such as biological disruption, linkage disequilibrium (LD), gene‐by‐gene (G × G), or gene‐by‐environment interaction. We propose a versatile likelihood ratio test that allows joint testing for mean and variance heterogeneity (LRT_MV) or either effect alone (LRT_M or LRT_V) in the presence of covariates. Using extensive simulations for our method and others, we found that all parametric tests were sensitive to nonnormality regardless of any trait transformations. Coupling our test with the parametric bootstrap solves this issue. Using simulations and empirical data from a known mean‐only functional variant, we demonstrate how LD can produce variance‐heterogeneity loci (vQTL) in a predictable fashion based on differential allele frequencies, high D′, and relatively low r² values. We propose that a joint test for mean and variance heterogeneity is more powerful than a variance‐only test for detecting vQTL. This takes advantage of loci that also have mean effects without sacrificing much power to detect variance only effects. We discuss using vQTL as an approach to detect G × G interactions and also how vQTL are related to relationship loci, and how both can create prior hypothesis for each other and reveal the relationships between traits and possibly between components of a composite trait.     

Detecting Genotype × Age Interaction

This paper explores several extensions to the variance component method, which incorporate genotype × age interaction effects. We evaluate the performance of these methods for detecting genotype × age interaction in quantitative genetic analyses of a quantitative trait (Q4), contrasting this with false positive detection rates obtained from a phenotype influenced by the same genes but without genotype × age interaction effects (Q3). We then assess the impact on linkage power and false positive rate of allowing a QTL‐specific genotype × age interaction in linkage analysis of these same traits. © 2001 Wiley‐Liss, Inc.