Genetic linkage analysis of a dichotomous trait incorporating a tightly linked quantitative trait in affected sib pairs

Many complex diseases are usually considered as dichotomous traits but are also associated with quantitative biological markers or quantitative risk factors. For such dichotomous traits, although their associated quantitative traits may not directly underly the diagnosis of the disease status, if the associated quantitative trait is also linked to the chromosomal regions linked to the dichotomous trait, then joint analysis of dichotomous and quantitative traits should be more efficient than consideration of them separately. Previous studies have focused on the situation when a dichotomous trait can be modeled by a threshold process acting on a single underlying normal liability distribution. However, for many complex disorders, including most psychiatric disorders, diagnosis is generally based on a set of binary or discrete criteria. These traits cannot be modeled on the basis of a threshold process acting on an underlying continuous trait. We propose a likelihood-based method that efficiently combines such a discrete trait and an associated quantitative trait in the analysis, using affected-sib-pair data. Our simulation studies suggest that joint analysis increases the power to detect linkage of dichotomous traits. We also apply the proposed new method to an asthma genome-scan data set and incorporate the total serum immunoglobulin E level in the analysis.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. II. Alcoholism and Event-Related Potentials

The availability of robust quantitative biological markers that are correlated with qualitative psychiatric phenotypes can potentially improve the power of linkage methods to detect quantitative-trait loci influencing psychiatric disorders. We apply a variance-component method for joint multipoint linkage analysis of multivariate discrete and continuous traits to the extended pedigree data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate analysis of qualitative alcoholism phenotypes and quantitative event-related potentials. Joint consideration of the DSM-IV diagnosis of alcoholism and the amplitude of the P300 component of the Cz event-related potential significantly increases the evidence for linkage of these traits to a chromosome 4 region near the class I alcohol dehydrogenase locus ADH3. A likelihood-ratio test for complete pleiotropy is significant, suggesting that the same quantitative-trait locus influences both risk of alcoholism and the amplitude of the P300 component.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

Joint oligogenic segregation and linkage analysis using bayesian Markov chain Monte Carlo methods

One of the most challenging areas in human genetics is the dissection of quantitative traits. In this context, the efficient use of available data is important, including, when possible, use of large pedigrees and many markers for gene mapping. In addition, methods that jointly perform linkage analysis and estimation of the trait model are appealing because they combine the advantages of a model-based analysis with the advantages of methods that do not require prespecification of model parameters for linkage analysis. Here we review a Markov chain Monte Carlo approach for such joint linkage and segregation analysis, which allows analysis of oligogenic traits in the context of multipoint linkage analysis of large pedigrees. We provide an outline for practitioners of the salient features of the method, interpretation of the results, effect of violation of assumptions, and an example analysis of a two-locus trait to illustrate the method.     

Exploring pleiotropy using principal components

A standard multivariate principal components (PCs) method was utilized to identify clusters of variables that may be controlled by a common gene or genes (pleiotropy). Heritability estimates were obtained and linkage analyses performed on six individual traits (total cholesterol (Chol), high and low density lipoproteins, triglycerides (TG), body mass index (BMI), and systolic blood pressure (SBP)) and on each PC to compare our ability to identify major gene effects. Using the simulated data from Genetic Analysis Workshop 13 (Cohort 1 and 2 data for year 11), the quantitative traits were first adjusted for age, sex, and smoking (cigarettes per day). Adjusted variables were standardized and PCs calculated followed by orthogonal transformation (varimax rotation). Rotated PCs were then subjected to heritability and quantitative multipoint linkage analysis. The first three PCs explained 73% of the total phenotypic variance. Heritability estimates were above 0.60 for all three PCs. We performed linkage analyses on the PCs as well as the individual traits. The majority of pleiotropic and trait-specific genes were not identified. Standard PCs analysis methods did not facilitate the identification of pleiotropic genes affecting the six traits examined in the simulated data set. In addition, genes contributing 20% of the variance in traits with over 0.60 heritability estimates could not be identified in this simulated data set using traditional quantitative trait linkage analyses. Lack of identification of pleiotropic and trait-specific genes in some cases may reflect their low contribution to the traits/PCs examined or more importantly, characteristics of the sample group analyzed, and not simply a failure of the PC approach itself.     

Sample-size guidelines for linkage analysis of a dominant locus for a quantitative trait by the method of lod scores.

Sample-size guidelines for linkage studies of quantitative traits partially determined by a dominant major locus are needed to provide a rough estimate of the amount of pedigree material that should be sampled to map the loci that influence such traits. After pedigrees are sampled, a specific power calculation can be carried out to evaluate the linkage information provided by the sampled pedigrees. Using computer simulation, I provide sample-size guidelines for linkage studies by the method of lod scores of quantitative traits partially determined by a dominant major locus. I consider the effects of a trait model, marker characteristics, and sampling strategy, with particular attention to sampling strategy because it is the one factor which the investigator can fully control. My results suggest that linkage studies of quantitative traits are practical, particularly if the investigator chooses an efficient sampling design and an efficient strategy to select pedigrees for linkage analysis.     

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. I. Likelihood Formulation and Simulation Results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.     

A score test for the linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs

We propose a general likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from sib-pairs. We consider the likelihood of IBD data conditional on phenotypes and test the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction theta between the two loci. This method unifies the linkage analysis of qualitative and quantitative traits into a single inferential framework, yielding a simple and intuitive test statistic. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows sib-pairs from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. In particular, it allows the selection of sib-pairs based on their trait values and the analysis of only those pairs having the most informative phenotypes. The score test is based on the full likelihood, i.e. the likelihood based on all phenotype data rather than just differences of sib-pair phenotypes. Considering only phenotype differences, as in Haseman and Elston (1972) and Kruglyak and Lander (1995), may result in important losses in power. The linkage score test is derived under general genetic models for the trait, which may include multiple unlinked genes. Population genetic assumptions, such as random mating or linkage equilibrium at the trait loci, are not required. This score test is thus particularly promising for the analysis of complex human traits. The score statistic readily extends to accommodate incomplete IBD data at the test locus, by using the hidden Markov model implemented in the programs MAPMAKER/SIBS and GENEHUNTER (Kruglyak and Lander, 1995; Kruglyak et al., 1996). Preliminary simulation studies indicate that the linkage score test generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes.     

Selecting pedigrees for linkage analysis of a quantitative trait: the expected number of informative meioses.

With evidence of segregation at a major locus for a quantitative trait having been found, a logical next step is to select a subset of the pedigrees to include in a linkage study to map the major locus. Ideally this subset should include much of the linkage information in the sample but include only a fraction of the pedigrees. We previously described a strategy for selecting pedigrees for linkage analysis of a quantitative trait on the basis of a pedigree likelihood-ratio statistic. For quantitative traits controlled by a major locus with a rare dominant allele, the likelihood-ratio strategy extracted nearly all the information for linkage while typically requiring marker data on only about one-third of the pedigrees. Here, we describe a new strategy to select pedigrees for linkage analysis on the basis of the expected number of potentially informative meioses in each pedigree. We demonstrate that this informative-meioses strategy provides an efficient and more general means to select pedigrees for a linkage study of a quantitative trait.     

Assessment of parent-of-origin effects in linkage analysis of quantitative traits

Methods are presented for incorporation of parent-of-origin effects into linkage analysis of quantitative traits. The estimated proportion of marker alleles shared identical by descent is first partitioned into a component derived from the mother and a component derived from the father. These parent-specific estimates of allele sharing are used in variance-components or Haseman-Elston methods of linkage analysis so that the effect of the quantitative-trait locus carried on the maternally derived chromosome is potentially different from the effect of the locus on the paternally derived chromosome. Statistics for linkage between trait and marker loci derived from either or both parents are then calculated, as are statistics for testing whether the effect of the maternally derived locus is equal to that of the paternally derived locus. Analyses of data simulated for 956 siblings from 263 nuclear families who had participated in a linkage study revealed that type I error rates for these statistics were generally similar to nominal values. Power to detect an imprinted locus was substantially increased when analyzed with a model allowing for parent-of-origin effects, compared with analyses that assumed equal effects; for example, for an imprinted locus accounting for 30% of the phenotypic variance, the expected LOD score was 4.5 when parent-of-origin effects were incorporated into the analysis, compared with 3.1 when these effects were ignored. The ability to include parent-of-origin effects within linkage analysis of quantitative traits will facilitate genetic dissection of complex traits.     

Approaches to mapping genetically correlated complex traits

Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL) using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent (IBD) scoring methods. Each method used all marker data for all markers on a chromosome. Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL, corroborating previously published results. However, these results were not replicated in a classical linkage analysis of the data or by using IBD scoring methods.We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method accommodating genetically complex traits and linkage heterogeneity, validation of these signals remains elusive.     

Smoothing of the bivariate LOD score for non-normal quantitative traits

Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality. Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.     

Bivariate association analysis for quantitative traits using generalized estimation equation

Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.     

A score test for linkage analysis of ordinal traits based on IBD sharing

Statistical methods for linkage analysis are well established for both binary and quantitative traits. However, numerous diseases including cancer and psychiatric disorders are rated on discrete ordinal scales. To analyze pedigree data with ordinal traits, we recently proposed a latent variable model which has higher power to detect linkage using ordinal traits than methods using the dichotomized traits. The challenge with the latent variable model is that the likelihood is usually very complicated, and as a result, the computation of the likelihood ratio statistic is too intensive for large pedigrees. In this paper, we derive a computationally efficient score statistic based on the identity-by-decent sharing information between relatives. Using simulation studies, we examined the asymptotic distribution of the test statistic and the power of our proposed test under various levels of heritability. We compared the computing time as well as power of the score test with the likelihood ratio test. We then applied our method for the Collaborative Study on the Genetics of Alcoholism and performed a genome scan to map susceptibility genes for alcohol dependence. We found a strong linkage signal on chromosome 4.     

SASQuant: a SAS software program to estimate genetic effects and heritabilities of quantitative traits in populations consisting of 6 related generations

Plant breeders are interested in the analysis of phenotypic data to measure genetic effects and heritability of quantitative traits and predict gain from selection. Measurement of phenotypic values of 6 related generations (parents, F(1), F(2), and backcrosses) allows for the simultaneous analysis of both Mendelian and quantitative traits. In 1997, Liu et al. released a SAS software based program (SASGENE) for the analysis of inheritance and linkage of qualitative traits. We have developed a new program (SASQuant) that estimates gene effects (Hayman's model), genetic variances, heritability, predicted gain from selection (Wright's and Warner's models), and number of effective factors (Wright's, Mather's, and Lande's models). SASQuant makes use of traditional genetic models and allows for their easy application to complex data sets. SASQuant is freely available and is intended for scientists studying quantitative traits in plant populations.     

LOT: a tool for linkage analysis of ordinal traits for pedigree data

SUMMARY: Existing linkage-analysis methods address binary or quantitative traits. However, many complex diseases and human conditions, particularly behavioral disorders, are rated on ordinal scales. Herein, we introduce, LOT, a tool that performs linkage analysis of ordinal traits for pedigree data. It implements a latent-variable proportional-odds logistic model that relates inheritance patterns to the distribution of the ordinal trait. The likelihood-ratio test is used for testing evidence of linkage. AVAILABILITY: The LOT program is available for download at http://c2s2.yale.edu/software/LOT/     

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

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

利用DH或RIL群体检测QTL体系并估计其遗传效应

利用ＤＨ和ＲＩＫＬ群体并结合重复内分组随机区组设计对和物产量等遗传率较低的数量性状进行分离分析可提高遗传分析的精度。根据混合分布理论菜了利用ＤＨ或ＲＩＬ群体重复实验数据鉴定数量性状混合遗传模型的分离分析法,特别是２对链锁主基因＋多基因模型。该方法可鉴定数量性状的遗传模型和主基因的作用方式,估计主基因、多基因的遗传疚和遗传方差,在两主基因存在连锁可可估计其重组率。下面通过应用举例说明该方法。     

Some capabilities for model-based and model-free linkage analysis using the program package S.A.G.E. (Statistical Analysis for Genetic Epidemiology)

For both model-free and model-based linkage analysis the S.A.G.E. (Statistical Analysis for Genetic Epidemiology) program package has some unique capabilities in analyzing both continuous traits and binary traits with variable age of onset. Here we highlight model-based linkage analysis of a quantitative trait (plasma dopamine β hydroxylase) that is known to be largely determined by monogenic inheritance, using a prior segregation analysis to produce the best fitting model for the trait. For a binary trait with variable age of onset (schizophrenia), we illustrate how using age of onset information to obtain a quantitative susceptibility trait leads to more statistically significant linkage signals, suggesting better power.