Accounting for epistasis in linkage analysis of general pedigrees

Complex traits are generally believed to be influenced by multiple loci. Identification of loci involved in complex traits is more difficult for interacting than for additive loci. Here we describe an extension of the program lm_twoqtl in the package MORGAN to handle two quantitative trait loci (QTLs) with gene-gene interaction. We investigate whether parametric linkage analysis that accounts for such epistasis improves prospects for linkage detection and accuracy of localization of QTLs. Through use of simulated data we show that analysis that accounts for epistasis provides higher lod scores and better localization than does analysis without epistasis. In addition, we demonstrate that the difference between lod scores in the presence vs. absence of use of an interaction model in analysis is greater in extended than in nuclear pedigrees.     

Faster sequential genetic linkage computations.

Linkage analysis using maximum-likelihood estimation is a powerful tool for locating genes. As available data sets have grown, the computation required for analysis has grown exponentially and become a significant impediment. Others have previously shown that parallel computation is applicable to linkage analysis and can yield order-of-magnitude improvements in speed. In this paper, we demonstrate that algorithmic modifications can also yield order-of-magnitude improvements, and sometimes much more. Using the software package LINKAGE, we describe a variety of algorithmic improvements that we have implemented, demonstrating both how these techniques are applied and their power. Experiments show that these improvements speed up the programs by an order of magnitude, on problems of moderate and large size. All improvements were made only in the combinatorial part of the code, without restoring to parallel computers. These improvements synthesize biological principles with computer science techniques, to effectively restructure the time-consuming computations in genetic linkage analysis.     

Optimizing exact genetic linkage computations.

Genetic linkage analysis is a challenging application which requires Bayesian networks consisting of thousands of vertices. Consequently, computing the probability of data, which is needed for learning linkage parameters, using exact computation procedures calls for an extremely efficient implementation that carefully optimizes the order of conditioning and summation operations. In this paper, we present the use of stochastic greedy algorithms for optimizing this order. Our algorithm has been incorporated into the newest version of SUPERLINK, which is a fast genetic linkage program for exact likelihood computations in general pedigrees. We demonstrate an order of magnitude improvement in run times of likelihood computations using our new optimization algorithm and hence enlarge the class of problems that can be handled effectively by exact computations.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees.

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

Multipoint quantitative-trait linkage analysis in general pedigrees.

Multipoint linkage analysis of quantitative-trait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variance-component linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint identity-by-descent (IBD) probability calculations. We extend the sib-pair multipoint mapping approach of Fulker et al. to general relative pairs. This multipoint IBD method uses the proportion of alleles shared identical by descent at genotyped loci to estimate IBD sharing at arbitrary points along a chromosome for each relative pair. We have derived correlations in IBD sharing as a function of chromosomal distance for relative pairs in general pedigrees and provide a simple framework whereby these correlations can be easily obtained for any relative pair related by a single line of descent or by multiple independent lines of descent. Once calculated, the multipoint relative-pair IBDs can be utilized in variance-component linkage analysis, which considers the likelihood of the entire pedigree jointly. Examples are given that use simulated data, demonstrating both the accuracy of QTL localization and the increase in power provided by multipoint analysis with 5-, 10-, and 20-cM marker maps. The general pedigree variance component and IBD estimation methods have been implemented in the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package.     

Powerful regression-based quantitative-trait linkage analysis of general pedigrees

We present a new method of quantitative-trait linkage analysis that combines the simplicity and robustness of regression-based methods and the generality and greater power of variance-components models. The new method is based on a regression of estimated identity-by-descent (IBD) sharing between relative pairs on the squared sums and squared differences of trait values of the relative pairs. The method is applicable to pedigrees of arbitrary structure and to pedigrees selected on the basis of trait value, provided that population parameters of the trait distribution can be correctly specified. Ambiguous IBD sharing (due to incomplete marker information) can be accommodated in the method by appropriate specification of the variance-covariance matrix of IBD sharing between relative pairs. We have implemented this regression-based method and have performed simulation studies to assess, under a range of conditions, estimation accuracy, type I error rate, and power. For normally distributed traits and in large samples, the method is found to give the correct type I error rate and an unbiased estimate of the proportion of trait variance accounted for by the additive effects of the locus-although, in cases where asymptotic theory is doubtful, significance levels should be checked by simulations. In large sibships, the new method is slightly more powerful than variance-components models. The proposed method provides a practical and powerful tool for the linkage analysis of quantitative traits.     

Exact multipoint quantitative-trait linkage analysis in pedigrees by variance components

Methods based on variance components are powerful tools for linkage analysis of quantitative traits, because they allow simultaneous consideration of all pedigree members. The central idea is to identify loci making a significant contribution to the population variance of a trait, by use of allele-sharing probabilities derived from genotyped marker loci. The technique is only as powerful as the methods used to infer these probabilities, but, to date, no implementation has made full use of the inheritance information in mapping data. Here we present a new implementation that uses an exact multipoint algorithm to extract the full probability distribution of allele sharing at every point in a mapped region. At each locus in the region, the program fits a model that partitions total phenotypic variance into components due to environmental factors, a major gene at the locus, and other unlinked genes. Numerical methods are used to derive maximum-likelihood estimates of the variance components, under the assumption of multivariate normality. A likelihood-ratio test is then applied to detect any significant effect of the hypothesized major gene. Simulations show the method to have greater power than does traditional sib-pair analysis. The method is freely available in a new release of the software package GENEHUNTER.     

Robust variance-components approach for assessing genetic linkage in pedigrees.

To assess evidence for genetic linkage from pedigrees, I developed a limited variance-components approach. In this method, variability among trait observations from individuals within pedigrees is expressed in terms of fixed effects from covariates and effects due to an unobservable trait-affecting major locus, random polygenic effects, and residual nongenetic variance. The effect attributable to a locus linked to a marker is a function of the additive and dominance components of variance of the locus, the recombination fraction, and the proportion of genes identical by descent at the marker locus for each pair of sibs. For unlinked loci, the polygenic variance component depends only on the relationship between the relative pair. Parameters can be estimated by either maximum-likelihood methods or quasi-likelihood methods. The forms of quasi-likelihood estimators are provided. Hypothesis tests derived from the maximum-likelihood approach are constructed by appeal to asymptotic theory. A simulation study showed that the size of likelihood-ratio tests was appropriate but that the monogenic component of variance was generally underestimated by the likelihood approach.     

Replication of genetic linkage by follow-up of previously studied pedigrees.

Independent replication of linkage in previously studied pedigrees is desirable when genetic heterogeneity is suspected or when the illness is very rare. When the likelihood of the new data in this type of replication study is computed as conditional on the previously reported linkage results, it can be considered independent. We describe a simulation method using the SLINK program in which the initial data are fixed and newly genotyped individuals are simulated under theta = .01 and theta = .50. These give appropriate lod score criteria for rejection and acceptance of linkage in the follow-up study, which take into account the original marker genotypes in the data. An estimate of the power to detect linkage in the follow-up data is also generated.     

A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

Maximum likelihood haplotyping for general pedigrees

Haplotype data is valuable in mapping disease-susceptibility genes in the study of Mendelian and complex diseases. We present algorithms for inferring a most likely haplotype configuration for general pedigrees, implemented in the newest version of the genetic linkage analysis system SUPERLINK. In SUPERLINK, genetic linkage analysis problems are represented internally using Bayesian networks. The use of Bayesian networks enables efficient maximum likelihood haplotyping for more complex pedigrees than was previously possible. Furthermore, to support efficient haplotyping for larger pedigrees, we have also incorporated a novel algorithm for determining a better elimination order for the variables of the Bayesian network. The presented optimization algorithm also improves likelihood computations. We present experimental results for the new algorithms on a variety of real and semiartificial data sets, and use our software to evaluate MCMC approximations for haplotyping.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

Efficient computations in multilocus linkage analysis.

This paper describes efficient methods for likelihood calculations and maximum-likelihood estimation in multilocus linkage analysis of reference families and general disease pedigrees, and it documents their performance as implemented in the LINKAGE programs. This information should be of considerable value in determining computing needs for linkage investigations, and in evaluating the merits of alternative algorithms.     

Segregation and linkage analyses of 72 leprosy pedigrees

Data on 72 families with multiple cases of leprosy were analyzed for a susceptibility gene linked to the HLA loci. We conducted segregation analysis with the program POINTER and identity of HLA types by descent analysis to determine the most likely mode of inheritance. We then conducted linkage analysis with the program LINKAS, first assuming linkage equilibrium and then allowing for linkage disequilibrium and etiological heterogeneity. Segregation results suggest a recessive mode of inheritance, especially for the tuberculoid forms of leprosy. The linkage results, limited to tuberculoid forms and assuming a recessive model, suggest a hypothesis of loose linkage with no unlinked locus. When an additive model is assumed, the best fit is obtained with a hypothesis of complete linkage (theta = 0.0) with heterogeneity. We currently favor the additive model as the more plausible one.     

Genomic imprinting and linkage test for quantitative-trait Loci in extended pedigrees

Genomic imprinting is a mechanism in which only one of the two copies of a gene is expressed. Some genes that affect development and behavior in mammals are known to be imprinted. Deregulation of imprinted genes has been found in a number of human diseases. Incorporating imprinting information into linkage analysis results in a more powerful test for linkage. Here, we propose an efficient method to test for linkage and imprinting of quantitative traits in extended pedigrees. We compared the results obtained by using the extended-pedigree-analysis approach proposed in this study with other existing approaches. We found that the proposed method is more powerful and uses extended-pedigree information most efficiently.     

Software for genetic linkage analysis

Recent developments in human genetic linkage analysis have included the appearance of new software and collections of data and program resources, accessible by means of the Internet. Many of these new programs and collections are described, including their availability, literature background, and specific technical information.     

A framework for structural equation models in general pedigrees

Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed. Methods: This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used. Results: A simulation study shows that our method is computationally feasible, and has good statistical properties. Conclusion: Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.