The covariance between relatives conditional on genetic markers

The development of molecular genotyping techniques makes it possible to analyze quantitative traits on the basis of individual loci. With marker information, the classical theory of estimating the genetic covariance between relatives can be reformulated to improve the accuracy of estimation. In this study, an algorithm was derived for computing the conditional covariance between relatives given genetic markers. Procedures for calculating the conditional relationship coefficients for additive, dominance, additive by additive, additive by dominance, dominance by additive and dominance by dominance effects were developed. The relationship coefficients were computed based on conditional QTL allelic transmission probabilities, which were inferred from the marker allelic transmission probabilities. An example data set with pedigree and linked markers was used to demonstrate the methods developed. Although this study dealt with two QTLs coupled with linked markers, the same principle can be readily extended to the situation of multiple QTL. The treatment of missing marker information and unknown linkage phase between markers for calculating the covariance between relatives was discussed.     

The use of multiple restriction fragment length polymorphisms in prenatal risk estimation. I. X-linked diseases.

An analytical procedure for estimating the risk of X-linked diseases based on presence/absence of a series of restriction sites is presented. Multiple-locus linkage phase of the carrier mother is first inferred from previous offspring, from parents, and by molecular means. Bayesian risk estimates are then obtained using this information and the recombination-segregation distribution. The improvement afforded by using multiple flanking markers rather than a single marker is dramatic. Whereas the upper bound on the probability that a family will be informative using a single diallelic X-linked marker is .5, in the case of m markers, the bound on the probability of an informative family becomes 1 - .5m. With a single linked marker, the precision in the risk estimate is bounded by the frequency of recombination, whereas the requirement of very tight linkage is relaxed somewhat when multiple flanking markers are used. Recombination interference and multiple-locus linkage disequilibria can further improve the risk estimates, but it is important to understand how the statistical confidence in these parameters affects the reliability of the risk estimates.     

The probabilistic determination of identity-by-descent sharing for pairs of relatives from pedigrees.

Methods for detecting genetic linkage are more powerful when they fully use all of the data collected from pedigrees. We first discuss a method for obtaining the probability that a pedigree member has a given genotype, conditional on the phenotypes of his relatives. We then develop a rapid method to obtain the conditional probabilities of identity-by-descent sharing of marker alleles for all related pairs of individuals from extended pedigrees. The method assumes that the individuals are noninbred and that the relationship between genotype and phenotype is known for the marker locus studied. The probabilities of identity-by-descent sharing among relative pairs, conditional on marker phenotype information, can then be used in any of the model free tests for linkage between a trait locus and a marker locus.     

Genome sharing in large pedigrees: multiple imputation of ibd for linkage detection

Our objective is the development of robust methods for assessment of evidence for linkage of loci affecting a complex trait to a marker linkage group, using data on extended pedigrees. Using Markov chain Monte Carlo (MCMC) methods, it is possible to sample realizations from the distribution of gene identity by descent (IBD) patterns on a pedigree, conditional on observed data YM at multiple marker loci. Measures of gene IBDW which capture joint genome sharing in extended pedigrees often have unknown and highly skewed distributions, particularly when conditioned on marker data. MCMC provides a direct estimate of the distribution of such measures. Let W be the IBD measure from data YM, and W* the IBD measure from pseudo-data Y*M simulated with the same data availability and genetic marker model as the true data YM, but in the absence of linkage. Then measures of the difference in distributions of W and W* provide evidence for linkage. This approach extracts more information from the data YM than either comparison to the pedigree prior distribution of W or use of statistics that are expectations of W given the data YM. A small example is presented.     

A user-friendly Hypercard interface for human linkage analysis

The availability of a large number of highly informative geneticmarkers has made human linkage analysis faster and easier toperform. However, current linkage analysis software does notprovide an organizational database into which a large body oflinkage data can be easily stored and manipulated. This manualentry and editing of linkage data is often time consuming andprone to typing errors. In addition, the large number of allelesin many of these markers must be reduced in order to performlinkage analysis with multiple loci across large genetic distances.This reduction in allele number is often difficult and confusing,especially in large pedigrees. We have taken advantage of theMacintosh-based Hypercard program to develop an interface withwhich linkage data can be easily stored, retrieved and edited.For each family, the components of the pedigree, including IDnumbers, sex and affection status, only need to be entered once.The program (Linkage Interface) retrieves this information eachtime the data from a new polymorphic marker is entered. LinkageInterface has flexible editing capabilities that allow the userto change any portion of the pedigree, including the additionor deletion of family members, without affecting previouslyentered genotype data. Linkage Interface can also analyze boththe pedigree and marker data and will detect any inconsistenciesin inheritance patterns. In addition, the program can reducethe number of alleles for a polynwrphic marker. Linkage Interfacewill then compare the ‘reduced’ data to the originalmarker data and assists in maintaining all informative meiosesby pointing out which meioses have become non-informative. Oncepolymorphic marker data are entered, the pedigree data, includingthe marker genotypes, are easily exported to a text file. Thistext file can be transferred to an IBM-compatible computer fordirect use with DOS-based linkage programs.     

The problem of ascertainment for linkage analysis.

It is generally believed that ascertainment corrections are unnecessary in linkage analysis, provided individuals are selected for study solely on the basis of trait phenotype and not on the basis of marker genotype. The theoretical rationale for this is that standard linkage analytic methods involve conditioning likelihoods on all the trait data, which may be viewed as an application of the ascertainment assumption-free (AAF) method of Ewens and Shute. In this paper, we show that when the observed pedigree structure depends on which relatives within a pedigree happen to have been the probands (proband-dependent, or PD, sampling) conditioning on all the trait data is not a valid application of the AAF method and will result in asymptotically biased estimates of genetic parameters (except under single ascertainment). Furthermore, this result holds even if the recombination fraction R is the only parameter of interest. Since the lod score is proportional to the likelihood of the marker data conditional on all the trait data, this means that when data are obtained under PD sampling the lod score will yield asymptotically biased estimates of R, and that so-called mod scores (i.e., lod scores maximized over both R and parameters theta of the trait distribution) will yield asymptotically biased estimates of R and theta. Furthermore, the problem appears to be intractable, in the sense that it is not possible to formulate the correct likelihood conditional on observed pedigree structure. In this paper we do not investigate the numerical magnitude of the bias, which may be small in many situations. On the other hand, virtually all linkage data sets are collected under PD sampling. Thus, the existence of this bias will be the rule rather than the exception in the usual applications.     

Evaluating pedigree data. I. The estimation of pedigree error in the presence of marker mistyping

Pedigrees used in the analysis of genetic or medical data are usually ascertained from sources subject to a variety of errors including misidentification of individuals, faults in historical documents or record linkage, nonpaternity, and unidentified adoption. Genetic markers can be used to verify putative family and pedigree data through the search for inconsistencies, or genetic exclusions, between putative parents and offspring. The probability of observing an exclusion given the occurrence of an error depends upon the gene frequencies at the loci under study and the forms of error. In addition, inconsistencies can arise from laboratory errors in marker determination. Together, these problems make the proper statistical analysis of such data desirable. Here we give a model that specifies the combined effects of various kinds of pedigree error along with genetic marker error. This model allows the maximum-likelihood estimation of the rates of various forms of pedigree error and laboratory error from genetic marker data collected on putative families. The method is illustrated by applying it to data obtained from a South Pacific island population, Tokelau. From the observed distribution of genetic marker inconsistencies between the parents and offspring of putative families, derived from the extensive genealogy of this population, we are able to estimate that the error of a paternal link is 4%, the error of a maternal link is zero, and the overall system typing error is 1%.     

Evaluating pedigree data. II. Identifying the cause of error in families with inconsistencies

Pedigree data can be evaluated, and subsequently corrected, by analysis of the distribution of genetic markers, taking account of the possibility of mistyping . Using a model of pedigree error developed previously, we obtained the maximum likelihood estimates of error parameters in pedigree data from Tokelau. Posterior probabilities for the possible true relationships in each family are conditional on the putative relationships and the marker data are calculated using the parameter estimates. These probabilities are used as a basis for discriminating between pedigree error and genetic marker errors in families where inconsistencies have been observed. When applied to the Tokelau data and compared with the results of retyping inconsistent families, these statistical procedures are able to discriminate between pedigree and marker error, with approximately 90% accuracy, for families with two or more offspring. The large proportion of inconsistencies inferred to be due to marker error (61%) indicates the importance of discriminating between error sources when judging the reliability of putative relationship data. Application of our model of pedigree error has proved to be an efficient way of determining and subsequently correcting sources of error in extensive pedigree data collected in large surveys.     

KELVIN: a software package for rigorous measurement of statistical evidence in human genetics

This paper describes the software package KELVIN, which supports the PPL (posterior probability of linkage) framework for the measurement of statistical evidence in human (or more generally, diploid) genetic studies. In terms of scope, KELVIN supports two-point (trait-marker or marker-marker) and multipoint linkage analysis, based on either sex-averaged or sex-specific genetic maps, with an option to allow for imprinting; trait-marker linkage disequilibrium (LD), or association analysis, in case-control data, trio data, and/or multiplex family data, with options for joint linkage and trait-marker LD or conditional LD given linkage; dichotomous trait, quantitative trait and quantitative trait threshold models; and certain types of gene-gene interactions and covariate effects. Features and data (pedigree) structures can be freely mixed and matched within analyses. The statistical framework is specifically tailored to accumulate evidence in a mathematically rigorous way across multiple data sets or data subsets while allowing for multiple sources of heterogeneity, and KELVIN itself utilizes sophisticated software engineering to provide a powerful and robust platform for studying the genetics of complex disorders.     

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.     

Efficiency and robustness of pedigree segregation analysis.

Different pedigree structures and likelihoods are examined to determine their efficiency for parameter estimation under one-locus models. For the cases simulated, family size has little effect; estimates based on unconditional likelihoods are generally more efficient than those based on conditional likelihoods. The proposed method of pedigree analysis under a one-locus model is found to be robust in the analysis of nuclear families: skewness of the data and polygenic inheritance will not lead to the spurious detection of major loci unless they occur simultaneously, and together with a moderate amount of environmental correlation among sibs.     

Calculating risk changes after negative mutation test outcomes for autosomal dominant hereditary late-onset disorders

We demonstrate, in a specific scenario, the effect of negative test results from relatives in families at risk for an autosomal dominant hereditary late-onset disorder. A hypothetical pedigree, of a family at risk of Huntington's disease, was used to demonstrate the consequences for the risk status of various family members in the case where relatives have been tested, and found to be mutation negative. We argue that accurate assessment of conditional probabilities in clinical genetics is important for individuals at risk for hereditary disorders with Mendelian transmission patterns; our formulae offer the opportunity -- when simplifying assumptions are met -- to determine the changed risk status of individuals in such cases.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

Linear models for joint association and linkage QTL mapping

Background

Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.

Results

We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders'' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.

Conclusion

The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.     

Autosomal dominant avascular necrosis of femoral head in two Taiwanese pedigrees and linkage to chromosome 12q13

Avascular necrosis of the femoral head (ANFH) is a debilitating disease that commonly leads to destruction of the hip joint in adults. The etiology of ANFH is unknown, but previous studies have indicated that heritable thrombophilia (increased tendency to form thrombi) and hypofibrinolysis (reduced ability to lyse thrombi), alcohol intake, and steroid use are risk factors for ANFH. We recently identified two families with ANFH showing autosomal dominant inheritance. By applying linkage analysis to a four-generation pedigree, we excluded linkage between the family and three genes related to thrombophilia and hypofibrinolysis: protein C, protein S, and plasminogen activator inhibitor. Furthermore, by a genomewide scan, a significant two-point LOD score of 3.45 (recombination fraction [theta] = 0) was obtained between the family with ANFH and marker D12S85 on chromosome 12. High-resolution mapping was conducted in a second family with ANFH and replicated the linkage to D12S368 (pedigree I: LOD score 2.47, theta = 0.05; pedigree II: LOD score 2.81, theta = 0.10). When an age-dependent-penetrance model was applied, the combined multipoint LOD score was 6.43 between D12S1663 and D12S85. Thus, we mapped the candidate gene for autosomal dominant ANFH to a 15-cM region between D12S1663 and D12S1632 on chromosome 12q13.     

Estimating the power of a proposed linkage study: a practical computer simulation approach.

I describe a simulation method to estimate the power to detect linkage given a set of pedigrees of known structure and for which family history data may be available. This method can be applied to autosomal and X-linked dominant diseases; depending on the pedigrees under consideration, it will often be applicable for autosomal and X-linked recessive diseases. This power calculation can most usefully be undertaken after family history data are gathered, but prior to examination and testing of pedigree members to obtain marker information. Of key importance, the power calculation is straightforward to carry out and not too time-consuming; it is practical even on a microcomputer. The result of the power calculation is an objective answer to the question: Will my families be sufficient to demonstrate linkage?     

Determining informativity of marker typing for genetic counseling in a pedigree

Summary For the situation of a Mendelian disease linked to a genetic marker, a new method is described that allows evaluating for genetic counseling the information potentially available from the linked marker before the marker data are actually obtained, that is, prior to drawing blood for marker typing. For a consultand in a family pedigree, the method determines the risk distribution (small families) or an approximation to it (larger families) and calculates the probability that the risk will deviate beyond certain limits from its a priori value, which exists without marker data, for example, that the risk will be smaller than 0.10 or larger than 0.90. The method was applied here to a pedigree of 15 individuals for which analytical calculations would be difficult to carry out.     

Genomic View of Bipolar Disorder Revealed by Whole Genome Sequencing in a Genetic Isolate

Bipolar disorder is a common, heritable mental illness characterized by recurrent episodes of mania and depression. Despite considerable effort to elucidate the genetic underpinnings of bipolar disorder, causative genetic risk factors remain elusive. We conducted a comprehensive genomic analysis of bipolar disorder in a large Old Order Amish pedigree. Microsatellite genotypes and high-density SNP-array genotypes of 388 family members were combined with whole genome sequence data for 50 of these subjects, comprising 18 parent-child trios. This study design permitted evaluation of candidate variants within the context of haplotype structure by resolving the phase in sequenced parent-child trios and by imputation of variants into multiple unsequenced siblings. Non-parametric and parametric linkage analysis of the entire pedigree as well as on smaller clusters of families identified several nominally significant linkage peaks, each of which included dozens of predicted deleterious variants. Close inspection of exonic and regulatory variants in genes under the linkage peaks using family-based association tests revealed additional credible candidate genes for functional studies and further replication in population-based cohorts. However, despite the in-depth genomic characterization of this unique, large and multigenerational pedigree from a genetic isolate, there was no convergence of evidence implicating a particular set of risk loci or common pathways. The striking haplotype and locus heterogeneity we observed has profound implications for the design of studies of bipolar and other related disorders.     

Diagnosis of susceptibility to malignant hyperthermia with flanking DNA markers.

OBJECTIVE--To define the region on human chromosome 19 carrying the gene for malignant hyperthermia susceptibility and to evaluate the use of flanking DNA markers in diagnosing susceptibility. DESIGN--Prospective molecular genetic linkage studies in a large malignant hyperthermia pedigree. SETTING--Irish malignant hyperthermia testing centre. SUBJECTS--A large Irish malignant hyperthermia pedigree. MAIN OUTCOME MEASURES--Routine diagnosis of susceptibility to malignant hyperthermia with in vitro contracture test on muscle biopsy specimens and genetic linkage between susceptibility and polymorphic DNA markers in a malignant hyperthermia family. RESULTS--Genetic typing of polymorphic DNA markers in a large Irish malignant hyperthermia pedigree generated a lod score of greater than 3 for the marker D19S9 and showed that the gene for susceptibility is flanked by the markers D19S9 and D19S16. These tightly linked flanking markers allowed non-invasive presymptomatic diagnosis of susceptibility in five untested subjects in the large pedigree with an accuracy of greater than 99.7%. CONCLUSIONS--DNA markers flanking the gene for susceptibility to malignant hyperthermia can be used with high accuracy to diagnose susceptibility in subjects in large known malignant hyperthermia pedigrees and may replace the previous in vitro contracture test for diagnosing this inherited disorder in large families with malignant hyperthermia.