Genetic prediction and family structure in Huntington's chorea.

A deoxyribonucleic acid marker linked to the locus for Huntington''s chorea exists, but its possible use in the prediction of this disorder depends on the pedigree structure of individual families. Analysis of data from a population register for Huntington''s chorea in south Wales showed that only a minority of subjects at risk had the appropriate members of their family living to allow the presence or absence of the gene to be definitively predicted. However, the structure of the family allowed a degree of prediction (in particular, exclusion of the disorder) to be made for the fetus during pregnancies of these subjects in almost 90% of cases. Such a prediction need not alter the risk state for the parent at risk. The structure of the family will remain crucial for prediction even when current limitations of the linked marker have been overcome.     

Two-locus models of disease: comparison of likelihood and nonparametric linkage methods.

The power to detect linkage for likelihood and nonparametric (Haseman-Elston, affected-sib-pair, and affected-pedigree-member) methods is compared for the case of a common, dichotomous trait resulting from the segregation of two loci. Pedigree data for several two-locus epistatic and heterogeneity models have been simulated, with one of the loci linked to a marker locus. Replicate samples of 20 three-generation pedigrees (16 individuals/pedigree) were simulated and then ascertained for having at least 6 affected individuals. The power of linkage detection calculated under the correct two-locus model is only slightly higher than that under a single locus model with reduced penetrance. As expected, the nonparametric linkage methods have somewhat lower power than does the lod-score method, the difference depending on the mode of transmission of the linked locus. Thus, for many pedigree linkage studies, the lod-score method will have the best power. However, this conclusion depends on how many times the lod score will be calculated for a given marker. The Haseman-Elston method would likely be preferable to calculating lod scores under a large number of genetic models (i.e., varying both the mode of transmission and the penetrances), since such an analysis requires an increase in the critical value of the lod criterion. The power of the affected-pedigree-member method is lower than the other methods, which can be shown to be largely due to the fact that marker genotypes for unaffected individuals are not used.     

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.     

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%.     

HC Forum: a web site based on an international human cytogenetic database

Familial structural rearrangements of chromosomes represent a factor of malformation risk that could vary over a large range, making genetic counseling difficult. However, they also represent a powerful tool for increasing knowledge of the genome, particularly by studying breakpoints and viable imbalances of the genome. We have developed a collaborative database that now includes data on more than 4100 families, from which we have developed a web site called HC Forum (http://HCForum.imag.fr). It offers geneticists assistance in diagnosis and in genetic counseling by assessing the malformation risk with statistical models. For researchers, interactive interfaces exhibit the distribution of chromosomal breakpoints and of the genome regions observed at birth in trisomy or in monosomy. Dedicated tools including an interactive pedigree allow electronic submission of data, which will be anonymously shown in a forum for discussions. After validation, data are definitively registered in the database with the email of the sender, allowing direct location of biological material. Thus HC Forum constitutes a link between diagnosis laboratories and genome research centers, and after 1 year, more than 700 users from about 40 different countries already exist.     

The genetic variance for multiple linked quantitative trait loci conditional on marker information in a crossed population

In the prediction of genetic values and quantitative trait loci (QTLs) mapping via the mixed model method incorporating marker information in animal populations, it is important to model the genetic variance for individuals with an arbitrary pedigree structure. In this study, for a crossed population originated from different genetic groups such as breeds or outbred strains, the variance of additive genetic values for multiple linked QTLs that are contained in a chromosome segment, especially the segregation variance, is investigated assuming the use of marker data. The variance for a finite number of QTLs in one chromosomal segment is first examined for the crossed population with the general pedigree. Then, applying the concept of the expectation of identity-by-descent proportion, an approximation to the mean of the conditional probabilities for the linked QTLs over all loci is obtained, and using it an expression for the variance in the case of an infinite number of linked QTLs marked by flanking markers is derived. It appears that the approach presented can be useful in the segment mapping using, and in the genetic evaluation of, crosses with general pedigrees in the population of concern. The calculation of the segregation variance through the current approach is illustrated numerically, using a small data-set.     

Utility and efficiency of linked marker genes for genetic counseling. II. Identification of linkage phase by offspring phenotypes

For a linked marker locus to be useful for genetic counseling, the counselee must be heterozygous for both disease and marker loci and his or her linkage phase must be known. It is shown that when the phenotypes of the counselee's previous children for the disease and marker loci are known, the linkage phase can often be inferred with a high probability, and thus it is possible to conduct genetic counseling. To evaluate the utility of linked marker genes for genetic counseling, the accuracy of prediction of the risk for a prospective child with a given marker gene to develop the genetic disease and the proportion of families in which a particular marker locus can be used for genetic counseling are studied for X-linked recessive, autosomal dominant, and autosomal recessive diseases. In the case of X-linked genetic diseases, information from children is very useful for determining the linkage phase of the counselee and predicting the genetic disease. In the case of autosomal dominant diseases, not all children are informative, but if the number of children is large, the phenotypes of children are often more informative than the information from grandparents. In the case of autosomal recessive diseases, information from grandparents is usually useless, since they show a normal phenotype for the disease locus. If we use information on the phenotypes of children, however, the linkage phase of the counselee and the risk of a prospective child can be inferred with a high probability. The proportion of informative families depends on the dominance relationship and frequencies of marker alleles, and the number of children. In general, codominant markers are more useful than are dominant markers, and a locus with high heterozygosity is more useful than is a locus with low heterozygosity.     

Information gain for genetic parameter estimation with incorporation of marker data

Genetic marker data has been increasingly incorporated into segregation analysis, as combined segregation and linkage analysis has been performed more frequently. In this article, we study the extent of information gains with incorporation of marker data in segregation analysis, a topic that has not been investigated rigorously. Specifically, the current study is to investigate the influence of marker data on genetic model parameter estimation. A variance matrix criterion (as the inverse of the Fisher information matrix) and a relative entropy criterion (a measure of flatness of expected log-likelihood surface) are used to quantify the information gains. Our results indicate that substantial information gain can be achieved with the incorporation of marker data. The amount of variance reduction increases as the heterozygosity of the linked marker increases and as the trait gets closer to the linked marker(s). Incorporation of marker data in larger pedigrees also yields greater information gains based on both criteria. The effect of pedigree structure is also studied.     

Some developments on the affected-pedigree-member method of linkage analysis.

Some improvements are presented for the affected-pedigree-member method of linkage analysis, which is a generalization of the sib-pair method. The test statistic is extended to include contrasts between affected and unaffected pedigree members, so that it now utilizes marker information from all typed pedigree members rather than just the typed affected members. Computer simulation using a sample pedigree of 14 individuals shows that this modification can substantially increase statistical power where there is a direct association between marker variation and disease and where disease risk is elevated in carriers of the disease allele. Data on Huntington disease in 16 British families, which were analyzed previously using only the affected individuals, are reanalyzed with the unaffected individuals included. Strong rejection of the null hypothesis of no association between Huntington disease and the HindIII polymorphism is confirmed, but the particular families in which the association is significant differs from that obtained through an analysis based only on affected individuals and reflects more closely the results obtained from a lod-score analysis. The test statistic is also modified here to incorporate contrasts between individuals of zero kinship, if needed. This enables contrasts between individuals from different pedigrees, as well as contrasts involving individuals sampled from the general population, to be incorporated into the test of association. For population data, the methodology reduces to a type of contingency-table analysis, in which the rows of the table correspond to different marker-locus genotypes and in which the two columns categorize subjects into an "affected" group versus an "unaffected," or control, group. This aspect of the methodology is illustrated using two population data sets, the first relating APO-E genotype to the frequency of individuals undergoing maintenance hemodialysis and the second relating APO-B genotype to the frequency of coronary artery disease. The present methodology confirms the lack of association between marker and disease in the former data set and confirms the presence of association in the latter. Finally, the methodology is formulated here in terms of ordinary, multiperson kinship coefficients rather than in terms of the generalized kinship coefficients originally proposed. This greatly reduces the number of coefficients to be calculated, thereby enhancing the computational efficiency of the computer program.     

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.     

Detecting linkage for genetically heterogeneous diseases and detecting heterogeneity with linkage data.

Interest in searching for genetic linkage between diseases and marker loci has been greatly increased by the recent introduction of DNA polymorphisms. However, even for the most well-behaved Mendelian disorders, those with clear-cut mode of inheritance, complete penetrance, and no phenocopies, genetic heterogeneity may exist; that is, in the population there may be more than one locus that can determine the disease, and these loci may not be linked. In such cases, two questions arise: (1) What sample size is necessary to detect linkage for a genetically heterogeneous disease? (2) What sample size is necessary to detect heterogeneity given linkage between a disease and a marker locus? We have answered these questions for the most important types of matings under specified conditions: linkage phase known or unknown, number of alleles involved in the cross at the marker locus, and different numbers of affected and unaffected children. In general, the presence of heterogeneity increases the recombination value at which lod scores peak, by an amount that increases with the degree of heterogeneity. There is a corresponding increase in the number of families necessary to establish linkage. For the specific case of backcrosses between disease and marker loci with two alleles, linkage can be detected at recombination fractions up to 20% with reasonable numbers of families, even if only half the families carry the disease locus linked to the marker. The task is easier if more than two informative children are available or if phase is known. For recessive diseases, highly polymorphic markers with four different alleles in the parents greatly reduce the number of families required.     

A CA-repeat polymorphism close to the adenomatous polyposis coli (APC) gene offers improved diagnostic testing for familial APC.

Presymptomatic genetic testing for the presence of a mutant allele causing familial adenomatous polyposis coli (APC) has been difficult to perform effectively in the past because DNA markers surrounding the APC gene on chromosome 5q have not been very informative. We report results of genetic linkage studies on both research families and clinical families by using D5S346, a highly polymorphic dinucleotide (CA)-repeat locus 30-70 kb from the APC gene. Linkage analysis with this marker in a large APC pedigree showed an increase of at least 9.0 LOD units, in likelihood of linkage of the disease-causing allele to the APC locus, when compared with the highest LOD score attained with any other closely linked marker. When the first 14 APC families that requested genotypic analysis by the DNA Diagnostic Laboratory at the University of Utah were tested with D5S346, 20 of the 31 at-risk individuals were identified as either carriers or noncarriers of an APC-predisposing allele. We see this marker as an important tool for research studies and for the presymptomatic diagnosis of APC.     

HAPLORE: a program for haplotype reconstruction in general pedigrees without recombination

MOTIVATION: Haplotype reconstruction is an essential step in genetic linkage and association studies. Although many methods have been developed to estimate haplotype frequencies and reconstruct haplotypes for a sample of unrelated individuals, haplotype reconstruction in large pedigrees with a large number of genetic markers remains a challenging problem. METHODS: We have developed an efficient computer program, HAPLORE (HAPLOtype REconstruction), to identify all haplotype sets that are compatible with the observed genotypes in a pedigree for tightly linked genetic markers. HAPLORE consists of three steps that can serve different needs in applications. In the first step, a set of logic rules is used to reduce the number of compatible haplotypes of each individual in the pedigree as much as possible. After this step, the haplotypes of all individuals in the pedigree can be completely or partially determined. These logic rules are applicable to completely linked markers and they can be used to impute missing data and check genotyping errors. In the second step, a haplotype-elimination algorithm similar to the genotype-elimination algorithms used in linkage analysis is applied to delete incompatible haplotypes derived from the first step. All superfluous haplotypes of the pedigree members will be excluded after this step. In the third step, the expectation-maximization (EM) algorithm combined with the partition and ligation technique is used to estimate haplotype frequencies based on the inferred haplotype configurations through the first two steps. Only compatible haplotype configurations with haplotypes having frequencies greater than a threshold are retained. RESULTS: We test the effectiveness and the efficiency of HAPLORE using both simulated and real datasets. Our results show that, the rule-based algorithm is very efficient for completely genotyped pedigree. In this case, almost all of the families have one unique haplotype configuration. In the presence of missing data, the number of compatible haplotypes can be substantially reduced by HAPLORE, and the program will provide all possible haplotype configurations of a pedigree under different circumstances, if such multiple configurations exist. These inferred haplotype configurations, as well as the haplotype frequencies estimated by the EM algorithm, can be used in genetic linkage and association studies. AVAILABILITY: The program can be downloaded from http://bioinformatics.med.yale.edu.     

Detection of parent-of-origin effects for quantitative traits using general pedigree data

Genomic imprinting is a genetic phenomenon in which certain alleles are differentially expressed in a parent-of-origin-specific manner, and plays an important role in the study of complex traits. For a diallelic marker locus in human, the parental-asymmetry tests Q-PAT(c) with any constant c were developed to detect parent-of-origin effects for quantitative traits. However, these methods can only be applied to deal with nuclear families and thus are not suitable for extended pedigrees. In this study, by making no assumption about the distribution of the quantitative trait, we first propose the pedigree parental-asymmetry tests Q-PPAT(c) with any constant c for quantitative traits to test for parent-of-origin effects based on nuclear families with complete information from general pedigree data, in the presence of association between marker alleles under study and quantitative traits. When there are any genotypes missing in pedigrees, we utilize Monte Carlo (MC) sampling and estimation and develop the Q-MCPPAT(c) statistics to test for parent-of-origin effects. Various simulation studies are conducted to assess the performance of the proposed methods, for different sample sizes, genotype missing rates, degrees of imprinting effects and population models. Simulation results show that the proposed methods control the size well under the null hypothesis of no parent-of-origin effects and Q-PPAT(c) are robust to population stratification. In addition, the power comparison demonstrates that Q-PPAT(c) and Q-MCPPAT(c) for pedigree data are much more powerful than Q-PAT(c) only using two-generation nuclear families selected from extended pedigrees.     

A resolution of the ascertainment sampling problem. III. Pedigrees.

When nuclear families are sampled by an ascertainment procedure whose properties are not known, biased estimates of genetic parameters will arise if an incorrect specification of the ascertainment procedure is made. Elsewhere we have put forward a resolution of this problem by introducing an ascertainment-assumption-free (AAF) method, for nuclear family data, which gives asymptotically unbiased estimators no matter what the true nature of the ascertainment process. In the present paper we extend this method to cover pedigree data. Problems that arise with pedigrees but not with families--for example, the question of which families in a pedigree are "ascertainable"--are also considered. Comparisons of numerical results for pedigrees and nuclear families are also made.     

A genomewide linkage study of 1,933 families affected by premature coronary artery disease: The British Heart Foundation (BHF) Family Heart Study

Coronary artery disease (CAD) and its most important complication, myocardial infarction (MI), are the leading cause of premature death in the Western world. CAD has a substantial genetic basis, especially when it occurs early. We investigated the genetic determinants of premature CAD by performing a genomewide linkage analysis of 4,175 affected subjects from 1,933 families recruited throughout the United Kingdom. Each family had at least two available siblings with CAD, with validated onset before age 66 years. Linkage analysis was performed using 416 microsatellite markers. We observed suggestive linkage, for both CAD and MI, to a region on chromosome 2. For CAD, a LOD score of 1.86 was observed at marker D2S2271, which, in an ordered subset analysis, increased to 2.70 in families (n=1,698) with a minimum age at diagnosis of 56 years or younger. For MI, an overlapping peak with a LOD score of 1.15 was observed at marker D2S2216, which increased to 2.1 in families (n=801) with a minimum age at diagnosis of 59 years or younger. Exclusion mapping showed that 100% of the autosomal genome could be excluded for locus-specific sibling relative risks of 1.5 and 1.6 for CAD and MI, respectively. The region identified on chromosome 2 overlaps linked regions observed in two other smaller genome scans for CAD. Together, these findings strongly suggest that there is a locus on chromosome 2 that influences coronary atherosclerosis risk. The exclusion of a common locus that increases risk of CAD to siblings by >50% has important implications for strategies for further defining the genetic basis of CAD.     

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.     

Improving estimates of genetic maps: a maximum likelihood approach

As a result of previous large, multipoint linkage studies there is a substantial amount of existing marker data. Due to the increased sample size, genetic maps estimated from these data could be more accurate than publicly available maps. However, current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals, or cannot make full use of marker data that are observed at several loci on members of large, extended pedigrees. In this article, a maximum likelihood (ML) method for map estimation that can make full use of the marker data in a large, multipoint linkage study is described. The method is applied to replicate sets of simulated marker data involving seven linked loci, and pedigree structures based on the real multipoint linkage study of Abkevich et al. (2003, American Journal of Human Genetics 73, 1271-1281). The variance of the ML estimate is accurately estimated, and tests of both simple and composite null hypotheses are performed. An efficient procedure for combining map estimates over data sets is also suggested.     

Parental contribution and coefficient of coancestry among maize inbreds: pedigree, RFLP, and SSR data

The genetic relationship between inbreds i and j can be estimated from pedigree or from molecular marker data. The objectives of this study were to: (1) determine whether pedigree, restriction fragment length polymorphism (RFLP), and simple sequence repeat (SSR) data give similar estimates of parental contribution and coefficient of coancestry (f _ij ) among a set of maize (Zea mays L.) inbreds, and (2) compare the usefulness of RFLP and SSR markers for estimating genetic relationship. We studied 13 maize inbreds with known pedigrees. The inbreds were genotyped using 124 RFLP and 195 SSR markers. For each type of marker, parental contributions were estimated from marker similarity among an inbred and both of its parents, and were subsequently used to estimate f _ij . Estimates of parental contribution differed significantly (α<0.05) between pedigree data and either type of marker, but not between the marker systems. The RFLP estimates of parental contribution failed to sum to 1.0, reflecting a higher frequency of non-parental bands with RFLP than with SSR markers. The f _ij estimated from pedigree, RFLP, and SSR data were highly correlated (r=0.87–0.97), although significant differences were found among the three sets of f _ij estimates. We concluded that pedigree and marker data often lead to different estimates of parental contribution and f _ij , and that SSR markers are superior to RFLP markers for estimating genetic relationship. A relevant question is whether or not the inbreds previously genotyped with an older marker system (e.g., RFLP) need to be re-analyzed with a newer marker system (e.g., SSR) for the purpose of estimating genetic relationship. Such re-analysis seems unnecessary if data for the same type of marker are available for a given inbred and both of its parents. Received: 2 June 1999 / Accepted: 30 July 1999