Identifying pedigrees segregating at a major locus for a quantitative trait: an efficient strategy for linkage analysis

Having found evidence for segregation at a major locus for a quantitative trait, a logical next step is to identify those pedigrees in which major-locus segregation is occurring. If the quantitative trait is a risk factor for an associated disease, identifying such segregating pedigrees can be important in classifying families by etiology, in risk assessment, and in suggesting treatment modalities. Identifying segregating pedigrees can also be helpful in selecting pedigrees to include in a subsequent linkage study to map the major locus. Here, we describe a strategy to identify pedigrees segregating at a major locus for a quantitative trait. We apply this pedigree selection strategy to simulated data generated under a major-locus or mixed model with a rare dominant allele and sampled according to one of several fixed-structure or sequential sampling designs. We demonstrate that for the situations considered, the pedigree selection strategy is sensitive and specific and that a linkage study based only on the pedigrees classified as segregating extracts essentially all the linkage information in the entire sample of pedigrees. Our results suggest that for large-scale linkage studies involving many genetic markers, the savings from this strategy can be substantial and that, compared with fixed-structure sampling, sequential sampling of pedigrees can greatly improve the efficiency for linkage analysis of a quantitative trait.     

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.     

Comparison of sequential and fixed-structure sampling of pedigrees in complex segregation analysis of a quantitative trait.

In designing a study to demonstrate the existence of a major locus for a quantitative trait, an investigator chooses a sampling rule to ascertain pedigrees. The choice of sampling rule can significantly affect the study's power. Here, we compare two types of sampling rules for family studies: fixed-structure rules, in which the same set of relatives are sampled for each proband, and sequential rules, in which the relative or relatives to be sampled next may depend on the trait values of the individuals already observed. We compare fixed-structure and sequential sampling in the setting of extended pedigrees, a quantitative trait, and the genetic mixed model. Using computer simulation, we show that sequential sampling can increase power to detect segregation at a dominant major locus by over 60% in comparison with fixed-structure sampling. Just as important, this substantially increased power is obtained with an easily implemented sampling rule, one that might reasonably be employed in a family study of a quantitative trait.     

Linkage analysis of quantitative trait loci in the presence of heterogeneity

Variance component modeling for linkage analysis of quantitative traits is a powerful tool for detecting and locating genes affecting a trait of interest, but the presence of genetic heterogeneity will decrease the power of a linkage study and may even give biased estimates of the location of the quantitative trait loci. Many complex diseases are believed to be influenced by multiple genes and therefore genetic heterogeneity is likely to be present for many real applications of linkage analysis. We consider a mixture of multivariate normals to model locus heterogeneity by allowing only a proportion of the sampled pedigrees to segregate trait-influencing allele(s) at a specific locus. However, for mixtures of normals the classical asymptotic distribution theory of the maximum likelihood estimates does not hold, so tests of linkage and/or heterogeneity are evaluated using resampling methods. It is shown that allowing for genetic heterogeneity leads to an increase in power to detect linkage. This increase is more prominent when the genetic effect of the locus is small or when the percentage of pedigrees not segregating trait-influencing allele(s) at the locus is high.     

Identification of quantitative trait loci for wood quality and growth across eight full-sib coastal Douglas-fir families

Typical linkage and quantitative trait locus (QTL) analyses in forest trees have been conducted in single pedigrees with sex-averaged linkage maps. The results of a QTL analysis for wood quality and growth traits of coastal Douglas-fir using eight full-sib families, each consisting of 40 progeny, replicated on four sites are presented. The resulting map of segregating genetic markers consisted of 120 amplified fragment length polymorphism (AFLP) loci distributed across 19 linkage groups. The wood quality traits represent the widest suite of traits yet examined for QTL analysis in a tree species in a single study. Wood fiber traits showed the lowest number of QTLs (3) with relatively small effect (ca. 4%); wood density traits also showed just three QTLs but with slightly larger effect; wood chemistry traits showed more QTLs (7), while ring density traits showed many QTLs with large numbers of QTLs (78) and interesting patterns of temporal variation. Growth traits gave just five QTLs but of major effect (10–16%). Trees, with their long generation times, provide a rich resource for studies of temporal variation of QTL expression.     

Estimating the power of a proposed linkage study for a complex genetic trait.

Many genetic traits have complex modes of inheritance; they may exhibit incomplete or age-dependent penetrance or fail to show any clear Mendelian inheritance pattern. As primary linkage maps for the human genome near completion, it is becoming increasingly possible to map these traits. Prior to undertaking a linkage study, it is important to consider whether the pedigrees available for the proposed study are likely to provide sufficient information to demonstrate linkage, assuming a linked marker is tested. In the current paper, we describe a computer simulation method to estimate the power of a proposed study to detect linkage for a complex genetic trait, given a hypothesized genetic model for the trait. Our method simulates trait locus genotypes consistent with observed trait phenotypes, in such a way that the probability to detect linkage can be estimated by sample statistics of the maximum lod score distribution. The method uses terms available when calculating the likelihood of the trait phenotypes for the pedigree and is applicable to any trait determined by one or a few genetic loci; individual-specific environmental effects can also be dealt with. Our method provides an objective answer to the question, Will these pedigrees provide sufficient information to map this complex genetic trait?     

Use of a Quantitative Trait to Map a Locus Associated with Severity of Positive Symptoms in Familial Schizophrenia to Chromosome 6p

A number of recent linkage studies have suggested the presence of a schizophrenia susceptibility locus on chromosome 6p. We evaluated 28 genetic markers, spanning chromosome 6, for linkage to schizophrenia in 10 moderately large Canadian families of Celtic ancestry. Parametric analyses of these families under autosomal dominant and recessive models, using broad and narrow definitions of schizophrenia, produced no significant evidence for linkage. A sib-pair analysis using categorical disease definitions also failed to produce significant evidence for linkage. We then conducted a separate sibpair analysis using scores on positive-symptom (psychotic), negative-symptom (deficit), and general psychopathology-symptom scales as quantitative traits. With the positive symptom-scale scores, the marker D6S1960 produced P = 1.2 x 10(-5) under two-point and P = 5.4 x 10(-6) under multipoint analyses. Using simulation studies, we determined that these nominal P values correspond to empirical P values of .034 and .0085, respectively. These results suggest that a schizophrenia susceptibility locus on chromosome 6p may be related to the severity of psychotic symptoms. Assessment of behavioral quantitative traits may provide increased power over categorical phenotype assignment for detection of linkage in complex psychiatric disorders.     

Robust score statistics for QTL linkage analysis

The traditional variance components approach for quantitative trait locus (QTL) linkage analysis is sensitive to violations of normality and fails for selected sampling schemes. Recently, a number of new methods have been developed for QTL mapping in humans. Most of the new methods are based on score statistics or regression-based statistics and are expected to be relatively robust to non-normality of the trait distribution and also to selected sampling, at least in terms of type I error. Whereas the theoretical development of these statistics is more or less complete, some practical issues concerning their implementation still need to be addressed. Here we study some of these issues such as the choice of denominator variance estimates, weighting of pedigrees, effect of parameter misspecification, effect of non-normality of the trait distribution, and effect of incorporating dominance. We present a comprehensive discussion of the theoretical properties of various denominator variance estimates and of the weighting issue and then perform simulation studies for nuclear families to compare the methods in terms of power and robustness. Based on our analytical and simulation results, we provide general guidelines regarding the choice of appropriate QTL mapping statistics in practical situations.     

Transmission-disequilibrium tests for quantitative traits.

The transmission-disequilibrium test (TDT) of Spielman et al. is a family-based linkage-disequilibrium test that offers a powerful way to test for linkage between alleles and phenotypes that is either causal (i.e., the marker locus is the disease/trait allele) or due to linkage disequilibrium. The TDT is equivalent to a randomized experiment and, therefore, is resistant to confounding. When the marker is extremely close to the disease locus or is the disease locus itself, tests such as the TDT can be far more powerful than conventional linkage tests. To date, the TDT and most other family-based association tests have been applied only to dichotomous traits. This paper develops five TDT-type tests for use with quantitative traits. These tests accommodate either unselected sampling or sampling based on selection of phenotypically extreme offspring. Power calculations are provided and show that, when a candidate gene is available (1) these TDT-type tests are at least an order of magnitude more efficient than two common sib-pair tests of linkage; (2) extreme sampling results in substantial increases in power; and (3) if the most extreme 20% of the phenotypic distribution is selectively sampled, across a wide variety of plausible genetic models, quantitative-trait loci explaining as little as 5% of the phenotypic variation can be detected at the .0001 alpha level with <300 observations.     

Evaluation of candidate genes in case-control studies: a statistical method to account for related subjects

Traditional case-control studies provide a powerful and efficient method for evaluation of association between candidate genes and disease. The sampling of cases from multiplex pedigrees, rather than from a catchment area, can increase the likelihood that genetic cases are selected. However, use of all the related cases without accounting for their biological relationship can increase the type I error rate of the statistical test. To overcome this problem, we present an analysis method that is used to compare genotype frequencies between cases and controls, according to a trend in proportions as the dosage of the risk allele increases. This method uses the appropriate variance to account for the correlated family data, thus maintaining the correct type I error rate. The magnitude of the association is estimated by the odds ratio, with the variance of the odds ratio also accounting for the correlated data. Our method makes efficient use of data collected from multiplex families and should prove useful for the analysis of candidate genes among families sampled for linkage studies. An application of our method, to family data from a prostate cancer study, is presented to illustrate the method's utility.     

Collection of pedigree data for genetic analysis in isolate populations

Pedigree data are useful for a wealth of research purposes in human population biology and genetics. The collection of extended pedigrees represents the most powerful sampling design for quantitative genetic and linkage studies of both normal and disease-related quantitative traits. In this paper we outline an approach for collecting pedigree data in stable isolate populations. As an example, the pedigree for the Jirel population, which was obtained using the methods presented, is described. The Jirel pedigree contains 2,000 study participants and more than 62,000 pairwise relationships that are informative for genetic analysis. Once such pedigrees are genetically characterized by a genome scan for a given trait, they become an invaluable resource for future genetic studies of any quantitative trait.     

The detection of linkage and heterogeneity in nuclear families for complex disorders: one versus two marker loci.

Using exact expected likelihoods, we have computed the average number of phase-unknown nuclear families needed to detect linkage and heterogeneity. We have examined the case of both dominant and recessive inheritance with reduced penetrance and phenocopies. Most of our calculations have been carried out under the assumption that 50% of families are linked to a marker locus. We have varied both the number of offspring per family and the sampling scheme. We have also investigated the increased power when the disease locus is midway between two marker loci 10 cM apart. For recessive inheritance, both linkage and heterogeneity can be detected in clinically feasible sample sizes. For dominant inheritance, linkage can be detected but heterogeneity cannot be detected unless larger sibships (four offspring) are sampled or two linked markers are available. As expected, if penetrance is reduced, sampling families with all sibs affected is most efficient. Our results provide a basis for estimating the amount of resources needed to find genes for complex disorders under conditions of heterogeneity.     

Optimizing sampling design and sequencing strategy for the genomic analysis of quantitative traits in natural populations

Mapping the genes underlying ecologically relevant traits in natural populations is fundamental to develop a molecular understanding of species adaptation. Current sequencing technologies enable the characterization of a species’ genetic diversity across the landscape or even over its whole range. The relevant capture of the genetic diversity across the landscape is critical for a successful genetic mapping of traits and there are no clear guidelines on how to achieve an optimal sampling and which sequencing strategy to implement. Here we determine, through simulation, the sampling scheme that maximizes the power to map the genetic basis of a complex trait in an outbreeding species across an idealized landscape and draw genomic predictions for the trait, comparing individual and pool sequencing strategies. Our results show that quantitative trait locus detection power and prediction accuracy are higher when more populations over the landscape are sampled and this is more cost-effectively done with pool sequencing than with individual sequencing. Additionally, we recommend sampling populations from areas of high genetic diversity. As progress in sequencing enables the integration of trait-based functional ecology into landscape genomics studies, these findings will guide study designs allowing direct measures of genetic effects in natural populations across the environment.     

Evidence of a founder effect and refinement of the hereditary neuralgic amyotrophy (HNA) locus on 17q25 in American families

Hereditary neuralgic amyotrophy (HNA) is an autosomal dominant disorder that is associated with episodic recurrent brachial plexus neuropathy. A mutation for HNA maps to chromosome 17q25. To refine the HNA locus further, we carried out genetic linkage studies in seven pedigrees with a high density set of DNA markers from chromosome 17q25. All pedigrees demonstrated linkage to chromosome 17q25, and an analysis of recombinant events placed the HNA locus within an interval of approximately 1 Mb flanked by markers D17S722 and D17S802. In order to test the power of linkage disequilibrium mapping, we compared genotypes of 12 markers from seven pedigrees that were from the United States and that showed linkage to chromosome 17q25. The haplotypes identified a founder effect in six of the seven pedigrees with a minimal shared haplotype that further refines the HNA locus to an interval of approximately 500 kb. These findings suggest that, for the pedigrees from the United States, there are at least two different mutations in the HNA gene.     

Selection strategies for linkage studies using twins.

Genetic linkage analysis for complex diseases offers a major challenge to geneticists. In these complex diseases multiple genetic loci are responsible for the disease and they may vary in the size of their contribution; the effect of any single one of them is likely to be small. In many situations, like in extensive twin registries, trait values have been recorded for a large number of individuals, and preliminary studies have revealed summary measures for those traits, like mean, variance and components of variance, including heritability. Given the small effect size, a random sample of twins will require a prohibitively large sample size. It is well known that selective sampling is far more efficient in terms of genotyping effort. In this paper we derive easy expressions for the information contributed by sib pairs for the detection of linkage to a quantitative trait locus (QTL). We consider random samples as well as samples of sib pairs selected on the basis of their trait values. These expressions can be rapidly computed and do not involve simulation. We extend our results for quantitative traits to dichotomous traits using the concept of a liability threshold model. We present tables with required sample sizes for height, insulin levels and migraine, three of the traits studied in the GenomEUtwin project.     

Inter- and intrafamilial heterogeneity: effective sampling strategies and comparison of analysis methods.

Heterogeneity, both inter- and intrafamilial, represents a serious problem in linkage studies of common complex diseases. In this study we simulated different scenarios with families who phenotypically have identical diseases but who genotypically have two different forms of the disease (both forms genetic). We examined the proportion of families displaying intrafamilial heterogeneity, as a function of mode of inheritance, gene frequency, penetrance, and sampling strategies. Furthermore, we compared two different ways of analyzing linkage in these data sets: a two-locus (2L) analysis versus a one-locus (SL) analysis combined with an admixture test. Data were simulated with tight linkage between one disease locus and a marker locus; the other disease locus was not linked to a marker. Our findings are as follows: (1) In contrast to what has been proposed elsewhere to minimize heterogeneity, sampling only "high-density" pedigrees will increase the proportion of families with intrafamilial heterogeneity, especially when the two forms are relatively close in frequency. (2) When one form is dominant and one is recessive, this sampling strategy will greatly decrease the proportions of families with a recessive form and may therefore make it more difficult to detect linkage to the recessive form. (3) An SL analysis combined with an admixture test achieves about the same lod scores and estimate of the recombination fraction as does a 2L analysis. Also, a 2L analysis of a sample of families with intrafamilial heterogeneity does not perform significantly better than an SL analysis. (4) Bilineal pedigrees have little effect on the mean maximum lod score and mean maximum recombination fraction, and therefore there is little danger that including these families will lead to a false exclusion of linkage.     

Combining information within and between pedigrees for mapping complex traits.

This paper is concerned with efficient strategies for gene mapping using pedigrees containing small numbers of affecteds and identity-by-descent data from closely spaced markers throughout the genome. Particular attention is paid to additive traits involving phenocopies and/or locus heterogeneity. For a sample of pedigrees containing a particular configuration of affecteds, e.g., pairs of siblings together with a first cousin, we use a likelihood analysis to find 1-df statistics that are very efficient over a broad range of penetrances and allele frequencies. We identify configurations of affecteds that are particularly powerful for detecting linkage, and we show how pedigrees containing different numbers and configurations of affecteds can be efficiently combined in an overall test statistic.     

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.     

Consistent linkage of dominantly inherited osteogenesis imperfecta to the type I collagen loci: COL1A1 and COL1A2

The segregation of COL1A1 and COL1A2, the two genes which encode the chains of type I collagen, was analyzed in 38 dominant osteogenesis imperfecta (OI) pedigrees by using polymorphic markers within or close to the genes. This was done in order to estimate the consistency of linkage of OI genes to these two loci. None of the 38 pedigrees showed evidence of recombination between the OI gene and both collagen loci, suggesting that the frequency of unlinked loci in the population must be low. From these results, approximate 95% confidence limits for the proportion of families linked to the type I collagen genes can be set between .91 and 1.00. This is high enough to base prenatal diagnosis of dominantly inherited OI on linkage to these genes even in families which are too small for the linkage to be independently confirmed to high levels of significance. When phenotypic features were compared with the concordant collagen locus, all eight pedigrees with Sillence OI type IV segregated with COL1A2. On the other hand, Sillence OI type I segregated with both COL1A1 (17 pedigrees) and COL1A2 (7 pedigrees). The concordant locus was uncertain in the remaining six OI type I pedigrees. Of several other features, the presence or absence of presenile hearing loss was the best predictor of the mutant locus in OI type I families, with 13 of the 17 COL1A1 segregants and none of the 7 COL1A2 segregants showing this feature.     

Handling marker-marker linkage disequilibrium: pedigree analysis with clustered markers

Single-nucleotide polymorphisms (SNPs) are rapidly replacing microsatellites as the markers of choice for genetic linkage studies and many other studies of human pedigrees. Here, we describe an efficient approach for modeling linkage disequilibrium (LD) between markers during multipoint analysis of human pedigrees. Using a gene-counting algorithm suitable for pedigree data, our approach enables rapid estimation of allele and haplotype frequencies within clusters of tightly linked markers. In addition, with the use of a hidden Markov model, our approach allows for multipoint pedigree analysis with large numbers of SNP markers organized into clusters of markers in LD. Simulation results show that our approach resolves previously described biases in multipoint linkage analysis with SNPs that are in LD. An updated version of the freely available Merlin software package uses the approach described here to perform many common pedigree analyses, including haplotyping and haplotype frequency estimation, parametric and nonparametric multipoint linkage analysis of discrete traits, variance-components and regression-based analysis of quantitative traits, calculation of identity-by-descent or kinship coefficients, and case selection for follow-up association studies. To illustrate the possibilities, we examine a data set that provides evidence of linkage of psoriasis to chromosome 17.