Linkage analysis of the nevoid basal cell carcinoma syndrome

Twelve pedigrees were informative for linkage between the gene locus for the nevoid basal cell carcinoma syndrome and the ABO, MNS, Rh, P, Kell, Lewis, Ddy, and Kidd blood group marker loci. Linkage with a recombination fraction less than θ= 0.1 was unlikely for any marker locus. The most favourable of the possible loose linkages, that between the syndrome locus and Rh locus, showed a 12% probability of linkage when the prior odds against two autosomel loci being on the same chromosome were taken into account. The other marker loci manifested probabilities averaging about 3%.     

A simple method to detect linkage for rare recessive diseases: An application to juvenile diabetes

A simple procedure designed specifically to detect linkage for rare recessive diseases is described. The method uses information on identity by descent scores for a pair of sibs at a marker locus conditioned on the number of affected sibs in the pair. A procedure for estimating the recombination fraction is described, and a table facilitating the likelihood ratio test of linkage is provided. The method, when applied to a collection of multiplex families segregating for juvenile diabetes mellitus, suggests the possibility that this disease is linked to the HLA complex. The method is found to compare favorably to the maximum likelihood approach, for which the computer program LIPED gives a maximum lod score of 2.48 at a male and female recombination fraction of theta = 0.20.     

A likelihood-based extended admixture model of oligogenic inheritance in 'model-based' and 'model-free' analysis

The admixture test of linkage heterogeneity is the most often and most successfully applied oligogenic-model linkage and/or LD analysis method. Full two-locus model linkage analysis is possible, but can be computationally intensive and difficult to interpret because of the need to specify so many indeterminate parameters. A novel, computationally efficient method is proposed for combining single locus lod scores which can allow for varying degrees of epistatic interaction. This method can be applied to two-point or multipoint (using complex-valued recombination fractions) linkage and/or linkage disequilibrium analysis to jointly test for multiple unlinked disease loci. Unlike the traditional admixture test, this algorithm permits joint analysis of multiple disease loci with different modes of inheritance for each, and can be applied to 'model-free' analysis as well through the use of 'pseudomarkers'. Software is available for computation of the various likelihood ratio tests described, for comparison of a variety of possible hypotheses regarding locus homogeneity, locus heterogeneity, and epistasis.     

Quantitative linkage: a statistical procedure for its detection and estimation

A new approach for detecting and estimating quantitative linkage which uses sibship data is presented. Using a nested analysis of variance design (with marker genotype nested within sibship), it is shown that under the null hypothesis of no linkage, the expected between marker genotype within sibship mean square (EMSbeta) is equal to the expected within marker genotype within sibship mean square (EMSe), while under the alternative hypothesis of linkage, the first is greater than the second. Thus the regular F-ratio, MSbeta/MSe, can be used to test for quantitative linkage. This is true for both backcross and intercross matings and whether or not there is dominance at the marker locus. A second test involving the comparison of the within marker genotype within sibship variances is available for intercross matings. A maximum likelihood procedure for the estimation for the recombination frequency is also presented.     

Rapid computer analysis of linkage data

A well tested and useful computer program for screening large amounts of pedigree data for linkage is described. All types of pedigree and genetic systems with up to six alleles present in the pedigree are allowed. An original procedure fills in uncertain genotypes and searches for internal inconsistencies in the data and is extremely thoroughgoing. Population gene frequencies are not used, although the program does take account of rare alleles. The scoring method is based on the division of the pedigree into sibships and the application of z-scores for the sexes considered separately wherever possible. About 2000 pedigrees have been analysed and scores for about the same number of pairs of loci are on tape. A mathematical exercise showed that the method of z-scores with score corrections, which is very much quicker than calculating complete likelihood, is acceptably efficient and its efficiency approaches 100% when scoring rare recessive systems. It is shown that the maximum value of the score is a good criterion for linkage, values of 3.1 and 4.0 indicating roughly 95% and 99% probabilities of linkage. The calculation of 2-unit support limits for the estimate of the recombination fraction between linked loci is advocated, and tables of these are given for syntenic loci. No new linkages were confirmed.     

Estimating parental relationship in linkage analysis of recessive traits

In linkage analysis of recessive traits, parental relationship is important. For the case that it is unknown, the question is investigated as to whether estimating parental relationship and using the estimated relationship in linkage analysis is beneficial. Results show that estimating parental relationship can reliably be carried out on the basis of 50–100 genetic marker loci (analysis based on theory by Thompson [1975: Am J Hum Genet 39:173–188]). Misspecification of parental relationship leads to a loss of linkage informativeness, but not to false-positive evidence for linkage. An asymptotic bias in the recombination fraction estimate occurs when parents are unrelated and falsely taken to be related, but no such bias is seen when related parents are taken to be unrelated. Results from this investigation suggest that an estimated parental relationship may be used in linkage analysis as if it were the correct relationship, when evidence for the estimated relationship is supported by a likelihood ratio of at least 10:1 against the parents being unrelated. © 1996 Wiley-Liss, Inc.     

The analysis of close linkage in large families

In large families, if two closely linked loci both have rare alleles and several distant members are ascertained through one having rare alleles at both loci, simple estimates of their recombination fraction are possible. This information is free from errors due to both reduced penetrance and erratic paternity. Simple estimates based on counting will often have high efficiency and limited bias. Some problems of linkage analysis between loci with codominant expression in complete three generation families are also considered. The omission of individuals of uncertain genotype at the test locus will be more efficient than their inclusion.     

The prior probability of autosomal linkage

An expression is derived for the prior probability of linkage between a random trait locus and any one of m random marker loci, and this probability is computed form=1, 10, 20, 30, 50 and 100. A similar expression is derived for two trait loci, and computed for m=1, 10, 20 and 30. When one trait locus and 30 marker loci are being studied, a priori there is over a three-quarter probability that the trait locus should be syntenic with at least one of the markers, and about a one-half probability that there should be a linkage mappable from recombination frequencies. If two traits are studied, then the prior probability that at least one should be syntenic with one of the 30 markers is 0-94, and there is a three-quarter probability that such a linkage should be mappable.     

Further Investigation of Linkage Disequilibrium SNPs and their Ability to Identify Associated Susceptibility Loci

There is currently considerable interest in the use of single‐nucleotide polymorphisms (SNPs) to map disease susceptibility genes. The success of this method will depend on a number of factors including the strength of linkage disequilibrium (LD) between marker and disease loci. We used a data set of SNP genotypings in the region of the APOE disease susceptibility locus to investigate the likely usefulness of SNPs in case‐control studies. Using the estimated haplotype structure surrounding and including the APOE locus, and assuming a codominant disease model, we treated each SNP in turn as if it were a disease susceptibility locus and obtained, for each disease locus and markers, the expected likelihood ratio test (LRT) to assess disease association.We were particularly interested in the power to detect association with the susceptibility polymorphism itself, the power of nearby markers to detect association, and the ability to distinguish between the susceptibility polymorphism and marker loci also showing association. We found that the expected LRT depended critically on disease allele frequencies. For disease loci with a reasonably common allele we were usually able to detect association. However, for only a subset of markers in the close neighbourhood of the disease locus was association detectable. In these cases we were usually, but not always, able to distinguish the disease locus from nearby associated marker loci. For some disease loci, no other loci demonstrated detectable association with the disease phenotype. We conclude that one may need to use very dense SNP maps in order to avoid overlooking polymorphisms affecting susceptibility to a common phenotype.     

New linkage data for the X-linked types of muscular dystrophy and G6PD variants, colour blindness, and Xg blood groups

Six families in which Duchenne muscular dystrophy (DMD) and G6PD or deutan colour blindness are segregating are reported. The sum of the lod-scores of these families together with three published previously indicates that the DMD locus is far from the G6PD:deutan cluster. The lod-scores of two families with Becker muscular dystrophy (BMD) informative for the G6PD locus together with those of one family previously studied by Emery, Smith, and Sanger (1969) suggest that the BMD locus could be at a measurable distance from this cluster. The maximum likelihood estimate of the recombination fraction is 0·27 and the 90% confidence limits are 0·17 and 0·40. This difference in linkage estimates for DMD and BMD suggests that the BMD and the DMD genes are located at two different loci on the X chromosome.

Five more families with DMD and two with BMD informative for Xg blood groups support the conclusion of other authors that there is no hint of linkage between the loci for Xg and for the X-linked forms of muscular dystrophy.

     

A Note on the Asymptotic Properties of Affected-sib-pair Linkage Tests

This article concerns the asymptotic properties of linkage tests for affected‐sib‐pair data under the null hypothesis of no linkage. We consider a popular single‐locus analysis model where the unknown parameters are the disease allele frequency, the three penetrances for the three genotypes at the disease locus, and the recombination fraction between the marker locus and the disease locus. These parameters are completely confounded under the null hypothesis of no linkage. We show that 1) If the total variance of the trait (i.e., the additive variance plus the dominance variance) is “separated” from 0, then the likelihood ratio statistic has an asymptotic 0.5χ²₀+ 0.5χ²₁ distribution; 2) If the prevalence of the trait is “separated” from 0 and the recombination fraction is fixed at 0, then the likelihood ratio statistic has an asymptotic distribution which is a mixture of χ²₀, χ²₁ and χ²₂ . The implications of these results are discussed.     

Genetic localisation of the RP2 type of X linked retinitis pigmentosa in a large kindred.

Genetic linkage and deletion studies have led to the proposal that there are at least two loci on the X chromosome which are responsible for X linked retinitis pigmentosa (XLRP). One locus (RP3) has been closely defined by genetic linkage and deletion analyses and localised to the region between the ornithine transcarbamylase (OTC) and chronic granulomatous disease (CYBB) loci in Xp21.1-p11.4. The other locus (RP2) has been assigned by linkage analysis alone to region Xp11.4-p11.2, but its localisation is less well defined. The results of a multipoint linkage analysis of a single large XLRP kindred using eight informative loci provide further evidence on the localisation of RP2 to this region. The maximum likelihood location of this locus shows a multipoint lod score of 7.17 close to DXS255 (in Xp11.22) and TIMP (in Xp11.3-p11.23), neither of which show recombination with RP2, in an area extending from 2 cM proximal to DXS7 to 1 cM distal to DXS14 (approximate 95% confidence limits).     

The consistency of the posterior probability of linkage

When searching for trait loci along the genome, properly incorporating prior genomic information into the analysis will almost certainly increase the chance of success. Recently, we devised a method that utilizes such prior information in the mapping of trait genes for complex disorders (Vieland, 1998; Wang et al . 1999; Vieland et al . 2000). This method uses the posterior probability of linkage (PPL) based on the admixture model as a measure of linkage information. In this paper, we study the consistency of the PPL. It is shown that, as the number of pedigrees increases, the PPL converges in probability to 1 when there is linkage between the marker and a trait locus, and converges to 0 otherwise. This conclusion is shown to be true for general pedigrees and trait models, even when the likelihood functions are based on misspecified trait models. As part of the effort to prove this conclusion, it is shown that when there is no linkage, the maximum likelihood estimator of the recombination fraction in the admixture model is asymptotically 0.5, even when the admixture model misrepresents the true model.     

Identification of a sixth locus for autosomal dominant retinitis pigmentosa on chromosome 19

We report the mapping of a sixth locus for autosomal dominantretinitis pigmentosa (adRP) to 19q13.4. After a total genomelinkage search using over 300 markers in a single large pedigree,marker loci on the long arm of chromosome 19 showed significantlinkage with the disease locus. Since the mapping informationfor the marker loci used in this study was derived from twodifferent genome maps, we established genetic distances betweenrelevant marker loci so that linkage information could be combinedfrom both maps. A conventional three point analysis betweenthe adRP phenotype and markers D19S180 and D19S214 gave a maximumlod score of 4.87. Combining data from these and other markers,we used the recently described multiple two point programmeFASTMAP to simulate a multipoint analysis of the full data set.This gave a lod score of 5.34 in the Interval between markersD19S180 and D19S214. Recently this laboratory has also reportedthe linkage of another form of retinal degeneration known ascone-rod dystrophy (CRD) to a genetically different set of markersfrom 19q. Linkage data presented here clearly supports the existenceof two separate retinal genes in this part of the genome.     

Linked polymorphic DNA markers in the prediction of X-linked muscular dystrophy

Ten polymorphic DNA markers, including gene specific markers of loci DXS164 and DXS206 , were tested for allele frequencies, degree of heterozygosity and linkage in 34 Finnish families with X-linked muscular dystrophy. With the exception of the Bam HI RFLP of DXS164 subclone pERT87-15, allele frequencies and the degree of heterozygosity failed to show any significant deviation from the data published elsewhere. We document a high degree of linkage disequilibrium between several RFLPs belonging to locus DXS164 . Our linkage data include one recombination between DMD and DXS164 enabling a tentative location of the mutation site distal to DXS164 . The maximum lod score for linkage between the disease locus and DX164 was 7.828 at a recombination fraction of 0.02. According to our data DXS28 and DXS43 may be located further away from the disease locus than previously thought. We use only gene specific markers for genetic counselling. Excluding deletions, 97.1 % of women were heterozygous for at least one such marker. A diagnostic procedure in which useful information can be obtained in over 90 % of all diagnostic situations, using only four filters, is proposed.     

Combined segregation and linkage analysis of nonsyndromic orofacial cleft in two candidate regions

We applied a complex segregation analysis to 46 pedigrees with a total of 121 nuclear families and 660 individuals, to verify hypotheses regarding the inheritance of OFC and linkage with markers on chromosomes 6 and 2. The pointer program for segregation analysis strongly rejected the hypothesis of no familial transmission of OFC in these families. When the hypothesis of a two-locus model was tested with comds , the analysis showed the presence of at least two loci and the model assuming a dominant major gene and a recessive modifier locus was statistically accepted. Given the fitted two-locus model, we tested for a possible linkage between the major OFC locus and the two markers studied. For D6S259, the estimate of the recombination fraction was θ=0.098, corresponding to a LOD score around 2.1. On the contrary, the data analysis concerning the D2S378 marker showed an estimate of the recombination fraction not significantly different from the independence hypothesis.     

The investigation of linkage between a quantitative trait and a marker locus

Procedures are given, using sib pairs, for estimating linkage between a knownm-allele locus and a hypothesized two-allele locus that governs a quantitative trait. Random mating and linkage equilibrium are assumed. Also given are parametric and nonparametric methods for detecting linkage when the trait in question is governed by several two-allele loci, provided there is no epistasis.This investigation was supported by a U.S. Public Health Service Training Grant (2 T01 GM00038), Research Career Development Award (1-K3-GM-31,732), and a research grant (GM HD 16697) from the National Institute of General Medical Sciences.     

Pairwise analysis of radiation hybrid mapping data

Two point lod scores are widely used in pedigree analysis as they provide a fast and efficient method of establishing linkage. Groups of markers that lie in close proximity to one another can be formed by admitting any locus that is linked to at least one existing member of the group with lod score greater than some predetermined value. It seems natural to extend this technique to Radiation Hybrid Mapping both for constructing groups of tightly linked loci that may then be analysed using more powerful statistics and as a method of ordering in its own right.
A general extension of two point analysis is derived and the problems associated with radiation hybrid data are discussed. In particular, the additional parameters representing the probabilities of different fragments being retained (which have no parallel in classical linkage analysis) lead to a range of estimators of the breakage probability, θ, which have equal and maximal likelihood. Ways of circumventing this problem are discussed along with the potential errors they introduce.
Importantly the ambiguity in estimation of θ is not carried through to the lod score as this depends only on the maximum value of the likelihood and not on the particular value of θ at which it occurs. Thus even though two point analysis fails to provide robust estimates of either breakage probabilities or the distance between loci, it represents a simple and effective method of constructing linkage groups that may be analysed with more powerful statistical methods. This is particularly important given the large number of microsatellites, ESTs and candidate genes currently being typed on radiation hybrids.     

An eighth locus for autosomal dominant retinitis pigmentosa is linked to chromosome 17q

Retinitis pigmentosa is one of the most common causes of severevisual handicap in middle to late life. Prior to this report,seven loci had previously been mapped for the autosomal dominantform of this disorder (adRP). We now report the identificationof a novel adRP locus on chromosome 17q. To map the new locus,we performed linkage analysis with microsatellite markers ina large South African kindred. After exclusion of 13 RP candidategene loci (including rhodopsin and peripherin-RDS), we obtainedsignificant positive lod scores at zero recombination fraction(     

The reliability of locus orderings

Locus orders are frequently presented in graphical form, supported by likelihood statements relating to less likely orders. Many imply genetic distances which are inconsistentwith the meiotic evidence, usually by a factor of about 2. While such orders may be the best possible on the data available, measures of their reliability are difficult: the common assumption that an order is correct because changes lead to less likely orders only relates to the subset of orders tested.
It is only possible to deduce the order of any set of loci if a recombinant separates every pair. This usually requires a number of recombinants substantially exceeding the number of loci. Orders may be inferred from distance in the absence of consistent separation. However, if reasonable reliability is to be achieved, the number of meioses necessary to define distances with sufficient precision will be many times the number of loci. Someestimates of the minimum number of recombinants necessary for a correct ordering to achieve a probability of a half, the' half-right ' solution, would be helpful. As a first approximation to this, we use the probability of no 'null gap', i.e. no pair of adjacent lociwith no recombination between them. Where the number of recombinant events is not available from counting, rough guidance can be given by estimating the number of equivalent meioses from lod scores.
Where data are not available from homologies from other mammals or from pulsed-field
studies, deductive methods of family analysis should be used, followed by pairwise optimizing methods for positioning. This will allow orders to be deduced independently for lociconveyed by the male and female gametes and provides a simple test of the procedure: if the orders are not identical a t least one must be wrong.