A robust identity-by-descent procedure using affected sib pairs: multipoint mapping for complex diseases

Multipoint linkage analysis is a powerful tool to localize susceptibility genes for complex diseases. However, the conventional lod score method relies critically on the correct specification of mode of inheritance for accurate estimation of gene position. On the other hand, allele-sharing methods, as currently practiced, are designed to test the null hypothesis of no linkage rather than estimate the location of the susceptibility gene(s). In this paper, we propose an identity-by-descent (IBD)-based procedure to estimate the location of an unobserved susceptibility gene within a chromosomal region framed by multiple markers. Here we deal with the practical situation where some of the markers might not be fully informative. Rather the IBD statistic at an arbitrary within the region is imputed using the multipoint marker information. The method is robust in that no assumption about the genetic mechanism is required other than that the region contains no more than one susceptibility gene. In particular, this approach builds upon a simple representation for the expected IBD at any arbitrary locus within the region using data from affected sib pairs. With this representation, one can carry out a parametric inference procedure to locate an unobserved susceptibility gene. In addition, here we derive a sample size formula for the number of affected sib pairs needed to detect linkage with multiple markers. Throughout, the proposed method is illustrated through simulated data. We have implemented this method including exploratory and formal model-fitting procedures to locate susceptibility genes, plus sample size and power calculations in a program, GENEFINDER, which will be made available shortly.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

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

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Multipoint linkage analysis and heterogeneity testing in 20 X-linked retinitis pigmentosa families

Using multipoint linkage analysis in 20 families segregating for X-linked retinitis pigmentosa (XLRP), the lod scores on a map of eight RFLP loci were obtained. Our results indicate that under the hypothesis of homogeneity the maximal multipoint lod score supports one disease locus located slightly distal to OTC at Xp21.1. Heterogeneity testing for two XLRP loci suggested that a second XLRP locus may be located 8.5 cM proximal to DXS28 at Xp21.3. Further heterogeneity testing for three disease loci failed to detect a third XLRP locus proximal to DXS7 in any of our 20 XLRP families.     

Percentiles of the null distribution of 2 maximum lod score tests

We here consider the null distribution of the maximum lod score (LOD-M) obtained upon maximizing over transmission model parameters (penetrance values, dominance, and allele frequency) as well as the recombination fraction. Also considered is the lod score maximized over a fixed choice of genetic model parameters and recombination-fraction values set prior to the analysis (MMLS) as proposed by Hodge et al. The objective is to fit parametric distributions to MMLS and LOD-M. Our results are based on 3,600 simulations of samples of n = 100 nuclear families ascertained for having one affected member and at least one other sibling available for linkage analysis. Each null distribution is approximately a mixture p(2)(0) + (1 - p)(2)(v). The values of MMLS appear to fit the mixture 0.20(2)(0) + 0.80chi(2)(1.6). The mixture distribution 0.13(2)(0) + 0.87chi(2)(2.8). appears to describe the null distribution of LOD-M. From these results we derive a simple method for obtaining critical values of LOD-M and MMLS.     

A unified sampling approach for multipoint analysis of qualitative and quantitative traits in sib pairs

Recent advances in molecular biology have enhanced the opportunity to conduct multipoint mapping for complex diseases. Concurrently, one sees a growing interest in the use of quantitative traits in linkage studies. Here, we present a multipoint sib-pair approach to locate the map position (tau) of a trait locus that controls the observed phenotype (qualitative or quantitative), along with a measure of statistical uncertainty. This method builds on a parametric representation for the expected identical-by-descent statistic at an arbitrary locus, conditional on an event reflecting the sampling scheme, such as affected sib pairs, for qualitative traits, or extreme discordant (ED) sib pairs, for quantitative traits. Our results suggest that the variance about tau&d4;, the estimator of tau, can be reduced by as much as 60%-70% by reducing the length of intervals between markers by one half. For quantitative traits, we examine the precision gain (measured by the variance reduction in tau&d4;) by genotyping extremely concordant (EC) sib pairs and including them along with ED sib pairs in the statistical analysis. The precision gain depends heavily on the residual correlation of the quantitative trait for sib pairs but considerably less on the allele frequency and exact genetic mechanism. Since complex traits involve multiple loci and, hence, the residual correlation cannot be ignored, our finding strongly suggests that one should incorporate EC sib pairs along with ED sib pairs, in both design and analysis. Finally, we empirically establish a simple linear relationship between the magnitude of precision gain and the ratio of the number of ED pairs to the number of EC pairs. This relationship allows investigators to address issues of cost effectiveness that are due to the need for phenotyping and genotyping subjects.     

On computation of p-values in parametric linkage analysis

Parametric linkage analysis is usually used to find chromosomal regions linked to a disease (phenotype) that is described with a specific genetic model. This is done by investigating the relations between the disease and genetic markers, that is, well-characterized loci of known position with a clear Mendelian mode of inheritance. Assume we have found an interesting region on a chromosome that we suspect is linked to the disease. Then we want to test the hypothesis of no linkage versus the alternative one of linkage. As a measure we use the maximal lod score Z(max). It is well known that the maximal lod score has asymptotically a (2 ln 10)(-1) x (1/2 chi2(0) + 1/2 chi2(1)) distribution under the null hypothesis of no linkage when only one point (one marker) on the chromosome is studied. In this paper, we show, both by simulations and theoretical arguments, that the null hypothesis distribution of Zmax has no simple form when more than one marker is used (multipoint analysis). In fact, the distribution of Zmax depends on the number of families, their structure, the assumed genetic model, marker denseness, and marker informativity. This means that a constant critical limit of Zmax leads to tests associated with different significance levels. Because of the above-mentioned problems, from the statistical point of view the maximal lod score should be supplemented by a p-value when results are reported.     

Robustness and power of the maximum-likelihood-binomial and maximum-likelihood-score methods,in multipoint linkage analysis of affected-sibship data.

The maximum-likelihood-binomial (MLB) method, based on the binomial distribution of parental marker alleles among affected offspring, recently was shown to provide promising results by two-point linkage analysis of affected-sibship data. In this article, we extend the MLB method to multipoint linkage analysis, using the general framework of hidden Markov models. Furthermore, we perform a large simulation study to investigate the robustness and power of the MLB method, compared with those of the maximum-likelihood-score (MLS) method as implemented in MAPMAKER/SIBS, in the multipoint analysis of different affected-sibship samples. Analyses of multiple-affected sibships by means of the MLS were conducted by consideration of all possible sib pairs, with (weighted MLS [MLSw]) or without (unweighted MLS [MLSu]) application of a classic weighting procedure. In simulations under the null hypothesis, the MLB provided very consistent type I errors regardless of the type of family sample (sib pairs or multiple-affected sibships), as did the MLS for samples with sib pairs only. When samples included multiple-affected sibships, the MLSu led to inflation of low type I errors, whereas the MLSw yielded very conservative tests. Power comparisons showed that the MLB generally was more powerful than the MLS, except in recessive models with allele frequencies <.3. Missing parental marker data did not strongly influence type I error and power results in these multipoint analyses. The MLB approach, which in a natural way accounts for multiple-affected sibships and which provides a simple likelihood-ratio test for linkage, is an interesting alternative for multipoint analysis of sibships.     

Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis

Most multipoint linkage programs assume linkage equilibrium among the markers being studied. The assumption is appropriate for the study of sparsely spaced markers with intermarker distances exceeding a few centimorgans, because linkage equilibrium is expected over these intervals for almost all populations. However, with recent advancements in high-throughput genotyping technology, much denser markers are available, and linkage disequilibrium (LD) may exist among the markers. Applying linkage analyses that assume linkage equilibrium to dense markers may lead to bias. Here, we demonstrated that, when some or all of the parental genotypes are missing, assuming linkage equilibrium among tightly linked markers where strong LD exists can cause apparent oversharing of multipoint identity by descent (IBD) between sib pairs and false-positive evidence for multipoint model-free linkage analysis of affected sib pair data. LD can also mimic linkage between a disease locus and multiple tightly linked markers, thus causing false-positive evidence of linkage using parametric models, particularly when heterogeneity LOD score approaches are applied. Bias can be eliminated by inclusion of parental genotype data and can be reduced when additional unaffected siblings are included in the analysis.     

Relationship estimation by Markov-process models in a sib-pair linkage study

The results of sib-pair linkage studies may be compromised if a substantial number of putative sib pairs are not actually sib pairs. For classification of pairs in a sib-pair genome scan, I propose multipoint methods that are based on a Markov-process model of allele sharing along the chromosome. These methods can be implemented by standard algorithms that compute multipoint marker allele-sharing probabilities for sib pairs. When marker data from at least half the genome are used, misclassification rates are small. The methods will be implemented in an upcoming version of the computer software package S.A.G.E.     

Evidence for a major gene influence on persistent developmental stuttering

Stuttering is a complex developmental speech disorder of unknown etiology. There is a substantial aggregation of stuttering in families, suggesting a genetic component to the disorder. However, the exact mode of transmission is still unknown. An earlier study of 56 multigenerational pedigrees ascertained through single adult probands (38 males and 18 females) found that biological relatives of persistent developmental stutterers have an approximately 10-fold higher risk than in the general population; risk is higher for male relatives, and proband's sex does not affect recurrence and relative risks. In the present paper we conduct a complex segregation analysis of the same data, using the logistic regression model of the SAGE software. Based on the comparisons of model likelihoods, the Mendelian model was selected over all other nongenetic models and the general transmission model. This model was further refined into the most parsimonious model, which shows an autosomal dominant major gene effect influenced by two covariates: sex and affection status of parents. With this model applied to 47 informative multiplex pedigrees, a power calculation based on linkage simulation produced an average lod score of 6.8 for 10-cM density genome scan markers. These results give impetus for a genomewide linkage analysis of susceptibility to persistent developmental stuttering.     

Linkage analysis in the presence of errors III: marker loci and their map as nuisance parameters

In linkage and linkage disequilibrium (LD) analysis of complex multifactorial phenotypes, various types of errors can greatly reduce the chance of successful gene localization. The power of such studies-even in the absence of errors-is quite low, and, accordingly, their robustness to errors can be poor, especially in multipoint analysis. For this reason, it is important to deal with the ramifications of errors up front, as part of the analytical strategy. In this study, errors in the characterization of marker-locus parameters-including allele frequencies, haplotype frequencies (i.e., LD between marker loci), recombination fractions, and locus order-are dealt with through the use of profile likelihoods maximized over such nuisance parameters. It is shown that the common practice of assuming fixed, erroneous values for such parameters can reduce the power and/or increase the probability of obtaining false positive results in a study. The effects of errors in assumed parameter values are generally more severe when a larger number of less informative marker loci, like the highly-touted single nucleotide polymorphisms (SNPs), are analyzed jointly than when fewer but more informative marker loci, such as microsatellites, are used. Rather than fixing inaccurate values for these parameters a priori, we propose to treat them as nuisance parameters through the use of profile likelihoods. It is demonstrated that the power of linkage and/or LD analysis can be increased through application of this technique in situations where parameter values cannot be specified with a high degree of certainty.     

Localization and replication of the systemic lupus erythematosus linkage signal at 4p16: interaction with 2p11, 12q24 and 19q13 in European Americans

Systemic lupus erythematosus (SLE) is a systemic autoimmune disease characterized by both population and phenotypic heterogeneity. Our group previously identified linkage to SLE at 4p16 in European Americans (EA). In the present study we replicate this linkage effect in a new cohort of 76 EA families multiplex for SLE by model-free linkage analysis. Using densely spaced microsatellite markers in the linkage region, we have localized the potential SLE susceptibility gene(s) to be telomeric to the marker D4S2928 by haplotype construction. In addition, marker D4S394 showed marginal evidence of linkage disequilibrium with the putative disease locus by the transmission disequilibrium test and significant evidence of association using a family-based association approach as implemented in the program ASSOC. We also performed both two-point and multipoint model-based analyses to characterize the genetic model of the potential SLE susceptibility gene(s), and the lod scores both maximized under a recessive model with penetrances of 0.8. Finally, we performed a genome-wide scan of the total 153 EA pedigrees and evaluated the possibility of interaction between linkage signals at 4p16 and other regions in the genome. Fourteen regions on 11 chromosomes (1q24, 1q42, 2p11, 2q32, 3p14.2, 4p16, 5p15, 7p21, 8p22, 10q22, 12p11, 12q24, 14q12, 19q13) showed evidence of linkage, among which, signals at 2p11, 12q24 and 19q13 also showed evidence of interaction with that at 4p16. These results provide important additional information about the SLE linkage effect at 4p16 and offer a unique approach to uncovering susceptibility loci involved in complex human diseases.     

Linkage heterogeneity between X-linked retinitis pigmentosa and a map of 10 RFLP loci.

In nine families in which X-linked retinitis pigmentosa (XLRP) is segregating, the lod scores of XLRP in a map of 10 RFLP loci were obtained by multipoint linkage analysis. The XLRP locus was located telomeric to DXS7 in seven of the families and centromeric to DXS7 in two of the families. Under the hypothesis of two XLRP loci, a heterogeneity (admixture) test was performed, providing significant evidence of heterogeneity in XLRP (P less than .01). No correlation was detected between the clinical manifestations of XLRP and the two different disease loci.     

Fine mapping of the diabetes-susceptibility locus, IDDM4, on chromosome 11q13.

Genomewide linkage studies of type 1 diabetes (or insulin-dependent diabetes mellitus [IDDM]) indicate that several unlinked susceptibility loci can explain the clustering of the disease in families. One such locus has been mapped to chromosome 11q13 (IDDM4). In the present report we have analyzed 707 affected sib pairs, obtaining a peak multipoint maximum LOD score (MLS) of 2.7 (lambda(s)=1.09) with linkage (MLS>=0.7) extending over a 15-cM region. The problem is, therefore, to fine map the locus to permit structural analysis of positional candidate genes. In a two-stage approach, we first scanned the 15-cM linked region for increased or decreased transmission, from heterozygous parents to affected siblings in 340 families, of the three most common alleles of each of 12 microsatellite loci. One of the 36 alleles showed decreased transmission (50% expected, 45.1% observed [P=.02, corrected P=.72]) at marker D11S1917. Analysis of an additional 1,702 families provided further support for negative transmission (48%) of D11S1917 allele 3 to affected offspring and positive transmission (55%) to unaffected siblings (test of heterogeneity P=3x10-4, corrected P=. 01]). A second polymorphic marker, H0570polyA, was isolated from a cosmid clone containing D11S1917, and genotyping of 2,042 families revealed strong linkage disequilibrium between the two markers (15 kb apart), with a specific haplotype, D11S1917*03-H0570polyA*02, showing decreased transmission (46.4%) to affected offspring and increased transmission (56.6%) to unaffected siblings (test of heterogeneity P=1.5x10-6, corrected P=4.3x10-4). These results not only provide sufficient justification for analysis of the gene content of the D11S1917 region for positional candidates but also show that, in the mapping of genes for common multifactorial diseases, analysis of both affected and unaffected siblings is of value and that both predisposing and nonpredisposing alleles should be anticipated.     

Lack of association and linkage between HLA and familial polyposis coli

Summary We investigated possible association of and linkage between HLA and familial polyposis coli (FPC). In 182 individuals from 66 pedigrees of FPC and 108 individuals from a normal population, HLA-A,-B, and-C antigens were determined. When the frequencies of HLA antigens in 66 unrelated patients and in normal controls were compared, no association of FPC with HLA was observed. For the linkage analysis, HLA haplotypes of 17 affected sib pairs were investigated by the affected sib pair method. The number of pairs which shared two, one, and no haplotypes identical by descent was not significantly different from the number expected with random occurrence (P>0.95). Finally, seven families were analyzed using Morton's sequential test. A maximum lod score of-0.056 at a recombination fraction of 0.4, and a lod of-3.089 at a recombination fraction of 0.05 were obtained. Therefore, there is neither an association of nor linkage between FPC and HLA.     

High-resolution linkage mapping for susceptibility genes in human polygenic disease: Insulin-dependent diabetes mellitus and chromosome 11q

Insulin-dependent diabetes mellitus (IDDM) has a complex pattern of genetic inheritance. In addition to genes mapping to the major histocompatibility complex (MHC), several lines of evidence point to the existence of other genetic susceptibility factors. Recent studies of the nonobese diabetic mouse (NOD) model of IDDM have suggested the presence, on mouse chromosome 9, of a susceptibility gene linked to the locus encoding the T-cell antigen, Thy-1. A region on human chromosome 11q is syntenic to this region on mouse chromosome 9. We have used a set of polymorphic DNA markers from chromosome 11q to investigate this region for linkage to a susceptibility gene in 81 multiplex diabetic pedigrees. The data were investigated by maximization of lod scores over genetic models and by multiple-locus affected-sib-pair analysis. We were able to exclude the presence of a susceptibility gene (location scores less than -2) throughout greater than 90% of the chromosome 11q homology region, under the assumption that the susceptibility factor would cause greater than 50% of affected sib pairs to share two alleles identical by descent. Theoretical estimates of the power to map susceptibility genes with a high-resolution map of linked markers in a candidate region were made, using HLA as a model locus. This result illustrates the feasibility that IDDM linkage studies using mapped sets of polymorphic DNA markers have, both for other areas of the genome in IDDM and for other polygenic diseases. The analytic approaches introduced here will be useful for affected-sib-pair studies of other complex phenotypes.     

Confirmation of chromosome 7q11 locus for predisposition to intracranial aneurysm

A significant linkage of intracranial aneurysm (IA) has recently been reported to chromosomal region 7q11 (MLS=3.22) in a genomic search of 85 Japanese nuclear families with at least two affected siblings (104 sib pairs). This region contains the elastin gene (ELN, OMIM 130160), which is a functional candidate gene for IA. We have replicated this finding through linkage analyses in 13 extended pedigrees from Utah, comprising 39 IA cases. We genotyped three markers flanking ELN and performed two-point and multipoint parametric analyses, employing simple dominant and recessive models. Analyses utilizing a recessive affecteds-only model yielded significant confirmation of linkage to the region (best evidence, multipoint TLOD=2.34, at D7S2421, corrected P=0.001). This study is the first to confirm the linkage of the 7q11 locus for IA.     

A Discordant-Sibship Test for Disequilibrium and Linkage: No Need for Parental Data

The sibship disequilibrium test (SDT) is designed to detect both linkage in the presence of association and association in the presence of linkage (linkage disequilibrium). The test does not require parental data but requires discordant sibships with at least one affected and one unaffected sibling. The SDT has many desirable properties: it uses all the siblings in the sibship; it remains valid if there are misclassifications of the affectation status; it does not detect spurious associations due to population stratification; asymptotically it has a chi2 distribution under the null hypothesis; and exact P values can be easily computed for a biallelic marker. We show how to extend the SDT to markers with multiple alleles and how to combine families with parents and data from discordant sibships. We discuss the power of the test by presenting sample-size calculations involving a complex disease model, and we present formulas for the asymptotic relative efficiency (which is approximately the ratio of sample sizes) between SDT and the transmission/disequilibrium test (TDT) for special family structures. For sib pairs, we compare the SDT to a test proposed both by Curtis and, independently, by Spielman and Ewens. We show that, for discordant sib pairs, the SDT has good power for testing linkage disequilibrium relative both to Curtis''s tests and to the TDT using trios comprising an affected sib and its parents. With additional sibs, we show that the SDT can be more powerful than the TDT for testing linkage disequilibrium, especially for disease prevalence >.3.     

Model misspecification and multipoint linkage analysis.

Pairwise linkage analysis is robust to genetic model misspecification provided dominance is correctly specified, the primary effect being inflation of the recombination fraction. By contrast, we show that multipoint analysis under misspecified models is not robust when a putative disease locus is placed between close flanking markers, with potentially spuriously negative multipoint lod scores being produced. The problem is due to incorrect attribution of segregation of a disease allele and the consequent conclusion of (unlikely) double crossovers between flanking markers. As a possible solution, we propose the use of high disease allele frequencies, as this allows probabilistically for nonsegregation (through parental homozygosity or dual matings). We show analytically and through analysis of pedigree data simulated under a two-locus heterogeneity model that using a disease allele frequency of 0.05 in the dominant case and 0.25 in the recessive case is quite robust in producing positive multipoint lod scores with close flanking markers across a broad range of conditions including varying allele frequencies, epistasis, genetic heterogeneity and phenocopies.