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.     

Genome-wide Linkage Scan Reveals Three Putative Breast-Cancer-Susceptibility Loci

Despite all the research efforts made during the last few decades, most of the cases of families with breast cancer remain unexplained. Mutations in BRCA1 and BRCA2, and in other breast-cancer-susceptibility genes, account for about 25% of familial breast cancer. Linkage studies have failed to identify other breast-cancer-susceptibility genes. The selection criteria of the families, differences in the population background, or clinical and genetic heterogeneity, among other factors, might determine the power to detect the linkage signal. We have performed a SNP-based linkage scan with a total of 6000 SNP markers across the genome in 41 breast-cancer Spanish families, with an average of four breast-cancer cases per family not associated with BRCA1 or BRCA2 germline mutations. In addition, we have included three BRCA-positive families to test the power in linkage detection from a low-complexity family in which a high-penetrance mutation segregates. We have identified three regions of interest, located on 3q25, 6q24, and 21q22. The two former regions showed a suggestive linkage signal (HLOD scores 3.01 and 2.26, respectively), and the latter region showed a significant linkage signal (HLOD score 3.55). Moreover, we found that a subset of 13 families with bilateral breast cancer presented a HLOD of 3.13 on the 3q25 region. Our results suggest that several variables must be taken into account before performing a linkage study in familial breast cancer because of the high heterogeneity within non-BRCA1/2 families. Phenotypic and geographic homogeneity could be the most important factors.     

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.     

Genetic linkage analysis in familial breast and ovarian cancer: results from 214 families. The Breast Cancer Linkage Consortium.

Breast cancer is known to have an inherited component, consistent in some families with autosomal dominant inheritance; in such families the disease often occurs in association with ovarian cancer. Previous genetic linkage studies have established that in some such families disease occurrence is linked to markers on chromosome 17q. This paper reports the results of a collaborative linkage study involving 214 breast cancer families, including 57 breast-ovarian cancer families; this represents almost all the known families with 17q linkage data. Six markers on 17q, spanning approximately 30 cM, were typed in the families. The aims of the study were to define more precisely the localization of the disease gene, the extent of genetic heterogeneity and the characteristics of linked families and to estimate the penetrance of the 17q gene. Under the assumption of no genetic heterogeneity, the strongest linkage evidence was obtained with D17S588 (maximum LOD score [Zmax] = 21.68 at female recombination fraction [theta f] = .13) and D17S579 (Zmax = 13.02 at theta f = .16). Multipoint linkage analysis allowing for genetic heterogeneity provided evidence that the predisposing gene lies between the markers D17S588 and D17S250, an interval whose genetic length is estimated to be 8.3 cM in males and 18.0 cM in females. This position was supported over other intervals by odds of 66:1. The location of the gene with respect to D17S579 could not be determined unequivocally. Under the genetic model used in the analysis, the best estimate of the proportion of linked breast-ovarian cancer families was 1.0 (lower LOD-1 limit 0.79). In contrast, there was significant evidence of genetic heterogeneity among the families without ovarian cancer, with an estimated 45% being linked. These results suggest that a gene(s) on chromosome 17q accounts for the majority of families in which both early-onset breast cancer and ovarian cancer occur but that other genes predisposing to breast cancer exist. By examining the fit of the linkage data to different penetrance functions, the cumulative risk associated with the 17q gene was estimated to be 59% by age 50 years and 82% by age 70 years. The corresponding estimates for the breast-ovary families were 67% and 76%, and those for the families without ovarian cancer were 49% and 90%; these penetrance functions did not differ significantly from one another.     

Exome Sequencing of Germline DNA from Non-BRCA1/2 Familial Breast Cancer Cases Selected on the Basis of aCGH Tumor Profiling

The bulk of familial breast cancer risk (∼70%) cannot be explained by mutations in the known predisposition genes, primarily BRCA1 and BRCA2. Underlying genetic heterogeneity in these cases is the probable explanation for the failure of all attempts to identify further high-risk alleles. While exome sequencing of non-BRCA1/2 breast cancer cases is a promising strategy to detect new high-risk genes, rational approaches to the rigorous pre-selection of cases are needed to reduce heterogeneity. We selected six families in which the tumours of multiple cases showed a specific genomic profile on array comparative genomic hybridization (aCGH). Linkage analysis in these families revealed a region on chromosome 4 with a LOD score of 2.49 under homogeneity. We then analysed the germline DNA of two patients from each family using exome sequencing. Initially focusing on the linkage region, no potentially pathogenic variants could be identified in more than one family. Variants outside the linkage region were then analysed, and we detected multiple possibly pathogenic variants in genes that encode DNA integrity maintenance proteins. However, further analysis led to the rejection of all variants due to poor co-segregation or a relatively high allele frequency in a control population. We concluded that using CGH results to focus on a sub-set of families for sequencing analysis did not enable us to identify a common genetic change responsible for the aggregation of breast cancer in these families. Our data also support the emerging view that non-BRCA1/2 hereditary breast cancer families have a very heterogeneous genetic basis.     

A genomewide scan for type 1-diabetes susceptibility in Scandinavian families: identification of new loci with evidence of interactions

Type 1 diabetes mellitus (TIDM) has a multifactorial etiology, with major genetic-susceptibility determinants located in the HLA and insulin-gene (INS) regions. Linkage data implicating other disease-susceptibility loci are conflicting. This is likely due to (1) the limited power for detection of contributions of additional susceptibility loci, given the limited number of informative families available for study, (2) factors such as genetic heterogeneity between populations, and (3) potential gene-gene and gene-environment interactions. To circumvent some of these problems, we have conducted a genomewide linkage analysis for T1DM-susceptibility loci in 408 multiplex families from Scandinavia, a population expected to be homogeneous for genetic and environmental factors. In addition to verifying the HLA and INS susceptibility loci, the study provides confirmation of IDDM15 on chromosome 6q21. Suggestive evidence of additional susceptibility loci was found on chromosomes 2p, 5q, and 16p. For some loci, the support for linkage increased substantially when families were stratified on the basis of HLA or INS genotypes, with statistically significant heterogeneity between the stratified subgroups. Our data support both the existence of non-HLA genes of significance for T1DM and interaction between HLA and non-HLA loci in the determination of the T1DM phenotype.     

Confirmation of the HPCX prostate cancer predisposition locus in large Utah prostate cancer pedigrees

Several genetic predisposition loci for prostate cancer have been identified through linkage analysis, and it is now generally recognized that no single gene is responsible for more than a small proportion of prostate cancers. However, published confirmations of these loci have been few, and failures to confirm have been frequent. The genetic etiology of prostate cancer is clearly complex and includes significant genetic heterogeneity, phenocopies, and reduced penetrance. Powerful analyses that involve robust statistics and methods to reduce genetic heterogeneity are therefore necessary. We have performed linkage analysis on 143 Utah pedigrees for the previously published Xq27-28 (HPCX) prostate cancer susceptibility locus. We employed a robust multipoint statistic (TLOD) and a novel splitting algorithm to reduce intra-familial heterogeneity by iteratively removing the top generation from the large Utah pedigrees. In a dataset containing pedigrees having no more than five generations, we observed a multipoint TLOD of 2.74 (P=0.0002), which is statistically significant after correction for multiple testing. For both the full-structure pedigrees (up to seven generations) and the smaller sub-pedigrees, the linkage evidence was much reduced. This study thus represents the first significant confirmation of HPCX (Xq27-28) and argues for the continued utility of large pedigrees in linkage analyses for complex diseases.     

Chromosome 17q linkage studies of 18 Utah breast cancer kindreds.

In this paper we present linkage results from the analysis of 18 Utah breast cancer kindreds, for three 17q markers. Four kindreds had LOD scores greater than 1.0 for at least one of the marker loci. One of these kindreds has a LOD score of 6.07 with D17S579, and we believe it to be the most informative 17q family reported to date. Among the kindreds which appear unlinked to 17q were an early-onset breast cancer family, a large breast-ovarian family, and a kindred with mixed age at onset. Analysis of individual recombinants in the linked families localizes the BRCA1 gene between THRA1 and D17S579 (Mfd188). A comparison of the Cancer and Steroid Hormone Study (CASH) model and a model which assumes a rare dominant susceptibility locus with low penetrance and no phenocopies stresses the difficulties in assessing linkage if the assumptions of the CASH model in terms of age at onset of breast cancer are not appropriate for the BRCA1 locus. A hypothetical breast cancer pedigree is used to calculate gene carrier probabilities under the CASH model, thereby illustrating some of our concerns regarding the use of this model to detect and exclude 17q linkage in breast cancer families.     

Genomic rearrangements in BRCA1 and BRCA2: A literature review

Women with mutations in the breast cancer genes BRCA1 or BRCA2 have an increased lifetime risk of developing breast, ovarian and other BRCA-associated cancers. However, the number of detected germline mutations in families with hereditary breast and ovarian cancer (HBOC) syndrome is lower than expected based upon genetic linkage data. Undetected deleterious mutations in the BRCA genes in some high-risk families are due to the presence of intragenic rearrangements such as deletions, duplications or insertions that span whole exons. This article reviews the molecular aspects of BRCA1 and BRCA2 rearrangements and their frequency among different populations. An overview of the techniques used to screen for large rearrangements in BRCA1 and BRCA2 is also presented. The detection of rearrangements in BRCA genes, especially BRCA1, offers a promising outlook for mutation screening in clinical practice, particularly in HBOC families that test negative for a germline mutation assessed by traditional methods.     

Moderate frequency of BRCA1 and BRCA2 germ-line mutations in Scandinavian familial breast cancer.

Previous studies of high-risk breast cancer families have proposed that two major breast cancer-susceptibility genes, BRCA1 and BRCA2, may account for at least two-thirds of all hereditary breast cancer. We have screened index cases from 106 Scandinavian (mainly southern Swedish) breast cancer and breast-ovarian cancer families for germ-line mutations in all coding exons of the BRCA1 and BRCA2 genes, using the protein-truncation test, SSCP analysis, or direct sequencing. A total of 24 families exhibited 11 different BRCA1 mutations, whereas 11 different BRCA2 mutations were detected in 12 families, of which 3 contained cases of male breast cancer. One BRCA2 mutation, 4486delG, was found in two families of the present study and, in a separate study, also in breast tumors from three unrelated males with unknown family history, suggesting that at least one BRCA2 founder mutation exists in the Scandinavian population. We report 1 novel BRCA1 mutation, eight additional cases of 4 BRCA1 mutations described elsewhere, and 11 novel BRCA2 mutations (9 frameshift deletions and 2 nonsense mutations), of which all are predicted to cause premature truncation of the translated products. The relatively low frequency of BRCA1 and BRCA2 mutations in the present study could be explained by insufficient screening sensitivity to the location of mutations in uncharacterized regulatory regions, the analysis of phenocopies, or, most likely, within predisposed families, additional uncharacterized BRCA genes.     

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

The value of molecular haplotypes in a family-based linkage study

Novel methods that could improve the power of conventional methods of gene discovery for complex diseases should be investigated. In a simulation study, we aimed to investigate the value of molecular haplotypes in the context of a family-based linkage study. The term "haplotype" (or "haploid genotype") refers to syntenic alleles inherited on a single chromosome, and we use the term "molecular haplotype" to refer to haplotypes that have been determined directly by use of a molecular technique such as long-range allele-specific polymerase chain reaction. In our study, we simulated genotype and phenotype data and then compared the powers of analyzing these data under the assumptions that various levels of information from molecular haplotypes were available. (This information was available because of the simulation procedure.) Several conclusions can be drawn. First, as expected, when genetic homogeneity is expected or when marker data are complete, it is not efficient to generate molecular haplotyping information. However, with levels of heterogeneity and missing data patterns typical of complex diseases, we observed a 23%-77% relative increase in the power to detect linkage in the presence of heterogeneity with heterogeneity LOD scores >3.0 when all individuals are molecularly haplotyped (compared with the power when only standard genotypes are used). Furthermore, our simulations indicate that most of the increase in power can be achieved by molecularly haplotyping a single individual in each family, thereby making molecular haplotyping a valuable strategy for increasing the power of gene mapping studies of complex diseases. Maximization of power, given an existing family set, can be particularly important for late-onset, often-fatal diseases such as cancer, for which informative families are difficult to collect.     

Closing in on a breast cancer gene on chromosome 17q.

Linkage of early-onset familial breast and ovarian cancer to 11 markers on chromosome 17q12-q21 defines an 8-cM region which is very likely to include the disease gene BRCA 1. The most closely linked marker is D17S579, a highly informative CA repeat polymorphism. D17S579 has no recombinants with inherited breast or ovarian cancer in 79 informative meioses in the seven families with early-onset disease (lod score 9.12 at zero recombination). There is no evidence for linkage heterogeneity in the families with early-onset disease. The proportion of older-onset breast cancer attributable to BRCA 1 is not yet determinable, because both inherited and sporadic cases occur in older-onset families.     

Linkage of familial breast cancer to chromosome 17q21 may not be restricted to early-onset disease.

Lod scores for linkage between familial breast and ovarian cancer and markers on chromosome 17q21 are more frequently positive among families with disease diagnosed at younger ages than they are among older-onset families, suggesting that linkage is restricted to early-onset disease. However, for late-onset cases, the relative probability of sporadic rather than inherited disease is higher than previously suggested. If this correction is made, then later-onset families are much less informative; linkage heterogeneity based on age at onset is no longer significant; and for the sample of families as a whole, linkage is significant at a recombination fraction since demonstrated to be close to the correct local. There is probably more than one gene for inherited breast cancer, but heterogeneity may not be due to age at disease onset.     

Heterogeneity analysis of breast cancer families by using age at onset as a covariate.

An extension of the usual mixture model of heterogeneity (two family types, one with and one without linkage) is proposed by introducing age at onset as a covariate. The extended model defines age-dependent penetrances where the exact parametrization of age-at-onset distributions depends on the given genotype and family type (linked or unlinked). This extension was applied to breast cancer families. We postulated that the mean age at onset in individuals affected by the linked gene was lower than the mean age at onset in all other affected individuals. Linkage heterogeneity for breast cancer families was detected at a significance level of .003.     

Direct power comparisons between simple LOD scores and NPL scores for linkage analysis in complex diseases.

Several methods have been proposed for linkage analysis of complex traits with unknown mode of inheritance. These methods include the LOD score maximized over disease models (MMLS) and the "nonparametric" linkage (NPL) statistic. In previous work, we evaluated the increase of type I error when maximizing over two or more genetic models, and we compared the power of MMLS to detect linkage, in a number of complex modes of inheritance, with analysis assuming the true model. In the present study, we compare MMLS and NPL directly. We simulated 100 data sets with 20 families each, using 26 generating models: (1) 4 intermediate models (penetrance of heterozygote between that of the two homozygotes); (2) 6 two-locus additive models; and (3) 16 two-locus heterogeneity models (admixture alpha = 1.0,.7,.5, and.3; alpha = 1.0 replicates simple Mendelian models). For LOD scores, we assumed dominant and recessive inheritance with 50% penetrance. We took the higher of the two maximum LOD scores and subtracted 0.3 to correct for multiple tests (MMLS-C). We compared expected maximum LOD scores and power, using MMLS-C and NPL as well as the true model. Since NPL uses only the affected family members, we also performed an affecteds-only analysis using MMLS-C. The MMLS-C was both uniformly more powerful than NPL for most cases we examined, except when linkage information was low, and close to the results for the true model under locus heterogeneity. We still found better power for the MMLS-C compared with NPL in affecteds-only analysis. The results show that use of two simple modes of inheritance at a fixed penetrance can have more power than NPL when the trait mode of inheritance is complex and when there is heterogeneity in the data set.     

A bayesian random-effects markov model for tumor progression in women with a family history of breast cancer

SUMMARY: It makes intuitive sense to model the natural history of breast cancer, tumor progression from preclinical screen-detectable phase (PCDP) to clinical disease, as a multistate process, but the multilevel structure of the available data, which generally comes from cluster (family)-based service screening programs, makes the required parameter estimation intractable because there is a correlation between screening rounds in the same individual, and between subjects within clusters (families). There is also residual heterogeneity after adjusting for covariates. We therefore proposed a Bayesian hierarchical multistate Markov model with fixed and random effects and applied it to data from a high-risk group (women with a family history of breast cancer) participating in a family-based screening program for breast cancer. A total of 4867 women attended (representing 4464 families) and by the end of 2002, a total of 130 breast cancer cases were identified. Parameter estimation was carried out using Markov chain Monte Carlo (MCMC) simulation and the Bayesian software package WinBUGS. Models with and without random effects were considered. Our preferred model included a random-effect term for the transition rate from preclinical to clinical disease (sigma(2)(2f)), which was estimated to be 0.50 (95% credible interval = 0.22-1.49). Failure to account for this random effect was shown to lead to bias. The incorporation of covariates into multistate models with random effect not only reduced residual heterogeneity but also improved the convergence of stationary distribution. Our proposed Bayesian hierarchical multistate model is a valuable tool for estimating the rate of transitions between disease states in the natural history of breast cancer (and possibly other conditions). Unlike existing models, it can cope with the correlation structure of multilevel screening data, covariates, and residual (unexplained) variation.     

Absence of linkage to the ataxia telangiectasia locus in familial breast cancer

Heterozygotes for ataxia-telangiectasia (AT) are known to have an increased risk of breast cancer. The gene (or genes) responsible for almost all cases of AT has been localised to chromosome 11q by genetic linkage analysis. To examine the possibility that AT heterozygosity may account for a substantial proportion of familial breast cancer, we have typed five markers on chromosome 11q in 16 breast cancer families. We have found no evidence for linkage between breast cancer and chromosome 11q markers and conclude that the contribution of AT to familial breast cancer is likely to be minimal.     

Linkage analysis of 26 Canadian breast and breast-ovarian cancer families

We have examined 26 Canadian families with hereditary breast or ovarian cancer for linkage to markers flanking the BRCA1 gene on chromosome 17q12–q21. Of the 15 families that contain cases of ovarian cancer, 94% were estimated to be linked to BRCA1. In contrast, there was no overall evidence of linkage in the group of 10 families with breast cancer without ovarian cancer. A genetic recombinant in a breast-ovarian cancer family indicates a placement of BRCA1 telomeric to D17S776, and helps to define the region of assignment of the cancer susceptibility gene. Other cancers of interest that appeared in the BRCA1-linked families included primary peritoneal cancer, cancer of the fallopian tube, and malignant melanoma.     

Analysis of chromosome 1q42.2-43 in 152 families with high risk of prostate cancer

One hundred fifty-two families with prostate cancer were analyzed for linkage to markers spanning a 20-cM region of 1q42.2-43, the location of a putative prostate cancer-susceptibility locus (PCAP). No significant evidence for linkage was found, by use of both parametric and nonparametric tests, in our total data set, which included 522 genotyped affected men. Rejection of linkage may reflect locus heterogeneity or the confounding effects of sporadic disease in older-onset cases; therefore, pedigrees were stratified into homogeneous subsets based on mean age at diagnosis of prostate cancer and number of affected men. Analyses of these subsets also detected no significant evidence for linkage, although LOD scores were positive at higher recombination fractions, which is consistent with the presence of a small proportion of families with linkage. The most suggestive evidence of linkage was in families with at least five affected men (nonparametric linkage score of 1.2; P=.1). If heterogeneity is assumed, an estimated 4%-9% of these 152 families may show linkage in this region. We conclude that the putative PCAP locus does not account for a large proportion of these families with prostate cancer, although the linkage of a small subset is compatible with these data.