Sample-size guidelines for linkage analysis of a dominant locus for a quantitative trait by the method of lod scores.

Sample-size guidelines for linkage studies of quantitative traits partially determined by a dominant major locus are needed to provide a rough estimate of the amount of pedigree material that should be sampled to map the loci that influence such traits. After pedigrees are sampled, a specific power calculation can be carried out to evaluate the linkage information provided by the sampled pedigrees. Using computer simulation, I provide sample-size guidelines for linkage studies by the method of lod scores of quantitative traits partially determined by a dominant major locus. I consider the effects of a trait model, marker characteristics, and sampling strategy, with particular attention to sampling strategy because it is the one factor which the investigator can fully control. My results suggest that linkage studies of quantitative traits are practical, particularly if the investigator chooses an efficient sampling design and an efficient strategy to select pedigrees for linkage analysis.     

A Novel Large In-Frame Deletion within the CACNA1F Gene Associates with a Cone-Rod Dystrophy 3-Like Phenotype

Cone-rod dystrophies (CORDs) represent a heterogeneous group of monogenic diseases leading to early impairment of vision. The majority of CORD entities show autosomal modes of inheritance and X-linked traits are comparably rare. So far, three X-chromosomal entities were reported (CORDX1, -X2 and -X3). In this study, we analysed a large family of German origin with solely affected males over three generations showing a CORDX-like phenotype. Due to the heterogeneity of cone-rod dystrophies, we performed a combined linkage and X-exome sequencing approach and identified a novel large intragenic in-frame deletion encompassing exons 18 to 26 within the CACNA1F gene. CACNA1F is described causative for CORDX3 in a single family originating from Finland and alterations in this gene have not yet been reported in other CORDX pedigrees. Our data independently confirm CACNA1F as the causative gene for CORDX3-like phenotypes and detailed clinical characterization of the family expands the knowledge about the phenotypic spectrum of deleterious CACNA1F alterations.     

A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

Random search for shared chromosomal regions in four affected individuals: the assignment of a new hereditary ataxia locus.

Infantile-onset spinocerebellar ataxia (IOSCA) is an autosomal recessively inherited progressive neurological disorder of unknown etiology. This ataxia, identified so far only in the genetically isolated Finnish population, does not share gene locus with any of the previously identified hereditary ataxias, and a random mapping approach was adopted to assign the IOSCA locus. Based on the assumption of one founder mutation, a primary screening of the genome was performed using samples from just four affected individuals in two consanguineous pedigrees. The identification of a shared chromosomal region in these four patients provided the first evidence that the IOSCA gene locus is on chromosome 10q23.3-q24.1, which was confirmed by conventional linkage analysis in the complete family material. Strong linkage disequilibrium observed between IOSCA and the linked markers was utilized to define accurately the critical chromosomal region. The results showed the power of linkage disequilibrium in the locus assignment of diseases with very limited family materials.     

A multipedigree linkage study of X-linked deafness: Linkage to Xq13-q21 and evidence for genetic heterogeneity

A locus for X-linked nonsyndromic deafness has previously been allocated to the Xq13-q21 region based on linkage studies in two separate pedigrees. This has been substantiated by the observation of deafness as a clinical feature of male patients with cytogenetically detectable deletions across this region. The question of a second locus for deafness in this chromosomal region has been raised by the audiologically distinct nature of the deafness in some of the deleted patients compared to that observed in those patients upon whom the linkage data are based. We have performed detailed clinical evaluation and linkage studies on seven pedigrees with nonsyndromic X-linked deafness and conclude that there is evidence for at least two loci for this form of deafness, including one in the Xq13-q21 region. We have observed different radiological features among the pedigrees which map to Xq13-q21, suggesting that even among these pedigrees the deafness is due to different pathological processes. Given these findings, we suggest that the classification of nonsyndromic X-linked deafness based solely on audiological criteria may need to be reviewed.     

Regression models for linkage heterogeneity applied to familial prostate cancer

Linkage heterogeneity frequently occurs for complex genetic diseases, and statistical methods must account for it to avoid severe loss in power to discover susceptibility genes. A common method to allow for only a fraction of linked pedigrees is to fit a mixture likelihood and then to test for linkage homogeneity, given linkage (admixture test), or to test for linkage while allowing for heterogeneity, using the heterogeneity LOD (HLOD) score. Furthermore, features of the families, such as mean age at diagnosis, may help to discriminate families that demonstrate linkage from those that do not. Pedigree features are often used to create homogeneous subsets, and LOD or HLOD scores are then computed within the subsets. However, this practice introduces several problems, including reduced power (which results from multiple testing and small sample sizes within subsets) and difficulty in interpretation of results. To address some of these limitations, we present a regression-based extension of the mixture likelihood for which pedigree features are used as covariates that determine the probability that a family is the linked type. Some advantages of this approach are that multiple covariates can be used (including quantitative covariates), covariates can be adjusted for each other, and interactions among covariates can be assessed. This new regression method is applied to linkage data for familial prostate cancer and provides new insights into the understanding of prostate cancer linkage heterogeneity.     

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.     

Significant linkage of Parkinson disease to chromosome 2q36-37

Parkinson disease (PD) is the second most common neurodegenerative disorder, surpassed in frequency only by Alzheimer disease. Elsewhere we have reported linkage to chromosome 2q in a sample of sibling pairs with PD. We have now expanded our sample to include 150 families meeting our strictest diagnostic definition of verified PD. To further delineate the chromosome 2q linkage, we have performed analyses using only those pedigrees with the strongest family history of PD. Linkage analyses in this subset of 65 pedigrees generated a LOD score of 5.1, which was obtained using an autosomal dominant model of disease transmission. This result strongly suggests that variation in a gene on chromosome 2q36-37 contributes to PD susceptibility.     

A comparison of different linkage statistics in small to moderate sized pedigrees with complex diseases

ABSTRACT: BACKGROUND: In the last years GWA studies have successfully identified common SNPs associated with complex diseases. However, most of the variants found this way account for only a small portion of the trait variance. This fact leads researchers to focus on rare-variant mapping with large scale sequencing, which can be facilitated by using linkage information. The question arises why linkage analysis often fails to identify genes when analyzing complex diseases. Using simulations we have investigated the power of parametric and nonparametric linkage statistics (KC-LOD, NPL, LOD and MOD scores), to detect the effect of genes responsible for complex diseases using different pedigree structures. RESULTS: As expected, a small number of pedigrees with less than three affected individuals has low power to map disease genes with modest effect. Interestingly, the power decreases when unaffected individuals are included in the analysis, irrespective of the true mode of inheritance. Furthermore, we found that the best performing statistic depends not only on the type of pedigrees but also on the true mode of inheritance. CONCLUSIONS: When applied in a sensible way linkage is an appropriate and robust technique to map genes for complex disease. Unlike association analysis, linkage analysis is not hampered by allelic heterogeneity. So, why does linkage analysis often fail with complex diseases? Evidently, when using an insufficient number of small pedigrees, one might miss a true genetic linkage when actually a real effect exists. Furthermore, we show that the test statistic has an important effect on the power to detect linkage as well. Therefore, a linkage analysis might fail if an inadequate test statistic is employed. We provide recommendations regarding the most favorable test statistics, in terms of power, for a given mode of inheritance and type of pedigrees under study, in order to reduce the probability to miss a true linkage.     

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

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

Increase in linkage information by stratification of pedigree data into gold-standard and standard diagnoses: application to the NIMH Alzheimer Disease Genetics Initiative Dataset

Patients diagnosed with a standard clinical method (subject to misclassification error) are often combined with patients diagnosed with a gold-standard method (with zero or very small misclassification error) in family-based studies of complex disease. For example, non-autopsied patients (NAP) are often included along with autopsy-proven (AP) patients in family-based studies of complex diseases, such as Alzheimer's disease (AD). Theoretical and simulation studies suggest that certain misclassification errors can result in severe reduction of power in genetic linkage and association analyses and that phenotype (or diagnostic) error can produce misleading results. Morton's test for heterogeneity can identify genomic regions where error may have led to loss in power. We applied this test to pedigree data from the NIMH Alzheimer's Disease Genetics Initiative Database separated into AP and NAP pedigrees. Morton's test identified one highly significant region of heterogeneity on chromosome 2. The source of the heterogeneity was due to significant indication of linkage in the AP pedigrees at position 109 cM (p value = 6.68 x 10(-5)) with no indication in the NAP pedigrees. Furthermore, Morton's test showed no evidence for heterogeneity on chromosome 19 in early-onset pedigrees that showed highly significant evidence for linkage in other published reports. These results suggest that supplementing linkage analysis with Morton's test can be usefully applied to genetic data sets that have AP and NAP samples, or other sample mixtures that include a 'gold standard' subgroup with reduced error rate, to increase power to detect linkage in the presence of diagnostic misclassification.     

Improved inference of relationship for pairs of individuals

Linkage analyses of genetic diseases and quantitative traits generally are performed using family data. These studies assume the relationships between individuals within families are known correctly. Misclassification of relationships can lead to reduced or inappropriately increased evidence for linkage. Boehnke and Cox (1997) presented a likelihood-based method to infer the most likely relationship of a pair of putative sibs. Here, we modify this method to consider all possible pairs of individuals in the sample, to test for additional relationships, to allow explicitly for genotyping error, and to include X-linked data. Using autosomal genome scan data, our method has excellent power to differentiate monozygotic twins, full sibs, parent-offspring pairs, second-degree (2 degrees ) relatives, first cousins, and unrelated pairs but is unable to distinguish accurately among the 2 degrees relationships of half sibs, avuncular pairs, and grandparent-grandchild pairs. Inclusion of X-linked data improves our ability to distinguish certain types of 2 degrees relationships. Our method also models genotyping error successfully, to judge by the recovery of MZ twins and parent-offspring pairs that are otherwise misclassified when error exists. We have included these extensions in the latest version of our computer program RELPAIR and have applied the program to data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus (FUSION) study.     

Heterogeneity in the map distance between X-linked agammaglobulinemia and a map of nine RFLP loci

Summary In nine family pedigrees in which X-linked agammaglobulinemia (XLA) is segregating, a multi-point linkage analysis has been carried out. In each family, the map distance, d, between XLA and a fixed point in a known map of nine RFLP loci on the X chromosome was estimated by calculating the log likelihoods, L(d). Using a new method, the 10-point likelihood was approximated by appropriately combining three 4-point likelihoods. Homogeneity tests (admixture tests) were performed showing clear evidence for heterogeneity of XLA.     

Ignoring intermarker linkage disequilibrium induces false-positive evidence of linkage for consanguineous pedigrees when genotype data is missing for any pedigree member

Missing genotype data can increase false-positive evidence for linkage when either parametric or nonparametric analysis is carried out ignoring intermarker linkage disequilibrium (LD). Previously it was demonstrated by Huang et al. [1] that no bias occurs in this situation for affected sib-pairs with unrelated parents when either both parents are genotyped or genotype data is available for two additional unaffected siblings when parental genotypes are missing. However, this is not the case for autosomal recessive consanguineous pedigrees, where missing genotype data for any pedigree member within a consanguinity loop can increase false-positive evidence of linkage. False-positive evidence for linkage is further increased when cryptic consanguinity is present. The amount of false-positive evidence for linkage, and which family members aid in its reduction, is highly dependent on which family members are genotyped. When parental genotype data is available, the false-positive evidence for linkage is usually not as strong as when parental genotype data is unavailable. For a pedigree with an affected proband whose first-cousin parents have been genotyped, further reduction in the false-positive evidence of linkage can be obtained by including genotype data from additional affected siblings of the proband or genotype data from the proband's sibling-grandparents. For the situation, when parental genotypes are unavailable, false-positive evidence for linkage can be reduced by including genotype data from either unaffected siblings of the proband or the proband's married-in-grandparents in the analysis.     

The transmission/disequilibrium test for linkage on the X chromosome

The transmission/disequilibrium test (TDT), which detects linkage between a marker and disease loci in the presence of linkage disequilibrium, was introduced by Spielman et al. The original TDT requires families in which the genotypes are known for both parents and for at least one affected offspring, and this limits its applicability to diseases with late onset. The sib-TDT, or S-TDT, which utilizes families with affected and unaffected siblings, was introduced as an alternative method, by Spielman and Ewens, and the TDT and S-TDT can be combined in an overall test (i.e., a combined-TDT, or C-TDT). The TDT statistics described so far are for autosomal chromosomes. We have extended these TDT methods to test for linkage between X-linked markers and diseases that affect either males only or both sexes. For diseases of late onset, when parental genotypes are often unavailable, the X-linkage C-TDT may allow for more power than is provided by the X-linkage TDT alone.     

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?     

Approximating identity-by-descent matrices using multiple haplotype configurations on pedigrees

Identity-by-descent (IBD) matrix calculation is an important step in quantitative trait loci (QTL) analysis using variance component models. To calculate IBD matrices efficiently for large pedigrees with large numbers of loci, an approximation method based on the reconstruction of haplotype configurations for the pedigrees is proposed. The method uses a subset of haplotype configurations with high likelihoods identified by a haplotyping method. The new method is compared with a Markov chain Monte Carlo (MCMC) method (Loki) in terms of QTL mapping performance on simulated pedigrees. Both methods yield almost identical results for the estimation of QTL positions and variance parameters, while the new method is much more computationally efficient than the MCMC approach for large pedigrees and large numbers of loci. The proposed method is also compared with an exact method (Merlin) in small simulated pedigrees, where both methods produce nearly identical estimates of position-specific kinship coefficients. The new method can be used for fine mapping with joint linkage disequilibrium and linkage analysis, which improves the power and accuracy of QTL mapping.     

Evidence for a susceptibility gene, SLEV1, on chromosome 17p13 in families with vitiligo-related systemic lupus erythematosus

Both systemic lupus erythematosus (SLE) and vitiligo are autoimmune disorders that have strong evidence of complex genetic contributions to their etiology, but, to date, efforts using genetic linkage to find the susceptibility genes for either phenotype have met with limited success. Since autoimmune diseases are thought to share at least some of their genetic origins, and since only a small minority (16 of 92) of the European-American pedigrees multiplex for SLE in our collection have one or more affected members with vitiligo, we hypothesized that these pedigrees might be more genetically homogeneous at loci important to both SLE and vitiligo and, hence, have increased power for detection of linkage. We therefore evaluated genomewide microsatellite-marker-scan data for markers at an average marker density of approximately 11 cM in these 16 European-American pedigrees and identified a significant linkage at 17p13, where the maximum multipoint parametric LOD score was 3.64 (P<4.3x10(-5)) and the nonparametric linkage score was 4.02 (P<2.8x10(-5)), respectively. The segregation behavior of this linkage suggests a recessive mode of inheritance with a virtually homogeneous genetic effect in these 16 pedigrees. These results support the hypotheses that SLE and vitiligo may share important genetic effects and that sampling on the basis of clinical covariates dramatically improves power to identify genetic effects.     

X-linked agammaglobulinemia and the red blood cell determinants Xg and 12E7 are not closely linked

Summary Studies on the segregation of the red blood cell determinant Xg in 12 families with X-linked inheritance of agammaglobulinemia (XLA) in 3–4 generations suggested linkage of Xg with XLA. One extensive pedigree of a Dutch family with XLA in eight generations was investigated for Xg and the quantitative polymorphism 12E7. LIPED analysis indicated linkage disproven up to 25cM distance within this pedigree. Taken together with data obtained from two other informative XLA pedigrees and with published data, the results indicate no close linkage between XLA and Xg:12E7, the distance between XLA and Xg being more than 20cM.     

Molecular genetics and heterogeneity in manic depression

Recent research has shown that there are X-linked and possibly chromosome 11-linked forms of manic depression as well as at least one other autosomal form. Segregation analyses of large affected families and the finding of genetic linkage between chromosome specific markers and manic depression mutations provide strong evidence that bipolar as well as unipolar forms of manic depression (MD) within the same family are inherited as a dominant gene disorder. This clarification of the etiology of certain types of depression should bring changed attitudes within psychiatry and may serve to stimulate discussion of the role of evolutionary mechanisms. From a clinical point of view, it has now become possible to determine whether clinical (phenotypic) variation reflects the underlying genotypic heterogeneity of linkage. A preliminary analysis of data from four recent studies shows that there is no clear correlation between such clinical features as the ratio of unipolar to bipolar cases and the genotypic form of manic depression. Further recombinant DNA research, proven to be successful in other genetic diseases, can soon be applied to manic depression. The specific problems posed by manic depression for these techniques are discussed.