Estimating linkage heterogeneity

The admixture model for linkage heterogeneity is modified to take account of the difference in recombination fractions in the two sexes. The data used may concern a single (marker) locus on one chromosome, which is suspected of being sometimes near a (disease) locus for a particular condition of interest, or there may be data on more than one locus on this chromosome. There may be data on a locus or loci on a second chromosome, which is also suspected of sometimes carrying an allele for the condition in question. The general principle for the analysis is the same in all such cases, though details may differ. The object is to estimate the relevant recombination fractions, and the proportions of cases in which the allele for the condition falls on each chromosome.     

Estimation of admixture and detection of linkage in admixed populations by a Bayesian approach: application to African-American populations

We describe a novel method for analysis of marker genotype data from admixed populations, based on a hybrid of Bayesian and frequentist approaches in which the posterior distribution is generated by Markov chain simulation and score tests are obtained from the missing-data likelihood. We analysed data on unrelated individuals from eight African-American populations, genotyped at ten marker loci of which two ( FY and AT3 ) are linked (22 cM apart). Linkage between these two loci was detected by testing for association of ancestry conditional on parental admixture. The strength of this association was consistent with European gene flow into the African-American population between five and nine generations ago. To mimic the mapping of an unknown gene in an 'affecteds- only' analysis, a binary trait was constructed from the genotype at the AT3 locus and a score test was shown to detect linkage of this 'trait' with the FY locus. Mis-specification of the ancestry-specific allele frequencies – the probabilities of each allelic state given the ancestry of the allele – was detected at three of the ten marker loci. The methods described here have wide application to the analysis of data from admixed populations, allowing the effects of linkage and population structure (variation of admixture between individuals) to be distinguished. With more markers and a more complex statistical model, genes underlying ethnic differences in disease risk could be mapped by this approach.     

Binomial Mixture Model-based Association Tests under Genetic Heterogeneity

Most of the existing association tests for population-based case-control studies are based on comparing the mean genotype scores between the case and control groups, which may not be efficient under genetic heterogeneity. Given that most common diseases are genetically heterogeneous, caused by mutations in multiple loci, it may be beneficial to fully account for genetic heterogeneity in an association test. Here we first propose a binomial mixture model for such a purpose and develop a corresponding mixture likelihood ratio test (MLRT) for a single locus. We also consider two methods to combine single-locus-based MLRTs across multiple loci in linkage disequilibrium to boost power when causal SNPs are not genotyped. We show with a wide spectrum of numerical examples that under genetic heterogeneity the proposed tests are more powerful than some commonly used association tests.     

Linkage detection under heterogeneity and the mixture problem

Linkage analysis has contributed to the localization of many human disease genes. The presence of locus heterogeneity reduces statistical power and can prejudice the detection of linkage if the analysis assumes homogeneity. Nevertheless, mixed genetic models are not routinely used in gene searches. The null distribution of the test statistic is not uniquely defined. In this paper, a transformation is used to determine an approximate asymptotic distribution of the test statistic under a mixture model. The equivalent critical values of the test are computed and the performance of the test under various levels of heterogeneity and family size is investigated. For gene searches, we recommend the routine use of an admixture model with a critical lod score of 3·44.     

Computer simulation of linkage and heterogeneity in tuberous sclerosis: a critical evaluation of the collaborative family data.

The existence of locus heterogeneity for a genetic disease may complicate linkage studies considerably, especially when very few large families with the disease are available. In this situation a modest collection of families is unlikely to be sufficient for successful localisation of one or more disease genes. Recently, eight research groups working on tuberous sclerosis (TSC) brought together linkage data pertaining to the candidate chromosomes 9, 11, and 12 for a large group of families. In a series of simulation studies we determined the probability of detecting linkage and linkage heterogeneity in this set of families. On average TSC families are very small; in most cases there are fewer than two informative meioses. The size distribution of chromosome 9 linked families was similar to that of non-linked families. This indicates that a dramatic difference in the clinical severity of major genetic forms of TSC is unlikely. The results of our simulation studies show that this set of families can generate highly significant evidence for linkage and heterogeneity. When two TSC genes are equally common, the strongest evidence for linkage and heterogeneity could be obtained using a method based on the incorporation of multiple candidate regions in a single analysis, with an average lod score of 24.27.     

Genome-wide linkage analyses of hereditary prostate cancer families with colon cancer provide further evidence for a susceptibility locus on 15q11�Cq14

The search for susceptibility loci in hereditary prostate cancer (HPC) is challenging because of locus and disease heterogeneity. One approach to reduce disease heterogeneity is to stratify families on the basis of the occurrence of multiple cancer types. This method may increase the power for detecting susceptibility loci, including those with pleiotropic effects. We have completed a genome-wide SNP linkage analysis of 96 HPC families, each of which has one or more first-degree relatives with colon cancer (CCa), and further analyzed the subset of families with two or more CCa cases (n=27). When only a prostate cancer (PCa) phenotype was considered to be affected, we observed suggestive evidence for linkage (LOD ≥1.86) at 15q14, 18q21 and 19q13 in all families, and at 1p32 and 15q11–q14 in families with two or more CCa cases. When both the PCa and CCa phenotypes were considered affected, suggestive evidence for linkage was observed at 11q25, 15q14 and 18q21 in all families, and at 1q31, 11q14 and 15q11–14 in families with two or more CCa cases. The strongest linkage signal was identified at 15q14 when both PCa and CCa phenotypes were considered to be affected in families with two or more CCa cases (recessive HLOD=3.88). These results provide further support for the presence of HPC susceptibility loci on chromosomes 11q14, 15q11–q14 and 19q13 and highlight loci at 1q31, 11q, 15q11–14 and 18q21 as having possible pleiotropic effects. This study shows the benefit of using a comprehensive family cancer history to create more genetically homogenous subsets of HPC families for linkage analyses.     

Extension of conditional model-free likelihood-based linkage analysis to additive and other models

We have previously described extending our method of 'model-free' linkage analysis, implemented in the MFLINK program, in order to deal with liability classes. This allows a new form of conditional two-locus linkage analysis, meaning that the genotypes of a known risk locus can be used to define liability classes so that their effects can be incorporated in tests for linkage at additional loci. In this method, relationships between transmission models for different liability classes were constrained so that there was a constant multiplicative effect on penetrance values. Here we present further extensions to the method to allow for different relationships. In particular, rather than only having a multiplicative effect on risk of affection we now allow specification of a multiplicative effect on risk of non-affection, or a combination of both relationships, across liability classes. We now also allow specification of an additive effect on penetrance. By way of example, we apply these methods to genome scan data for Alzheimer's disease using apolipoprotein E genotype to define liability classes. We show that, although in general the different methods produce results which tend to be quite highly correlated, certain markers can produce quite different results according to the method applied and that these could well lead to differences of interpretation. Without knowing a priori which relationship is likely to be most appropriate to describe the overall combined effect of the two loci one might be obliged to apply a number of different methods. This in turn may lead to the familiar difficulties associated with multiple testing. Nevertheless, the new method allows researchers greater flexibility in analysing linkage data for diseases in which one or more risk polymorphisms have already been identified.     

An extension of the Maximum Lod Score method to X-linked loci

The Maximum Lod Score method for affected relative-pair analysis, introduced by Risch, is a powerful method for detecting linkage between an autosomal marker locus and disease. In order to use the method to detect linkage to markers on the X-chromosome, some modification is necessary. Here we extend the method to be applicable to X-chromosomal data, and derive genetic restrictions on the haplotype-sharing probabilities analogous to the 'possible triangle' restrictions described by Holmans for the autosomal case. Size criteria are derived using asymptotic theory and simulation, and the power is calculated for a number of possible underlying models. The method is applied to data from 284 type 1 diabetic families and evidence is found for the presence of one or more diabetogenic loci on the X-chromosome.     

A Novel Approach to Detect Parent-of-Origin Effects from Pedigree Data with Application to Beckwith-Wiedemann Syndrome

The parent-of-origin phenomenon in humans is now well recognized, and the deregulation of imprinted genes has been implicated in a number of human diseases. Recently, several linkage analysis methods have been developed to allow for parent-of-origin effects in the analysis of pedigree data. However, in general, one does not know a priori if disease-causing loci are imprinted or not. Linkage methods that allow for imprinting can lose power if there is no imprinting. Conversely, linkage methods that do not allow for imprinting will lose power if there is imprinting, because of penetrance values not being correctly specified. Therefore, it is important to know whether imprinting is a possible mode of disease inheritance before performing linkage analyses. In this paper we describe a simple covariate-coding scheme to test for the presence of parent-of-origin effects, and provide a formula for calculating parent-specific penetrance values prior to any linkage analysis. In simulation studies our coding scheme successfully detected parent-of-origin effects and, when pedigrees were ascertained sequentially or through a single proband, inclusion of this covariate more accurately estimated penetrance values than when such a covariate was not included. The use of accurate penetrance values in a linkage analysis that allows for imprinting can provide higher power when the disease locus is imprinted. Finally, we applied our approach to 27 pedigrees affected with Beckwith-Wiedemann syndrome (BWS), an overgrowth syndrome, and found that a maternally expressed parent-of-origin model based on the likelihood ratio test was the most parsimonious, suggesting a role for paternally imprinted genes in BWS.     

A Novel Genetic Study of Chinese Families with Autosomal Recessive Retinitis Pigmentosa

Autosomal recessive retinitis pigmentosa (arRP) is the commonest form of RP worldwide. To date 22 loci have been implicated in the pathogenesis of this disease; however none of these loci independently account for a significant proportion of recessive RP. Linkage studies of arRP in consanguineous families have been mainly based on homozygosity mapping, but this strategy cannot be applied in the case of non-consanguineous families. Therefore, we implemented a systematic approach for identifying the disease locus in three non-consanguineous Chinese families with arRP. Initially, linkage analysis using SNPs/microsatellite markers or mutation screening of known arRP genes excluded all loci/genes except RP25 on chromosome 6. Subsequently a whole genome scan for the three families using the 10K GeneChip Mapping Array was performed, in order to identify the possible disease locus. To the best of our knowledge this is the first report on the utilisation of the 10K GeneChip to study linkage in non-consanguineous Chinese arRP. This analysis indicates that the studied families are probably linked to the RP25 locus, a well defined arRP locus in other populations. The identification of another ethnic group linked to RP25 is highly suggestive that this represents a major locus for arRP.     

Linkage investigation of three putative tuberous sclerosis determining loci on chromosomes 9q, 11q, and 12q. The Tuberous Sclerosis Collaborative Group.

Previous linkage studies in tuberous sclerosis have implicated three disease determining loci at 9q, 11q, and 12q. We have collated phenotypic and genotypic data on 1622 members of 128 families with tuberous sclerosis in order to evaluate simultaneously the evidence for these putative loci. Affection status in the family members has been reassessed using uniform diagnostic criteria and genotypic data extensively checked before analysis under alternative models of locus heterogeneity. One tuberous sclerosis determining locus, accounting for approximately 50% of the families studied, has been found to map in the region of D9S10 on 9q34 but no evidence has been found to support the existence of major loci on 11q or 12q. A locus, or loci, elsewhere in the genome is likely to account for tuberous sclerosis in most non-chromosome 9 linked families.     

Age and sex based genetic locus heterogeneity in type 1 diabetes

BACKGROUND: Two genome scans for susceptibility loci for type 1 diabetes using large collections of families have recently been reported. Apart from strong linkage in both studies of the HLA region on chromosome 6p, clear consistent evidence for linkage was not observed at any other loci. One possible explanation for this is a high degree of locus heterogeneity in type 1 diabetes, and we hypothesised that the sex of affected offspring, age of diagnosis, and parental origin of shared alleles may be the bases of heterogeneity at some loci. METHODS: Using data from a genome wide linkage study of 356 affected sib pairs with type 1 diabetes, we performed linkage analyses using parental origin of shared alleles in subgroups based on (1) sex of affected sibs and (2) age of diagnosis. RESULTS: Among the results obtained, we observed that evidence for linkage to IDDM4 on chromosome 11q13 occurred predominantly from opposite sex, rather than same sex sib pairs. At a locus on chromosome 4q, evidence for linkage was observed in sibs where one was diagnosed above the age of 10 years and the other diagnosed below 10 years of age. CONCLUSIONS: We show that heterogeneity tests based on age of diagnosis, sex of affected subject, and parental origin of shared alleles may be helpful in reducing locus heterogeneity in type 1 diabetes. If repeated in other samples, these findings may assist in the mapping of susceptibility loci for type 1 diabetes. Similar analyses can be recommended in other complex diseases.     

Evidence for two schizophrenia susceptibility genes on chromosome 22q13

OBJECTIVE: Previous linkage scans and meta-analyses for schizophrenia susceptibility loci failed to include the most distal portion of chromosome 22q. Accordingly, 27 families having individuals affected with schizophrenia and schizophrenia-spectrum disorders were analyzed using a set of highly informative markers covering all of chromosome 22q. METHODS: Microsatellite and single nucleotide polymorphism markers were evaluated by nonparametric linkage, parametric linkage, and transmission disequilibrium testing of 22q. RESULTS: The maximum nonparametric logarithm of odd scores were 2.9 (P=0.0016) for schizophrenia and 2.7 (P=0.003) for a broader disease definition that included schizotypal personality disorder-both at 44.5 cM within the Sult4A1 locus. Parametric models assuming dominant modes of inheritance and genetic heterogeneity gave maximum multipoint logarithm of odd scores for the broader disease definition at the Sult4A1 locus of 3.3 (P=0.0006) and single point logarithm of odd scores of 3.1-4.8 for Sult4A1 markers (P=0.000015-0.0005). A distal locus, centered at 61 cM, shows a maximum nonparametric logarithm of odd scores of 1.5 (P=0.072) for the broader disease definition. Transmission disequilibrium testing for three adjacent microsatellite markers located near the distal linkage peak revealed significant values for marker D22s526 for schizophrenia (P=0.0016-0.14) and for broader disease definitions including schizotypal personality disorder (P=0.0002-0.0003), and both schizotypal personality disorder plus schizoaffective disorder (P=0.00001-0.000077). CONCLUSION: At least two separable, but closely linked, loci within 22q13 influencing susceptibility to schizophrenia-spectrum disorders, might be possible.     

Pedigree linkage disequilibrium mapping of quantitative trait loci

In this paper, we propose to use pedigrees of any size and any types of relatives in joint high-resolution linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) by variance component models. Two or multiple markers can be simultaneously used in modeling association with the trait locus, instead of using one marker a time in the analysis. The proposed method can provide a unified result by using two or multiple markers in the modeling. This may avoid the complications of different results obtained from the separate analysis of marker by marker. The models simultaneously incorporate both linkage and LD information. The measures of LD are modeled by mean coefficients, and linkage information is modeled by variance-covariance matrix. Using analytical formulas to calculate the regression coefficients, the genetic effects are shown to be decomposed into additive and dominance components. The noncentrality parameter approximations of test statistics of LD are provided to make power calculations. Power and type I error rates are explored to investigate the merit of the proposed method by both the analytical formulas and simulations. Comparing with the association between-family and association within-family ('AbAw') approach of Fulker and Abecasis et al, it is evident that the method proposed in this article is more powerful. The method is applied to investigate the relation between polymorphisms in the angiotensin 1-converting enzyme (ACE) genes and circulating ACE levels, with a better result than that of the 'AbAw' approach. Moreover, two markers I/D and 4656(CT)3/2 can fully interpret association with the trait locus at a 0.01 significance level, which provides a unique result for the ACE data.     

Genetic heterogeneity of autosomal dominant polycystic kidney disease in Argentina.

Autosomal dominant polycystic kidney disease (ADPKD) is an inherited disorder with genetic heterogeneity. Up to three loci are involved in this disease, PKD1 on chromosome 16p13.3, PKD2 on 4q21, and a third locus of unknown location. Here we report the existence of locus heterogeneity for this disease in the Argentinian population by performing linkage analysis on 12 families of Caucasian origin. Eleven families showed linkage to PKD 1 and one family showed linkage to PKD2. Two recombinants in the latter family placed the locus PKD2 proximal to D4S1563, in agreement with data recently published on the cloning of this gene. Analysis of clinical data suggests a milder ADPKD phenotype for the PKD2 family.     

A linkage survey of 20 dominant retinitis pigmentosa families: frequencies of the nine known loci and evidence for further heterogeneity.

Autosomal dominant retinitis pigmentosa (ADRP) is caused by mutations in two known genes, rhodopsin and peripherin/Rds, and seven loci identified only by linkage analysis. Rhodopsin and peripherin/Rds have been estimated to account for 20-31% and less than 5% of ADRP, respectively. No estimate of frequency has previously been possible for the remaining loci, since these can only be implicated when families are large enough for linkage analysis. We have carried out such analyses on 20 unrelated pedigrees with 11 or more meioses. Frequency estimates based on such a small sample provide only broad approximations, while the above estimations are based on mutation detection in much larger clinic based patient series. However, when markers are informative, linkage analysis cannot fail to detect disease causation at a locus, whereas mutation detection techniques might miss some mutations. Also diagnosing dominant RP from a family history taken in a genetic clinic may not be reliable. It is therefore interesting that 10 (50%) of the families tested have rhodopsin-RP, suggesting that, in large clearly dominant RP pedigrees, rhodopsin may account for a higher proportion of disease than had previously been suspected. Four (20%) map to chromosome 19q, implying that this is the second most common ADRP locus. One maps to chromosome 7p, one to 17p, and one to 17q, while none maps to 1cen, peripherin/Rds, 8q, or 7q. Three give exclusion of all of these loci, showing that while the majority of dominant RP maps to the known loci, a small proportion derives from loci yet to be identified.     

Prenatal prediction of spinal muscular atrophy.

Spinal muscular atrophy (SMA) is a common cause of inherited morbidity and mortality in childhood. The wide range of phenotypes in SMA, uncertainty regarding its mode of inheritance, and the suggestion of linkage heterogeneity have complicated the genetic counselling of parents of affected children. The locus responsible for autosomal recessive SMA has been mapped to 5q11.2-q13.3. The most likely order of loci is cen-D5S6-(SMA,D5S125)-(JK53CA1/2,D5S112)-D5S3 9-qter, with highly polymorphic loci being identified at JK53CA1/2 and D5S39. We describe linkage studies with another highly polymorphic locus, D5S127, that is closely linked to D5S39. This genetic map can be used as the basis for genetic counselling in families with autosomal recessive SMA. Appropriate allowance can be made for sporadic cases owing to non-inherited causes and for linkage heterogeneity or misdiagnoses.     

On extending the transmission/disequilibrium test (TDT)

The transmission/disequilibrium test (TDT), for evaluation of the null hypothesis of neither linkage nor association between a marker locus and disease, is extended to the more general situation of transmission of two multi-allele marker loci from parents to affected offspring. Transmission probabilities are derived for a generalized single locus disease model, where the disease locus is taken to lie between the two marker loci. There could be unlinked modifier loci for the disease. Examples of the extended TDT are given and it is shown how the contribution from each locus can be evaluated, both separately and jointly.     

Diagnosis of adult polycystic kidney disease by genetic markers and ultrasonographic imaging in a voluntary family register.

Diagnosis of autosomal dominant adult polycystic kidney disease (APKD) is possible by ultrasonographic scanning (USS) or by using DNA markers linked to the PKD1 locus. Ultrasonography is complicated by the age dependent penetrance of the gene and linkage studies are subject to recombination errors owing to meiotic crossing over and locus heterogeneity. This study draws on data collected from a voluntary family register of APKD over 10 years. Records of 150 families were examined, ultrasound reports were obtained from 242 people at 50% prior risk, and 37 families were typed for DNA markers. The fraction of APKD resulting from loci unlinked to PKD1 (designated PKD2 here) was calculated at 2.94% (upper confidence limit 8.62%). Some subjects who were negative on initial scan later gave a positive scan, but there was no example of a definite gene carrier aged over 30 giving a negative scan. In families large enough for linkage analysis, most people who were at 50% prior risk could be given a final risk below 5% or above 95%, by using combined ultrasound and DNA studies.     

Age of diagnosis-based linkage analysis in type 1 diabetes

Genetic linkage studies of type 1 diabetes have produced a number of conflicting results, suggesting a high degree of locus heterogeneity in this disease. Approaches which model such heterogeneity will increase the power to fine map susceptibility loci. Here, using data from a genome scan of 356 affected sib pairs with type 1 diabetes, we performed heterogeneity analysis based on similarity of age at diagnosis of the sib pairs. We observed linkage to the region on chromosome 4p16.3 in sib pairs both diagnosed over the age of 10 years, whilst there was no evidence for linkage in sib pairs diagnosed before age 10 years. In contrast the sib pairs diagnosed before the age of 10 years demonstrated linkage to IDDM10, on chromosome 10p. Age of diagnosis-based heterogeneity analyses in complex diseases may be particularly helpful in mapping some susceptibility loci.