Linkage analysis of two-locus diseases under single-locus and two-locus analysis models

The Neurobiology of Infantile Autism

Early infantile autism is the most severe of a group of neurodevelopmental syndromes called the pervasive developmental disorders. The clinical features of autism vary greatly, but, by definition, include deficits in social relatedness, communication, and interests or routines. The onset of autistic signs and behaviors typ ically occurs in infancy, and the syndrome is usually fully present by the fourth year. The presence of mental retardation affects the clinical picture greatly. Severely autistic children may be retarded and mute and are often preoccupied with repetitive activities; they often exhibit motor stereotypes, such as rocking or hand flapping. They can be profoundly withdrawn and may show extreme aversion to social or physical contact. More mildly affected children may have normal or even superior intelligence, with well-developed language skills. Their deficits in social relatedness and preoccupation with rituals and routines may set them apart as very odd, but not necessarily as autistic. Autism occurs in 1 of 2000 live births; boys outnumber girls about 3 or 4:1. Although there are no localizing neurological signs in autism, mild or "soft" neurological signs are common and grand mal seizures are frequently present after puberty (Lotspeich LJ, Ciaranello RD. The neurobiology and genetics of infantile autism. In: Bradley R, editor. International reviews of neurobiology. San Diego: Academic Press 1993:87-129). The Neuroscientist 1:361-367, 1995

Modifier gene study of meconium ileus in cystic fibrosis: statistical considerations and gene mapping results

Cystic fibrosis (CF) is a monogenic disease due to mutations in the CFTR gene. Yet, variability in CF disease presentation is presumed to be affected by modifier genes, such as those recently demonstrated for the pulmonary aspect. Here, we conduct a modifier gene study for meconium ileus (MI), an intestinal obstruction that occurs in 16-20% of CF newborns, providing linkage and association results from large family and case-control samples. Linkage analysis of modifier traits is different than linkage analysis of primary traits on which a sample was ascertained. Here, we articulate a source of confounding unique to modifier gene studies and provide an example of how one might overcome the confounding in the context of linkage studies. Our linkage analysis provided evidence of a MI locus on chromosome 12p13.3, which was segregating in up to 80% of MI families with at least one affected offspring (HLOD = 2.9). Fine mapping of the 12p13.3 region in a large case-control sample of pancreatic insufficient Canadian CF patients with and without MI pointed to the involvement of ADIPOR2 in MI (p = 0.002). This marker was substantially out of Hardy-Weinberg equilibrium in the cases only, and provided evidence of a cohort effect. The association with rs9300298 in the ADIPOR2 gene at the 12p13.3 locus was replicated in an independent sample of CF families. A protective locus, using the phenotype of no-MI, mapped to 4q13.3 (HLOD = 3.19), with substantial heterogeneity. A candidate gene in the region, SLC4A4, provided preliminary evidence of association (p = 0.002), warranting further follow-up studies. Our linkage approach was used to direct our fine-mapping studies, which uncovered two potential modifier genes worthy of follow-up.

The chromosome 6p epilepsy locus: exploring mode of inheritance and heterogeneity through linkage analysis

Juvenile myoclonic epilepsy (JME) is a common form of adolescent-onset, generalized epilepsy. JME is genetically linked to the HLA locus on chromosome 6. Families of JME patients also have a significant recurrence of other forms of generalized epilepsy. We used the linkage data to investigate the mode of inheritance of JME and the associated electroencephalographic (EEG) traits at the HLA-linked locus. We investigated how robust the linkage results were when we changed the assumptions of mode of inheritance and penetrance and whether absence and clonic-tonic-clonic in JME families are influenced by the same gene locus as JME. Our results show that the finding of linkage is stable within a wide range of assumptions of penetrance and mode of inheritance, and that the EEG traits seen in unaffected family members reflect the actions of the same gene that is involved in the expression of JME. Our data also suggest that the same locus is responsible for non-JME forms of epilepsy seen in JME families, and that either different doses of the disease allele at the JME locus may lead to different epilepsy phenotypes or that another locus influences the final disease phenotype.

Linkage analysis for autism in a subset families with obsessive-compulsive behaviors: evidence for an autism susceptibility gene on chromosome 1 and further support for susceptibility genes on chromosome 6 and 19

Although there is considerable evidence for a strong genetic component to idiopathic autism, several genome-wide screens for susceptibility genes have been carried out with limited concordance of linked loci, reflecting numerous genes of weak effect and/or sample heterogeneity. In the current study, linkage analysis was carried out in a sample of 62 autism-affected relative pairs with more severe obsessive-compulsive behaviors, selected from a larger (n=115) set of autism-affected relative pairs as a means of reducing sample heterogeneity. Obsessive-compulsive behaviors were assessed using the Autism Diagnostic Interview-Revised (ADI-R). In the sample with more severe obsessive-compulsive behaviors, multipoint NPL scores above 2 were observed on chromosomes 1, 4, 5, 6, 10, 11 and 19, with the strongest evidence for linkage on chromosome 1 at the marker D1S1656, where the multipoint NPL score was 3.06, and the two-point NPL score was 3.21. In follow-up analyses, analyzing the subset of families (n=35) where the patients had the most severe obsessive-compulsive behaviors generated a multipoint NPL score of 2.76, and a two-point NPL score of 2.79, indicating that the bulk of evidence for linkage was derived from the families most severely affected with obsessive-compulsive behaviors. The data suggest that there is an autism susceptibility gene on chromosome 1 and provide further support for the presence of autism susceptibility genes on chromosomes 6 and 19.

Determining trait locus position from multipoint analysis: accuracy and power of three different statistics

Previous work using two-point linkage analysis showed that performing a lod score (LOD) analysis twice, once assuming dominant and once assuming recessive inheritance, and then taking the larger of the two values (designated MMLS) usually has more power to detect linkage than any other method tested. Using computer simulation for a variety of complex inheritance models, we demonstrated power for the MMLS comparable with analysis assuming the true model. However, reports in the literature suggested that the MMLS approach might fail to detect linkage using multipoint analysis due to genetic model misspecification. Here, we tested the robustness of the MMLS approach under multipoint analysis. We simulated data under complex inheritance models, including heterogeneity, epistatic, and additive models. We examined the expected maximum LOD, LOD assuming heterogeneity (HLOD), and nonparametric linkage statistics and the corresponding estimated position in a chromosomal interval of 10 markers with 10% recombination between markers. The mean estimates of position were generally good for all three statistics except when heterogeneity existed, where the LOD and the NPL did not perform as well as the HLOD. The MMLS approach was as robust using multipoint as using two-point linkage analysis. LOD and/or the HLOD generally had more power to detect linkage than NPL across a variety of generating models, even after correcting for the multiple tests. For finding linkage to one locus of several contributing to disease expression, assuming the dominant and recessive models with reduced penetrance is a good approximation of the mode of inheritance at that locus.

Evidence for a susceptibility gene for autism on chromosome 2 and for genetic heterogeneity

Although there is considerable evidence for a strong genetic component to idiopathic autism, several genomewide screens for susceptibility genes have been performed with limited concordance of linked loci, reflecting either numerous genes of weak effect and/or sample heterogeneity. Because decreasing sample heterogeneity would increase the power to identify genes, the effect on evidence for linkage of restricting a sample of autism-affected relative pairs to those with delayed onset (at age >36 mo) of phrase speech (PSD, for phrase speech delay) was studied. In the second stage of a two-stage genome screen for susceptibility loci involving 95 families with two or more individuals with autism or related disorders, a maximal multipoint heterogeneity LOD score (HLOD) of 1.96 and a maximal multipoint nonparametric linkage (NPL) score of 2.39 was seen on chromosome 2q. Restricting the analysis to the subset of families (n=49) with two or more individuals having a narrow diagnosis of autism and PSD generated a maximal multipoint HLOD score of 2.99 and an NPL score of 3.32. The increased scores in the restricted sample, together with evidence for heterogeneity in the entire sample, indicate that the restricted sample comprises a population that is more genetically homogeneous, which could therefore increase the likelihood of positional cloning of susceptibility loci.

Parametric and nonparametric multipoint linkage analysis with imprinting and two-locus-trait models: application to mite sensitization

We present two extensions to linkage analysis for genetically complex traits. The first extension allows investigators to perform parametric (LOD-score) analysis of traits caused by imprinted genes-that is, of traits showing a parent-of-origin effect. By specification of two heterozygote penetrance parameters, paternal and maternal origin of the mutation can be treated differently in terms of probability of expression of the trait. Therefore, a single-disease-locus-imprinting model includes four penetrances instead of only three. In the second extension, parametric and nonparametric linkage analysis with two trait loci is formulated for a multimarker setting, optionally taking imprinting into account. We have implemented both methods into the program GENEHUNTER. The new tools, GENEHUNTER-IMPRINTING and GENEHUNTER-TWOLOCUS, were applied to human family data for sensitization to mite allergens. The data set comprises pedigrees from England, Germany, Italy, and Portugal. With single-disease-locus-imprinting MOD-score analysis, we find several regions that show at least suggestive evidence for linkage. Most prominently, a maximum LOD score of 4.76 is obtained near D8S511, for the English population, when a model that implies complete maternal imprinting is used. Parametric two-trait-locus analysis yields a maximum LOD score of 6.09 for the German population, occurring exactly at D4S430 and D18S452. The heterogeneity model specified for analysis alludes to complete maternal imprinting at both disease loci. Altogether, our results suggest that the two novel formulations of linkage analysis provide valuable tools for genetic mapping of multifactorial traits.

Multipoint oligogenic analysis of age-at-onset data with applications to Alzheimer disease pedigrees

It is usually difficult to localize genes that cause diseases with late ages at onset. These diseases frequently exhibit complex modes of inheritance, and only recent generations are available to be genotyped and phenotyped. In this situation, multipoint analysis using traditional exact linkage analysis methods, with many markers and full pedigree information, is a computationally intractable problem. Fortunately, Monte Carlo Markov chain sampling provides a tool to address this issue. By treating age at onset as a right-censored quantitative trait, we expand the methods used by Heath (1997) and illustrate them using an Alzheimer disease (AD) data set. This approach estimates the number, sizes, allele frequencies, and positions of quantitative trait loci (QTLs). In this simultaneous multipoint linkage and segregation analysis method, the QTLs are assumed to be diallelic and to interact additively. In the AD data set, we were able to localize correctly, quickly, and accurately two known genes, despite the existence of substantial genetic heterogeneity, thus demonstrating the great promise of these methods for the dissection of late-onset oligogenic diseases.

Results of a genome-wide genetic screen for panic disorder

Panic disorder is characterized by spontaneous and recurrent panic attacks, often accompanied by agoraphobia. The results of family, twin, and segregation studies suggest a genetic role in the etiology of the illness. We have genotyped up to 23 families that have a high density of panic disorder with 540 microsatellite DNA markers in a first-pass genomic screen. The thirteen best families (ELOD > 6.0 under the dominant genetic model) have been genotyped with an ordered set of markers encompassing all the autosomes, at an average marker density of 11 cM. Over 110,000 genotypes have been generated on the whole set of families, and the data have been analyzed under both a dominant and a recessive model, and with the program SIBPAIR. No lod scores exceed 2.0 for either parametric model. Two markers give lod scores over 1.0 under the dominant model (chromosomes 1p and 20p), and four do under the recessive model (7p, 17p, 20q, and X/Y). One of these (20p) may be particularly promising. Analysis with SIBPAIR yielded P values equivalent to a lod score of 1.0 or greater (i.e., P < .016, one-sided, uncorrected for multiple tests) for 11 marker loci (2, 7p, 8p, 8q, 9p, 11q, 12q, 16p, 20p and 20q).

Effect of genetic heterogeneity and assortative mating on linkage analysis: a simulation study

Linkage studies of complex genetic traits raise questions about the effects of genetic heterogeneity and assortative mating on linkage analysis. To further understand these problems, I have simulated and analyzed family data for a complex genetic disease in which disease phenotype is determined by two unlinked disease loci. Two models were studied, a two-locus threshold model and a two-locus heterogeneity model. Information was generated for a marker locus linked to one of the disease-defining loci. Random-mating and assortative-mating samples were generated. Linkage analysis was then carried out by use of standard methods, under the assumptions of a single-locus disease trait and a random-mating population. Results were compared with those from analysis of a single-locus homogeneous trait in samples with the same levels of assortative mating as those considered for the two-locus traits. The results show that (1) introduction of assortative mating does not, in itself, markedly affect the estimate of the recombination fraction; (2) the power of the analysis, reflected in the LOD scores, is somewhat lower with assortative rather than random mating. Loss of power is greater with increasing levels of assortative mating; and (3) for a heterogeneous genetic disease, regardless of mating type, heterogeneity analysis permits more accurate estimate of the recombination fraction but may be of limited use in distinguishing which families belong to each homogeneous subset. These simulations also confirmed earlier observations that linkage to a disease "locus" can be detected even if the disease is incorrectly defined as a single-locus (homogeneous) trait, although the estimated recombination fraction will be significantly greater than the true recombination fraction between the linked disease-defining locus and the marker locus.

Immunogenetics of leishmanial and mycobacterial infections: the Belem Family Study

In the 1970s and 1980s, analysis of recombinant inbred, congenic and recombinant haplotype mouse strains permitted us to effectively 'scan' the murine genome for genes controlling resistance and susceptibility to leishmanial infections. Five major regions of the genome were implicated in the control of infections caused by different Leishmania species which, because they show conserved synteny with regions of the human genome, immediately provides candidate gene regions for human disease susceptibility genes. A common intramacrophage niche for leishmanial and mycobacterial pathogens, and a similar spectrum of immune response and disease phenotypes, also led to the prediction that the same genes/candidate gene regions might be responsible for genetic susceptibility to mycobacterial infections such as leprosy and tuberculosis. Indeed, one of the murine genes (Nramp1) was identified for its role in controlling a range of intramacrophage pathogens including leishmania, salmonella and mycobacterium infections. In recent studies, multicase family data on visceral leishmaniasis and the mycobacterial diseases, tuberculosis and leprosy, have been collected from north-eastern Brazil and analysed to determine the role of these candidate genes/regions in determining disease susceptibility. Complex segregation analysis provides evidence for one or two major genes controlling susceptibility to tuberculosis in this population. Family-based linkage analyses (combined segregation and linkage analysis; sib-pair analysis), which have the power to detect linkage between marker loci in candidate gene regions and the putative disease susceptibility genes over 10-20 centimorgans, and transmission disequilibrium testing, which detects allelic associations over 1 centimorgan (ca. 1 megabase), have been used to examine the role of four regions in determining disease susceptibility and/or immune response phenotype. Our results demonstrate: (i) the major histocompatibility complex (MHC: H-2 in mouse, HLA in man: mouse chromosome 17/human 6p; candidates class II and class III including TNF alpha/beta genes) shows both linkage to, and allelic association with, leprosy per se, but is only weakly associated with visceral leishmaniasis and shows neither linkage to nor allelic association with tuberculosis; (ii) no evidence for linkage between NRAMP1, the positionally cloned candidate for the murine macrophage resistance gene Ity/Lsh/Bcg (mouse chromosome 1/human 2q35), and susceptibility to tuberculosis or visceral leishmaniasis could be demonstrated in this Brazilian population; (iii) the region of human chromosome 17q (candidates NOS2A, SCYA2-5) homologous with distal mouse chromosome 11, originally identified as carrying the Scl1 gene controlling healing versus nonhealing responses to Leishmania major, is linked to tuberculosis susceptibility; and (iv) the 'T helper 2' cytokine gene cluster (proximal murine chromosome 11/human 5q; candidates IL4, IL5, IL9, IRF1, CD14) controlling later phases of murine L. major infection, is not linked to human disease susceptibility for any of the three infections, but shows linkage to and highly significant allelic association with ability to mount an immune response to mycobacterial antigens. These studies demonstrate that the 'mouse-to-man' strategy, refined by our knowledge of the human immune response to infection, can lead to the identification of important candidate gene regions in man.

Analysis of two-locus traits under heterogeneity for recessive versus dominant inheritance

Complex traits have been modeled under various modes of two-locus inheritance. One example of a two-locus threshold model is the situation where an individual is susceptible to a disease trait if he or she carries three or more disease alleles. Under this model, if each locus is examined individually the inheritance appears recessive for some mating types and dominant for others. We developed a heterogeneity test, the Model-heterogeneity test, where an admixture of dominant and recessive sibships can be present. The properties of the Model-heterogeneity test were examined and compared to the Admixture test. The power of the Model-heterogeneity test to detect linkage is comparable to that of the Admixture test.

Schizophrenia: a genome scan targets chromosomes 3p and 8p as potential sites of susceptibility genes

Using a systematically ascertained sample of 57 families, each having 2 or more members with a consensus diagnosis of schizophrenia (DSM-III-R criteria), we have carried out linkage studies of 520 loci, covering approximately 70% of the genome for susceptibility loci for schizophrenia. A two-stage strategy based on lod score thresholds from simulation studies of our sample identified regions for further exploration. In each region, a dense map of highly informative dinucleotide repeat polymorphisms (heterozygosity greater than .70) was analyzed using dominant, recessive, and "affected only" models and nonparametric sib pair identity-by-descent methods. For one region, 8p22-p21, affected sib-pair analyses gave a P value = .0001, corresponding to a lod score approximately equal to 3.00. For 8p22-p21, the maximum two-point lod score occurred using the "affected only" recessive model (ZMAX = 2.35; theta M = theta F); allowing for a constant sex difference in recombination fractions found in reference pedigrees, ZMAX = 2.78 (theta M/theta F = 3). For a second region, 3p26-p24, the maximum two-point lod score was 2.34 ("affected only" dominant model), and the affected sib-pair P value was .01. These two regions are worthy of further exploration as potential sites of susceptibility genes for schizophrenia.

Linkage analysis of a complex disease: application to familial Alzheimer's disease

Evidence for linkage of the Alzheimer's gene to markers on chromosomes 19 and 21 was assessed using single-locus and two-locus models of inheritance. Families were divided into groups determined by their average age at onset. The youngest group produced higher lod scores for markers on chromosome 21 while an older group showed evidence for linkage to markers on chromosome 19. Two-locus models of disease were used to analyze the youngest group for linkage to pairs of markers on chromosome 21 and an older group with markers on chromosome 19.

Two-locus models of disease

Most complex diseases have not been amenable to genetic analysis under the assumption of single locus or multifactorial models. Consequently, interest has turned to the consideration of the properties of oligogenic models. i.e., genetic models involving a small number of genes. Nine two-locus models of disease, representing both epistatic and heterogeneous genetic models, are investigated: three models of heterogeneity and six models of epistatis. For each model we derive formulas for the recurrence risk to various classes of relatives in terms of penetrances and gene frequencies. We also develop formulas for the components of variance for the epistatic models in terms of the same genetic parameters. The range of penetrances and the associated gene frequencies that predict a predetermined value for the population prevalence and recurrence risk to the sibling of proband are calculated for various rates of the prevalence and risk to sibs. It is found that for many of these genetic models, there is a very limited range of penetrances that fit a particular set of assumed risks. Estimated population prevalence and risks to sibs and monozygotic twins for bipolar and schizophrenia illness are used to test for compatibility with expected values for recurrence risks under these models.