The Affected Sib Method. I. Statistical Features of the Affected Sib-Pair Method

The distribution of the number of HLA haplotypes shared by sibs affected with the same HLA-linked disease can be used to obtain information on the genetics of the disease. Since the inception of the use of sib-pair methods for the analysis of the HLA-associated diseases, the question has been raised of how to include families with more than two affected sibs in the sib-pair analysis. This paper presents appropriate weighting schemes. A procedure for estimating the frequency of the disease allele in the general population, under the assumptions of single-allele recessive, additive, dominant and intermediate models, with negligible recombination (theta = 0) between the disease-predisposing gene and the HLA region, and no selective disadvantage of the trait, is also given. Cluster-sampling techniques are used in the analysis.     

Evidence for recessive and against dominant inheritance at the HLA-"linked" locus in coeliac disease.

It has been proposed that gluten sensitive enteropathy (GSE) results from the interaction of two loci: one locus linked to HLA and associated with dominant inheritance, and the other, a non-HLA-linked GSE-associated B-cell alloantigen, exhibiting recessive inheritance. We have shown in previous analyses that a two-locus, dominant-recessive model is less compatible with the existing population prevalence and observed familial segregation data than is a recessive-recessive two-locus model. Here we present additional analyses of reported population and familial HLA data that support the recessive mode of inheritance for the HLA-linked disease locus. Reported data from HLA typing of affected sib pairs, the association of GSE with DR3 and DR7 in different populations, and the proportions of different HLA phenotypes and genotypes were compared with expected data derived by three different methods. The HLA data analyses consistently reject a dominant mode of inheritance for the presumed HLA-linked disease allele but do not reject a recessive model. The affected sib-pair data also support a recessive model. These analyses are consistent with our previous prediction that the HLA-"linked" disease allele in GSE is recessive inherited.     

Genetic interrelationship between insulin-dependent diabetes mellitus, the autoimmune thyroid diseases, and rheumatoid arthritis.

To investigate the possible coinheritance of autoimmune diseases that are associated with the same HLA antigen, we studied 70 families in which at least two siblings had either type I diabetes mellitus (IDDM), autoimmune thyroid disease (ATD), rheumatoid arthritis (RA), or a combination of these diseases. HLA-A, B, and C typing was performed on all affected sibs in one generation or more. First, we estimated by sib-pair analysis the disease allele frequency (pD) and the mode of inheritance for each disease. According to the method of ascertainment entered into the analysis, the pD for ATD ranged from .120 to .180, for an additive (dominant) mode of inheritance. For RA, the pD ranged from .254 to .341, also for additive inheritance, although recessive inheritance could not be excluded. For IDDM, the pD ranged from .336 to .337 for recessive inheritance; additive inheritance was rejected. Second, we examined the distribution of shared parental haplotypes in pairs of siblings that were discordant for their autoimmune diseases. The results suggested that the same haplotype may predispose to both IDDM and ATD, or IDDM and RA, but not to both RA and ATD. Analysis of pedigrees supported this hypothesis. In 16 families typed for HLA-DR also, the haplotype predisposing to both IDDM and ATD was assigned from pedigree information to DR3 (44%), DR4 (39%), or DR5, DR6, or DR7 (5.5% each). In some families, these haplotypes segregated over several generations with ATD only (either clinical or subclinical), suggesting that in such families, ATD was a marker for a susceptibility to IDDM. In several families, an IDDM haplotype segregated with RA but not with ATD. This suggests that ATD- and RA-associated susceptibilities to IDDM may be biologically different and thus independently increase the risk of IDDM.     

The use of association data to identify family members at high risk for marker-linked diseases.

The study of genetic markers linked and associated with disease has provided important evidence of a genetic contribution to numerous diseases and has helped to establish their modes of inheritance. However, this information has not been fully utilized in counseling individuals at risk for these disorders. In the case of recessive, marker-linked diseases, such as idiopathic hemochromatosis linked to HLA in family studies and associated with specific HLA alleles in population surveys, the only current clinical application has been to identify siblings who share both HLA-marker haplotypes with the affected proband. They are considered to be presymptomatically affected, and more definitive invasive investigations are considered appropriate. All other relatives, including parents, offspring, and other siblings, who share only one marker with the proband, have been counseled only that their risk is equivalent to the gene frequency of the disease allele, for example, 3%-6% for hemochromatosis. We have developed a generally applicable method to utilize population association data to derive more specific and accurate risk figures for these other relatives of patients with marker-linked and associated diseases. We have applied this method to idiopathic hemochromatosis. If the offspring of a patient with hemochromatosis lacks A3, B7, and B14, the risk to that offspring for developing hemochromatosis is less than 2%. On the other hand, if they receive HLA A3 from their unaffected parent, their risk climbs to 9%-10%; if they receive an A3-B14 haplotype, their risk increases to virtually 100%. As demonstrated by our example, the application of association data to family members already at a basal increased risk for marker-linked disease can significantly refine the disease risk estimates given to those relatives. This information can be utilized to select individuals in whom invasive diagnostic testing or preventative intervention is indicated.     

Selection against genetic defects in conservation schemes while controlling inbreeding

We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.     

Determining the mode of inheritance of RFLP-associated diseases using the affected sib-pair method

It is determined that the classical HLA sib-pair method can be used for the detection of linkage and determination of mode of inheritance of a disease when applied to non-HLA data, where attention is restricted to that subset of all parental matings that can produce affected sibs where unequivocal determination of haplotype sharing by descent values can be obtained. With the increasing use of restriction fragment length polymorphisms (RFLPs) to detect disease genes, it is predicted that this method will be applicable to many diseases.     

DRB genotyping supports recessive inheritance of DR3-associated susceptibility to insulin-dependent diabetes mellitus.

The mode of inheritance of HLA-associated susceptibility to insulin-dependent diabetes mellitus was investigated by the antigen genotype frequency among patients method in a white Caucasian population and a North Indian Asian population. DR genotypes were determined by DRB/DQB RFLP analysis. In white Caucasians, simple recessive and simple additive inheritance of a single HLA-associated disease susceptibility allele were rejected (P less than .025 and P less than 10(-6), respectively). The data were compatible with a three-allele model of disease susceptibility. In North Indian Asians, simple additive inheritance was rejected (P less than 10(-6)). The observed genotype frequencies were compatible with a single DR3-associated disease susceptibility allele which is inherited recessively. These data show that study of DR genotypes in populations of different ethnic origins may further the understanding of inherited susceptibility to insulin-dependent diabetes mellitus.     

Increasing the power and efficiency of disease-marker case-control association studies through use of allele-sharing information

Case-control disease-marker association studies are often used in the search for variants that predispose to complex diseases. One approach to increasing the power of these studies is to enrich the case sample for individuals likely to be affected because of genetic factors. In this article, we compare three case-selection strategies that use allele-sharing information with the standard strategy that selects a single individual from each family at random. In affected sibship samples, we show that, by carefully selecting sibships and/or individuals on the basis of allele sharing, we can increase the frequency of disease-associated alleles in the case sample. When these cases are compared with unrelated controls, the difference in the frequency of the disease-associated allele is therefore also increased. We find that, by choosing the affected sib who shows the most evidence for pairwise allele sharing with the other affected sibs in families, the test statistic is increased by >20%, on average, for additive models with modest genotype relative risks. In addition, we find that the per-genotype information associated with the allele sharing-based strategies is increased compared with that associated with random selection of a sib for genotyping. Even though we select sibs on the basis of a nonparametric statistic, the additional gain for selection based on the unknown underlying mode of inheritance is minimal. We show that these properties hold even when the power to detect linkage to a region in the entire sample is negligible. This approach can be extended to more-general pedigree structures and quantitative traits.     

The Evolutionary Advantage of Recombination. II. Individual Selection for Recombination

Based on the Fisher-Muller theory of the evolution of recombination, an argument can be constructed predicting that a recessive allele favoring recombination will be favored, if there are either favorable or deleterious mutants occurring at other loci. In this case there is no clear distinction between individual and group selection. Computer simulation of populations segregating for recessive or dominant recombination alleles showed selection favoring recombination, except in the case of a dominant recombination allele with deleterious background mutants. The relationship of this work to parallel investigations by Williams and by Strobeck, Maynard Smith, and Charlesworth is explored. All seem to rely on the same phenomenon. There seems no reason to assume that the evolution of recombination must have occurred by group selection.     

Inter- and intrafamilial heterogeneity: effective sampling strategies and comparison of analysis methods.

Heterogeneity, both inter- and intrafamilial, represents a serious problem in linkage studies of common complex diseases. In this study we simulated different scenarios with families who phenotypically have identical diseases but who genotypically have two different forms of the disease (both forms genetic). We examined the proportion of families displaying intrafamilial heterogeneity, as a function of mode of inheritance, gene frequency, penetrance, and sampling strategies. Furthermore, we compared two different ways of analyzing linkage in these data sets: a two-locus (2L) analysis versus a one-locus (SL) analysis combined with an admixture test. Data were simulated with tight linkage between one disease locus and a marker locus; the other disease locus was not linked to a marker. Our findings are as follows: (1) In contrast to what has been proposed elsewhere to minimize heterogeneity, sampling only "high-density" pedigrees will increase the proportion of families with intrafamilial heterogeneity, especially when the two forms are relatively close in frequency. (2) When one form is dominant and one is recessive, this sampling strategy will greatly decrease the proportions of families with a recessive form and may therefore make it more difficult to detect linkage to the recessive form. (3) An SL analysis combined with an admixture test achieves about the same lod scores and estimate of the recombination fraction as does a 2L analysis. Also, a 2L analysis of a sample of families with intrafamilial heterogeneity does not perform significantly better than an SL analysis. (4) Bilineal pedigrees have little effect on the mean maximum lod score and mean maximum recombination fraction, and therefore there is little danger that including these families will lead to a false exclusion of linkage.     

HLA and the inheritance of multiple sclerosis: linkage analysis of 72 pedigrees.

Linkage analysis of 72 pedigrees by the maximum-likelihood method provides evidence of linkage between HLA and the hypothesized multiple sclerosis susceptibility gene (MSSG) for both the dominant and recessive models of inheritance and for penetrance values ranging from 5%--65% (or higher). This MSSG, if it exists, is most likely located at 15%--20% recombination units from the HLA complex, probably on the B-D side. The analysis also shows that there is no heterogeneity in the estimates of linkage, and lod scores are not artifically inflated because of the association of multiple sclerosis (MS) with HLA-B7.     

Localization of a recessive gene for North American Indian childhood cirrhosis to chromosome region 16q22-and identification of a shared haplotype

North American Indian childhood cirrhosis (NAIC, or CIRH1A) is an isolated nonsyndromic form of familial cholestasis reported in Ojibway-Cree children and young adults in northwestern Quebec. The pattern of transmission is consistent with an autosomal recessive mode of inheritance. To map the NAIC locus, we performed a genomewide scan on three DNA pools of samples from 13 patients, 16 unaffected siblings, and 22 parents from five families. Analysis of 333 highly polymorphic markers revealed 3 markers with apparent excess allele sharing among affected individuals. Additional mapping identified a chromosome 16q segment shared by all affected individuals. When the program FASTLINK/LINKAGE was used and a completely penetrant autosomal recessive mode of inheritance was assumed, a maximum LOD score of 4.44 was observed for a recombination fraction of 0, with marker D16S3067. A five-marker haplotype (D16S3067, D16S752, D16S2624, D16S3025, and D16S3106) spanning 4.9 cM was shared by all patients. These results provide significant evidence of linkage for a candidate gene on chromosome 16q22.     

The genotypic distribution among non-insulin-dependent diabetes mellitus (NIDDM) patients of a restriction fragment length polymorphism

The genotypic distribution among patients of a marker allele, or restriction fragment length polymorphism (RFLP), can be used to determine the mode of inheritance of a disease-predisposing gene, if the association of the marker with the disease is sufficiently high. In the case of noninsulin-dependent diabetes mellitus (NIDDM), the RFLP in the 5'-flanking region of the human insulin gene does not allow discrimination between dominant and recessive modes of inheritance, or between any intermediate model. Also, it is demonstrated, in general, that the observation of a higher odds ratio for individuals with two copies of a marker allele than for individuals with at least one copy does not in itself imply a gene-dosage model.     

A combined segregation and linkage analysis of insulin-dependent diabetes mellitus.

In an effort to clarify the mode of inheritance of insulin-dependent diabetes mellitus (IDDM), a total of 230 nuclear families with pointers were analyzed using the computer program COMBIN. Each family was ascertained without deliberate selection for multiplex families, and most families were completely typed for HLA-B, HLA-DR, and properdin factor B (Bf). There were 186 families with normal parents, 44 families with one affected parent, and no families with two affected parents. The computer program COMBIN evaluates evidence for a major locus of disease susceptibility, linkage of the major locus to a known genetic marker locus, linkage disequilibrium between the marker haplotypes and disease susceptibility, pleiotropic effects, and presence of an unlinked modifier. The parameters of COMBIN are T, Q, and D, representing the displacement, gene frequency of the IDDM allele, and dominance, respectively, of the major locus--and TM, QM, and DM being the analogous parameters of the modifier. In addition, the recombination fraction, theta, between the IDDM locus and HLA as well as the coupling frequencies are estimated. Finally, COMBIN simultaneously performs segregation and linkage analysis, with the optimal model being adjusted by the fit to the haplotype sharing distribution of IDDM. The results of these analyses indicated that the best-fitting genetic model of diabetic susceptibility appears to be a single major locus with near recessivity on a scale of standardized genetic liability, with gene frequency of the IDDM susceptibility allele of approximately 14%. In addition, the recombination fraction between the major locus and HLA is zero in all models; that is, for the B-BF-DR haplotype, the IDDM locus is tightly linked, probably (according to data from previous studies) to HLA-DR. Information determined by magnitude of coupling frequencies indicated that there is significant positive linkage disequilibrium with the haplotypes B8-BfS-DR4 and B15-BfS-DR4, significant negative linkage disequilibrium with B7-BfS-DR2, and intermediate disequilibrium for B8-BfS-DR3, B18-BfF1-DR3, and B40-BfS-DR4. Significant evidence in favor of an unlinked (to HLA) modifier (either single major locus or polygenes) could not be demonstrated. In conclusion, genetic susceptibility to IDDM appears to be most consistent with a single major locus with near recessivity that is tightly linked to HLA.     

Segregation and linkage analyses of 72 leprosy pedigrees

Data on 72 families with multiple cases of leprosy were analyzed for a susceptibility gene linked to the HLA loci. We conducted segregation analysis with the program POINTER and identity of HLA types by descent analysis to determine the most likely mode of inheritance. We then conducted linkage analysis with the program LINKAS, first assuming linkage equilibrium and then allowing for linkage disequilibrium and etiological heterogeneity. Segregation results suggest a recessive mode of inheritance, especially for the tuberculoid forms of leprosy. The linkage results, limited to tuberculoid forms and assuming a recessive model, suggest a hypothesis of loose linkage with no unlinked locus. When an additive model is assumed, the best fit is obtained with a hypothesis of complete linkage (theta = 0.0) with heterogeneity. We currently favor the additive model as the more plausible one.     

Some developments on the affected-pedigree-member method of linkage analysis.

Some improvements are presented for the affected-pedigree-member method of linkage analysis, which is a generalization of the sib-pair method. The test statistic is extended to include contrasts between affected and unaffected pedigree members, so that it now utilizes marker information from all typed pedigree members rather than just the typed affected members. Computer simulation using a sample pedigree of 14 individuals shows that this modification can substantially increase statistical power where there is a direct association between marker variation and disease and where disease risk is elevated in carriers of the disease allele. Data on Huntington disease in 16 British families, which were analyzed previously using only the affected individuals, are reanalyzed with the unaffected individuals included. Strong rejection of the null hypothesis of no association between Huntington disease and the HindIII polymorphism is confirmed, but the particular families in which the association is significant differs from that obtained through an analysis based only on affected individuals and reflects more closely the results obtained from a lod-score analysis. The test statistic is also modified here to incorporate contrasts between individuals of zero kinship, if needed. This enables contrasts between individuals from different pedigrees, as well as contrasts involving individuals sampled from the general population, to be incorporated into the test of association. For population data, the methodology reduces to a type of contingency-table analysis, in which the rows of the table correspond to different marker-locus genotypes and in which the two columns categorize subjects into an "affected" group versus an "unaffected," or control, group. This aspect of the methodology is illustrated using two population data sets, the first relating APO-E genotype to the frequency of individuals undergoing maintenance hemodialysis and the second relating APO-B genotype to the frequency of coronary artery disease. The present methodology confirms the lack of association between marker and disease in the former data set and confirms the presence of association in the latter. Finally, the methodology is formulated here in terms of ordinary, multiperson kinship coefficients rather than in terms of the generalized kinship coefficients originally proposed. This greatly reduces the number of coefficients to be calculated, thereby enhancing the computational efficiency of the computer program.     

The haplotype-relative-risk (HRR) method for analysis of association in nuclear families.

One major problem in studying an association between a marker locus and a disease is the selection of an appropriate group of controls. However, this problem of population stratification can be circumvented in a quite elegant manner by family-based methods. The haplotype-relative-risk (HRR) method, which samples nuclear families with a single affected child and uses the parental haplotypes not transmitted to that child as a control individual, represents such a method for estimating the relative risk of a marker phenotype. In the special case of a recessive disease, it was already known that the equivalence of the HRR method with the classical relative risk (RR) obtained from independent samples holds only if the probability theta of a recombination between marker and disease locus is zero. We extend this result to an arbitrary mode of inheritance. Furthermore, we compare the distribution of the estimators for HRR and RR and show that, in the case of a positive linkage disequilibrium between a marker and disease allele, the distribution of the estimator for HRR is (stochastically) smaller than that for RR, irrespective of the recombination fraction. The practical implication of this result is that, for the HRR method, there is no tendency to give unduly high risk estimators, even for theta > 0. Finally, we give an expression for the standard error of the estimator for HRR by taking into account the nonindependence of transmitted and nontransmitted parental marker alleles in the case of theta > 0.     

Analysis of genetic interrelationship among HLA-associated diseases.

We have developed a method to study the genetic relationship between any two HLA-associated diseases. We have considered the following hypotheses: (1) both diseases are caused by a common allele; (2) different alleles at the same locus predispose to the two diseases; (3) one disease is predisposed by two alleles, one of which can also lead to the second disease; and (4) different HLA-linked loci are involved in the etiology of each disease. For each hypothesis, we have derived the expected HLA haplotype-sharing distribution in sib pairs who are affected with two diseases. The comparison of the expectations indicate that, in many cases, the alternate hypotheses can be distinguished, if the sample size is appropriately large. The knowledge of the mode of inheritance of each disease is not usually necessary; however, it can greatly increase the power of the test. Analyses of data on pairwise combinations of rheumatoid arthritis (RA), autoimmune thyroid disease (ATD), and insulin-dependent (type I) diabetes mellitus (IDDM) suggest that (a) IDDM is predisposed by two HLA-linked alleles, one of which also predisposes to ATD, (b) one of the IDDM alleles also confers susceptibility to RA, and (c) although the HLA-linked susceptibilities to RA and ATD appear to be primarily due to distinct alleles, the ATD allele may also have a minor role in predisposition to RA.     

Genomic control for association studies under various genetic models

Case-control studies are commonly used to study whether a candidate allele and a disease are associated. However, spurious association can arise due to population substructure or cryptic relatedness, which cause the variance of the trend test to increase. Devlin and Roeder derived the appropriate variance inflation factor (VIF) for the trend test and proposed a novel genomic control (GC) approach to estimate VIF and adjust the test statistic. Their results were derived assuming an additive genetic model and the corresponding VIF is independent of the candidate allele frequency. We determine the appropriate VIFs for recessive and dominant models. Unlike the additive test, the VIFs for the optimal tests for these two models depend on the candidate allele frequency. Simulation results show that, when the null loci used to estimate the VIF have allele frequencies similar to that of the candidate gene, the GC tests derived for recessive and dominant models remain optimal. When the underlying genetic model is unknown or the null loci and candidate gene have quite different allele frequencies, the GC tests derived for the recessive or dominant models cannot be used while the GC test derived for the additive model can be.     

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.