Genetic Analysis Workshop II: sib pair screening tests for linkage

For each marker locus and for every pair of sibs with data available in the 1983 workshop data, the proportion of genes identical by descent was estimated. The mean proportions were compared between concordant and discordant sib pairs, and the mean proportion for concordantly affected pairs was compared with one half. Together with standard tests of association, these found to be sensitive screening tests for linkage.     

Genetic analysis workshop III: Sib pair analyses to determine linkage groups and to order loci

The methods proposed by Haseman and Elston [1972] were used to estimate the proportion of genes identical by descent shared by each sib pair at each locus. These estimates were then used as a basis for obtaining all possible locus-locus correlations. The 12 significant correlations (P < .01) and their rank order indicated the correct linkage groups and the order of the loci.     

Conditional multipoint linkage analysis using affected sib pairs: an alternative approach

Recently, Liang et al. ([2001b] Genet. Epidemiol. 21:105-122) proposed a conditional approach to assess linkage evidence on the target region by incorporating linkage information from an unlinked (reference) region using allele shared IBD (identity-by-decent) from affected sib pairs. This is carried out by conditioning on the IBD sharing value at the estimated trait locus of the reference region. Since markers considered are typically non-fully informative, the IBD sharing at each marker needs to be estimated (or imputed). In this report, we propose an alternative approach to deal with the IBD sharing in the reference region. This new approach makes full use of the observed data without having to categorize the imputed IBD sharing as needed in Liang et al. ([2001b] Genet. Epidemiol. 21:105-122). We compare these two approaches by simulating data from a variety of two-locus models including heterogeneity, additive and multiplicative with either fully informative markers or non-fully informative markers. The performance of both approaches is quite comparable showing consistent estimates of the trait locus and key genetic parameters.     

Multipoint analysis using affected sib pairs: incorporating linkage evidence from unlinked regions

In this paper, we proposed a multipoint method to assess evidence of linkage to one region by incorporating linkage evidence from another region. This approach uses affected sib pairs in which the number of alleles shared identical by descent (IBD) is the primary statistic. This generalized estimating equation (GEE) approach is robust in that no assumption about the mode of inheritance is required, other than assuming the two regions being considered are unlinked and that there is no more than one susceptibility gene in each region. The method proposed here uses data from all available families to simultaneously test the hypothesis of statistical interaction between regions and to estimate the location of the susceptibility gene in the target region. As an illustration, we have applied this GEE method to an asthma sib pair study (Wjst et al. [1999] Genomics 58:1-8), which earlier reported evidence of linkage to chromosome 6 but showed no evidence for chromosome 20. Our results yield strong evidence to chromosome 20 (P value = 0.0001) after incorporating linkage information from chromosome 6. Furthermore, it estimates with 95% certainty that the map location of the susceptibility gene is flanked by markers D20S186 and D20S101, which are approximately 16.3 cM apart.     

Strategy for mapping minor histocompatibility genes involved in graft-versus-host disease: A novel application of discordant sib pair methodology

We introduce a novel application for linkage analysis: using bone marrow donor-recipient sib pairs to search for genes influential in graft-versus-host disease (GVHD), a major cause of morbidity and mortality following allogeneic bone marrow transplantation. In particular, we show that transplant sib pairs in which the recipient developed severe GVHD can be used to map genes in the same way as traditional discordant (affected/unaffected) sib pairs (DSPs). For a plausible GVHD model, we demonstrate that the transplant/discordant sib pair analog of the “possible triangle test” [Holmans (1993) Am J Hum Genet 52:362–374] has similar power to that of the simpler “restricted test” proposed by Risch [(1990b) Am J Hum Genet 46:229–241; (1992) Am J Hum Genet 51:673–675]. Moreover, we show that the restricted test has superior power in much of the DSP possible triangle and significantly inferior power in only a small region. Thus, we conclude that the restricted test is preferable for localizing genes with transplant/discordant sib pairs. Finally, we examine the effects of heterogeneity on the power to detect GVHD loci and demonstrate the gain in efficiency by dividing the sample into genetically more homogeneous subgroups. Genet. Epidemiol. 15:595–607,1998. © 1998 Wiley-Liss, Inc.     

Affected-sib-pair test for linkage based on constraints for identical-by-descent distributions corresponding to disease models with imprinting

Holmans' possible triangle test for affected sib pairs has proven to be a powerful tool for linkage analysis. This test is a likelihood-ratio test for which maximization is restricted to the set of possible sharing probabilities. Here, we extend the possible triangle test to take into account genomic imprinting, which is also known as parent-of-origin effect. While the classical test without imprinting looks at whether affected sib pairs share 0, 1, or 2 alleles identical-by-descent, the likelihood-ratio test allowing for imprinting further distinguishes whether the sharing of exactly one allele is through the father or mother. Thus, if the disease gene is indeed subject to imprinting, the extended test presented here can take into account that affecteds will have inherited the mutant allele preferentially from one particular parent. We calculate the sharing probabilities at a marker locus linked to a disease susceptibility locus. Using our formulation, the constraints on these probabilities given by Dudoit and Speed ([1999] Statistics in Genetics; New York: Springer) can easily be verified. Next, we derive the asymptotic distribution of the restricted likelihood-ratio test statistic under the null hypothesis of no linkage, and give LOD-score criteria for various test sizes. We show, for various disease models, that the test allowing for imprinting has significantly higher power to detect linkage if imprinting is indeed present, at the cost of only a small reduction in power in case of no imprinting. Altogether, unlike many methods currently available, our novel model-free sib-pair test adequately models the epigenetic parent-of-origin effect, and will hopefully prove to be a useful tool for the genetic mapping of complex traits.     

Two-stage global search designs for linkage analysis using pairs of affected relatives

We investigate the two-stage procedure proposed by Elston [(1992) Proceedings of the XVIth International Biometric Conference, Hamilton, New Zealand, December 7–11, 1992, pp 39–51, and (1994) “Genetic Approaches to Mental Disorders.” Washington, DC: American Psychiatric Press, pp 3–21] for performing a global search of the genome to locate disease genes by linkage analysis using affected relative pairs. The optimal design depends on the type of pairs studied, the effect of the disease locus, the relative costs of recruiting affected persons and typing markers, how informative the markers are, and the amount of genetic heterogeneity. It is specified by the initial number of markers to use, the number of affected relative pairs to study, the initial significance level α^* to use at the first stage, and the number of flanking markers to use at the second stage around markers significant at the first stage. Asymptotically, the optimal design does not depend separately on either the desired final significance level or power, but rather on a function of the two. Both as the effect of the disease locus increases and as the relative cost of recruiting a subject increases, the optimal number of initial markers increases and the optimal number of pairs decreases. The expected cost of the study decreases as the effect of the disease locus increases, but increases as the relative cost of recruiting a subject increases. The optimal initial number of markers decreases but the number of pairs increases when there is genetic heterogeneity present; conversely, the optimal initial number of markers increases when markers are less than fully informative. Compared to a one-stage procedure, a two-stage procedure typically halves the cost of a study. © 1996 Wiley-Liss, Inc.     

Homozygous parent affected sib pair method for detecting disease predisposing variants: Application to insulin dependent diabetes mellitus

For complex genetic diseases involving incomplete penetrance, genetic heterogeneity, and multiple disease genes, it is often difficult to determine the molecular variant (s) responsible for the disease pathogenesis. Linkage and association studies may help identify genetic regions and molecular variants suspected of being directly responsible for disease predisposition or protection, but, especially for complex diseases, they are less useful for determining when a predisposing molecular variant has been identified. In this paper, we expand upon the simple concept that if a genetic factor predisposing to disease has been fully identified, then a parent homozygous for this factor should transmit either of his/her copies at random to any affected children. Closely linked markers are used to determine identity by descent values in affected sib pairs from a parent homozygous for a putative disease predisposing factor. The expected deviation of haplotype sharing from 50%, when not all haplotypes carrying this factor are in fact equally predisposing, has been algebraically determined for a single locus general disease model. Equations to determine expected sharing for multiple disease alleles or multiple disease locus models have been formulated. The recessive case is in practice limiting and therefore can be used to estimate the maximum proportion of putative susceptibility haplotypes which are in fact predisposing to disease when the mode of inheritance of a disease is unknown. This method has been applied to 27 DR3/DR3 parents and 50 DR4/DR4 parents who have at least 2 children affected with insulin dependent diabetes mellitus (IDDM). The transmission of both DR3 and DR4 haplotypes is statistically different from 50% (P < 0.05 and P < 0.001, respectively). An upper estimate for the proportion of DR3 haplotypes associated with a high IDDM susceptibility is 49%, and for DR4 haplotypes 38%. Our results show that the joint presence of non-Asp at DQP position 57 and Arg at DQa position 52, which has been proposed as a strong IDDM predisposing factor, is insufficient to explain the HLA component of IDDM predisposition. © 1993 Wiley-Liss, Inc.     

The impact of varying diagnostic thresholds on affected sib pair linkage analysis

For Mendelian disorders, it is usually simple to classify individuals as either affected or unaffected. By contrast, for “complex” phenotypes, the diagnostic boundary of the disorder is often uncertain. This paper explores the following question: to most efficiently detect linkage in such a complex phenotype by the affected sib pair method, where should the diagnostic threshold be drawn? The model assumes that the disorder is due to a generalized two-allele single major locus (SML) where liability in each genotype is normally distributed. Evidence for linkage between the marker and disease loci is highly dependent on the location of the threshold. The relationship between the placement of the threshold and population linkage information (PLI) is Gaussian-like. At high thresholds, linkage efficiency (LE) (or the amount of linkage information per affected sib pair) is high but PLI is low because the number of affected sib pairs is very small. At low thresholds, the number of affected sib pairs is high, but PLI is low because LE is very low. The model is applied to published SML parameters for schizophrenia, and maximal PLI is achieved at thresholds broader than those for schizophrenia alone.     

Genetic epidemiology of coeliac disease

Segregation analysis favors a gene additive on liability with a frequency of 0.022, which is nearly recessive on the penetrance scale. Less than one-eighth of DR3 and DR7 haplotypes carry a determinant for coeliac disease. There is significant excess of DR3/7 heterozygotes among patients, indicating that the determinants are qualitatively different in DR3 and DR7 haplotypes. Linkage to HLA is highly significant (maximum lod score = 10.9). Evidence for recombination of 8% in males is attributed to residual errors in the model. We suggest an approach to a more precise model.     

Testing association and linkage using affected-sib-parent study designs

We have developed a method for jointly testing linkage and association using data from affected sib pairs and their parents. We specify a conditional logistic regression model with two covariates, one that quantifies association (either direct association or indirect association via linkage disequilibrium), and a second that quantifies linkage. The latter covariate is computed based on expected identity-by-descend (ibd) sharing of marker alleles between siblings. In addition to a joint test of linkage and association, our general framework can be used to obtain a linkage test comparable to the mean test (Blackwelder and Elston [1985] Genet. Epidemiol. 2:85-97), and an association test comparable to the Family-Based Association Test (FBAT; Rabinowitz and Laird [2000] Hum. Hered. 50:211-223). We present simulation results demonstrating that our joint test can be more powerful than some standard tests of linkage or association. For example, with a relative risk of 2.7 per variant allele at a disease locus, the estimated power to detect a nearby marker with a modest level of LD was 58.1% by the mean test (linkage only), 69.8% by FBAT, and 82.5% by our joint test of linkage and association. Our model can also be used to obtain tests of linkage conditional on association and association conditional on linkage, which can be helpful in fine mapping.     

Tests for the presence of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Under explicit assumptions about the number of disease genes in a region, generalized estimating equations (GEE) can be used to estimate the putative disease gene location(s) and expected identical-by-descent allele sharing in affected sib pairs at these gene(s). Extending the work of Liang et al. developed a method for simultaneous localization of two susceptibility genes in one region using marker identical-by-descent (IBD) sharing in affected sib pairs. Here we propose methods to evaluate the evidence for two versus one disease loci in a region in a quasi-likelihood/GEE framework. We describe tests based on approximate quasi-likelihood ratio and generalized score test statistics. Because of difficulties in determining the asymptotic null distributions of these statistics and the small sample sizes that can be available in genetic studies, we recommend that significance be evaluated empirically. Application of the described methods to data from a genome scan for type 1 diabetes yielded some evidence for two linked disease genes on chromosome 6, approximately 20 cM apart (p value for an approximate quasi-likelihood ratio test=0.049). In simulation studies, we found that both tests performed quite well for a range of scenarios. Power to detect the presence of two linked disease genes increased with the number of affected sib pairs, greater IBD sharing at the two loci, and larger distance between the two loci.     

Simultaneous localization of two linked disease susceptibility genes

For diseases with complex genetic etiology, more than one susceptibility gene may exist in a single chromosomal region. Extending the work of Liang et al. ([2001] Hum. Hered. 51:64-78), we developed a method for simultaneous localization of two susceptibility genes in one region. We derived an expression for expected allele sharing of an affected sib pair (ASP) at each point across a chromosomal segment containing two susceptibility genes. Using generalized estimating equations (GEE), we developed an algorithm that uses marker identical-by-descent (IBD) sharing in affected sib pairs to simultaneously estimate the locations of the two genes and the mean IBD sharing in ASPs at these two disease loci. Confidence intervals for gene locations can be constructed based on large sample approximations. Application of the described methods to data from a genome scan for type 1 diabetes (Mein et al. [1998] Nat. Genet. 19:297-300) yielded estimates of two putative disease gene locations on chromosome 6, approximately 20 cM apart. Properties of the estimators, including bias, precision, and confidence interval coverage, were studied by simulation for a range of genetic models. The simulations demonstrated that the proposed method can improve disease gene localization and aid in resolving large peaks when two disease genes are present in one chromosomal region. Joint localization of two disease genes improves with increased excess allele sharing at the disease gene loci, increased distance between the disease genes, and increased number of affected sib pairs in the sample.     

Sib-pair collection strategies for complex diseases

When planning an affected sib pair collection for use in a genomewide search for complex trait loci, researchers must ask: (a) Which family structures will yield the most informative pairs? And (b) should recruitment extend beyond the index sib pair? The optimal collection strategy will depend on the trait's genetic architecture, but this is rarely known for non-Mendelian diseases. In the present report, we study the consequences of collecting only those sib pairs arising from pedigrees with a precisely specified structure as opposed to a strategy that collects all affected sib pairs at random (i.e., blind to the affection status of first-degree relatives). The former approach turns out to be risky because the power of specific pedigree structures can vary dramatically even among models producing identical observable parameters (such as population prevalence and sibling recurrence rate). In contrast, the latter approach typically involves only a modest loss of power as compared with the optimal (but unknowable) design. Further, we compare the strategy of collecting all affected sib pairs at random with the alternative of imposing some modest limitations on family structure (e.g., presence of at least one unaffected sib or parent). The latter approach generally provides some increase in power but entails additional effort to contact and phenotype relatives: the overall merit of imposing such requirements needs to be evaluated in the context of the specific disease to be studied and of the clinical and analytical resources available. In addition, these findings suggest that a further explanation for failure to replicate positive complex trait linkages lies in differences in ascertainment strategy between data sets. Genet. Epidemiol. 15:317–340,1998. © 1998 Wiley-Liss, Inc.     

Effectiveness of extreme discordant sib pairs to detect oligogenic disease loci

A method for the genomic screening of quantitative traits using extreme discordant sib pairs (EDSPs) has recently been described by Risch and Zhang [1995; 1996]. For many models relevant to common, genetically complex diseases, EDSPs are the most powerful siblings for detecting linkage. Thus, if such siblings can be identified and collected, powerful studies with reasonable genotyping budgets can be conducted. Using a subset of the GAW10 data, we have simulated a genomic screen using EDSPs. From the 4,780 total families in the first 20 replicates of 239 families, there were 100,104,155,107, and 180 EDSP families for Q1, Q2, Q3, Q4, and Q5, respectively. EDSP data were analyzed for each trait using a modified version of MAPMAKER/SIBS capable of handling extreme discordant sib pairs. Four regions, one for Q1, one for Q2, and two for Q4, were able to exceed a threshold for linkage corresponding to a 0.001 pointwise significance level. In three cases, maximum lod score (MLS) peaks occurred within 3.8 cM of a major gene. In the fourth case, the MLS peak occurred 28.4 cM from a major gene. Omission of parents and an alternative definition of EDSP were also investigated. © 1997 Wiley-Liss, Inc.     

The power of two-locus affected sib-pair linkage analysis to detect interacting disease loci

It has been shown that two-locus linkage analysis can, for some two-locus disease models, be used to detect effects at disease loci that do not reach significance in a genome scan. However, few examples exist where two-locus linkage has been successfully used to map genes. We study the possible gain in power of affected sib-pair nonparametric two-locus linkage analysis for two-locus models which fulfil the two-locus triangle constraints. Using a new parameterization of the two-locus joint identity-by-descent sharing probabilities we can, for fixed marginal sharing at both of two unlinked disease loci, derive a two-locus distribution such that the power of a two-locus analysis is maximized. In a simulation study we look at two test statistics, the two-locus maximum likelihood score and the correlation between nonparametric linkage scores, and study power as a function of marginal sharing. We show that in a best-case scenario two-locus linkage can have considerable power to detect pairs of interacting loci if there is a moderate increase in allele sharing at one of the two loci, even if there is a very small increase in allele sharing at the other locus. But we also show that the power to detect interacting loci in a two-locus analysis decreases as the marginal sharing at the two loci decreases and for any distribution with a small increase in allele sharing at both loci the power of a two-locus analysis is always low.     

Modeling of HLA class II susceptibility to Type I diabetes reveals an effect associated with DPB1.

In this report, we present evidence that the HLA class II DPB1 locus (or a locus with alleles in linkage disequilibrium with DPB1) contributes to Type I diabetes (IDDM) susceptibility in addition to the contribution of the HLA DR and DQ loci. The marker association segregation chi-square (MASC) method, which fits both genotype frequency and affected sib-pair identity-by-descent (IBD) distributions, was applied to 257 sib pairs affected with IDDM. Fitting DR-DQ as the sole HLA susceptibility loci was strongly rejected. Next, we considered the DPB1 contribution to disease susceptibility. Published reports indicate a predisposing role for alleles DPB1*0301 and DPB1*0202, including our previous stratification analyses of association data on this sample. IDDM probands were stratified into those not carrying the alleles DPB1*0301 and DPB1*0202 (group DPB1-A), and those carrying at least one copy of either allele (group DPB1-B). Both groups of probands have almost identical frequencies of DR and DQ haplotypes but significantly different IBD distributions in the subset of families with probands who do not carry the highly predisposing DR3/DR4 genotype. In these data, DPB1 (or a locus in linkage disequilibrium), in addition to DR-DQ, is involved in IDDM susceptibility and affects IBD in the HLA region. Addition of DPB1 in a genetic model of IDDM gives a better fit to the data than consideration of DR-DQ alone. Our results are consistent with previous reports implicating DPB1 in IDDM susceptibility.     

Affected sibpair linkage tests for multiple linked susceptibility genes

Genome-wide searches for susceptibility genes using pairs of affected siblings are being undertaken to dissect out individual polygenes that contribute to human multi-factorial diseases. Efficient identity-by-descent (IBD)-based sibpair linkage tests are available that test individual markers or maps of linked markers for linkage to a single potative susceptibility gene. In order to assess the support for linkage to a second putative susceptibility gene that happens to map close to an established susceptibility gene, it is necessary to use a method that correctly allows for the IBD distortion that directly results from the linkage between the two genes. A maximum likelihood-based, multilocus linkage test is proposed, which accounts for this interdependency and evaluates the support for an interaction between constituent susceptibility genes. The size and power of a test for a second linked susceptibility gene is investigated by simulation studies. Genet. Epidemiol. 14:103–115,1997. © 1997 Wiley-Liss, Inc.     

Allele sharing and allelic association I: sib pair tests with increased power

Affected sib pair data contain information about allele sharing and allelic association. Either of these features can point to the presence of a risk-related gene. This study introduces the elliptical sib pair test, a generalization of traditional sib pair tests. The proposed test can be implemented using any of three strategies, the choice of which depends on the anticipated combination of sharing and association. The elliptical sib pair test can achieve substantial gains in power relative to traditional tests for likely alternative hypotheses at little or no cost for other alternatives. The proposed test is valid under most models of genetic risk, disease etiology, and genotype-haplotype distributions. This study also provides new insight into the trade-off between tests of allelic association and tests of allele sharing.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.