Multilocus linkage analysis of affected sib pairs

OBJECTIVE: The conventional affected sib pair methods evaluate the linkage information at a locus by considering only marginal information. We describe a multilocus linkage method that uses both the marginal information and information derived from the possible interactions among several disease loci, thereby increasing the significance of loci with modest effects. METHODS: Our method is based on a statistic that quantifies the linkage information contained in a set of markers. By a marker selection-reduction process, we screen a set of polymorphisms and select a few that seem linked to disease. RESULTS: We test our approach on genome scan data for inflammatory bowel disease (InfBD) and on simulated data. On real data we detect 6 of the 8 known InfBD loci; on simulated data we obtain improvements in power of up to 40% compared to a conventional single-locus method. CONCLUSION: Our extensive simulations and the results on real data show that our method is in general more powerful than single-locus methods in detecting disease loci responsible for complex traits. A further advantage of our approach is that it can be extended to make use of both the linkage and the linkage disequilibrium between disease loci and nearby markers.     

Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis

Most multipoint linkage programs assume linkage equilibrium among the markers being studied. The assumption is appropriate for the study of sparsely spaced markers with intermarker distances exceeding a few centimorgans, because linkage equilibrium is expected over these intervals for almost all populations. However, with recent advancements in high-throughput genotyping technology, much denser markers are available, and linkage disequilibrium (LD) may exist among the markers. Applying linkage analyses that assume linkage equilibrium to dense markers may lead to bias. Here, we demonstrated that, when some or all of the parental genotypes are missing, assuming linkage equilibrium among tightly linked markers where strong LD exists can cause apparent oversharing of multipoint identity by descent (IBD) between sib pairs and false-positive evidence for multipoint model-free linkage analysis of affected sib pair data. LD can also mimic linkage between a disease locus and multiple tightly linked markers, thus causing false-positive evidence of linkage using parametric models, particularly when heterogeneity LOD score approaches are applied. Bias can be eliminated by inclusion of parental genotype data and can be reduced when additional unaffected siblings are included in the analysis.     

Multipoint linkage analysis using sib pairs: an interval mapping approach for dichotomous outcomes.

I propose an interval mapping approach suitable for a dichotomous outcome, with emphasis on samples of affected sib pairs. The method computes a lod score for each of a set of locations in the interval between two flanking markers and takes as its estimate of trait-locus location the maximum lod score in the interval, provided it exceeds the prespecified critical value. Use of the method depends on prior knowledge of the genetic model for the disease only through available estimates of recurrence risk to relatives of affected individuals. The method gives an unbiased estimate of location, provided the recurrence risk are correctly specified and provided the marker identity-by-descent probabilities are jointly, rather than individually, estimated. I also discuss use of the method for traits determined by two loci and give an approximation that has good power for a wide range of two-locus models.     

Gene-environment interaction and affected sib pair linkage analysis

OBJECTIVES: Gene-environment (GxE) interaction influences risk for many complex disease traits. However, genome screens using affected sib pair linkage techniques are typically conducted without regard for GxE interaction. We propose a simple extension of the commonly used mean test and evaluate its power for several forms of GxE interaction. METHODS: We compute expected IBD sharing by sibling exposure profile, that is by whether two sibs are exposed (EE), unexposed (UU), or are discordant for exposure (EU). We describe a simple extension of the mean test, the "mean-interaction" test that utilizes heterogeneity in IBD sharing across EE, EU, and UU sib pairs in a test for linkage. RESULTS: The mean-interaction test provides greater power than the mean test for detecting linkage in the presence of moderate or strong GxE interaction, typically when the interaction relative risk (R(ge)) exceeds 3 or is less than 1/3. In the presence of strong interaction (R(ge) = 10), the required number of affected sib pairs to achieve 80% power for detecting linkage is approximately 30% higher when the environmental factor is ignored in the mean test, than when it is utilized in the mean-interaction test. CONCLUSION: Linkage methods that incorporate environmental data and allow for interaction can lead to increased power for localizing a disease gene involved in a GxE interaction.     

Genetic copy number variants in sib pairs both affected with schizophrenia

Background  

Schizophrenia is a complex disorder with involvement of multiple genes.     

Multipoint interval mapping of quantitative trait loci, using sib pairs.

The sib-pair interval-mapping procedure of Fulker and Cardon is extended to take account of all available marker information on a chromosome simultaneously. The method provides a computationally fast multipoint analysis of sib-pair data, using a modified Haseman-Elston approach. It gives results very similar to those of the earlier interval-mapping procedure when marker information is relatively uniform and a coarse map is used. However, there is a substantial improvement over the original method when markers differ in information content and/or when a dense map is employed. The method is illustrated by using simulated sib-pair data.     

Nonparametric trend statistic incorporating dispersion differences in sib pair linkage for quantitative traits

The Haseman-Elston (HE) regression method and its extensions are widely used in genetic studies for detecting linkage to quantitative trait loci (QTL) using sib pairs. The principle underlying the simple HE regression method is that the similarity in phenotypes between two siblings increases as they share an increasing number of alleles identical by descent (IBD) from their parents at a particular marker locus. In such a procedure, similarity was identified with the locations, that is, means of groups of sib pairs sharing 0, 1, and 2 alleles IBD. A more powerful, rank-based nonparametric test to detect increasing similarity in sib pairs is presented by combining univariate trend statistics not only of locations, but also of dispersions of the squared phenotypic differences of two siblings for three groups. This trend test does not rely on distributional assumptions, and is applicable to the skewed or leptokurtic phenotypic distributions, in addition to normal or near normal phenotypic distributions. The performances of nonparametric trend statistics, including nonparametric regression slope, are compared with the HE regression methods as genetic linkage strategies.     

A note on linkage analysis with affected sib triplets

Previously, it has been shown for affected sib pairs that the mean test is the uniformly (in theta) most powerful test in case of a multiplicative mode of inheritance and that the mean test is equivalent to parametric linkage analysis calculated under an assumed multiplicative mode of inheritance. Here, these two results are extended to samples consisting of affected sib triplets. For affected sib quadruplets, however, it is shown that these results are no longer valid.     

Mapping quantitative trait loci with extreme discordant sib pairs: sampling considerations.

Elsewhere we have proposed the use of extreme discordant sib pairs (EDSPs) for mapping quantitative trait loci in humans. Here we present sample sizes necessary to achieve a given level of power with this study design, as well as the number of sibs that need to be screened to obtain the required sample. Further, we present simple formulas for adjusting sample sizes to account for variable significance levels and power, as well as the density and informativeness of linkage markers in a multipoint sib-pair analysis. We conclude that with EDSPs, the most powerful study design, the smallest genetic effect detectable with a realistic sample size is approximately 10% of the variance of the trait.     

Efficiency robust tests for mapping quantitative trait loci using extremely discordant sib pairs

In 1972, Haseman and Elston proposed a pioneering regression method for mapping quantitative trait loci using randomly selected sib pairs. Recently, the statistical power of their method was shown to be increased when extremely discordant sib pairs are ascertained. While the precise genetic model may not be known, prior information that constrains IBD probabilities is often available. We investigate properties of tests that are robust against model uncertainty and show that the power gain from further constraining IBD probabilities is marginal. The additional linkage information contained in the trait values can be incorporated by combining the Haseman-Elston regression method and a robust allele sharing test.     

The power of interval mapping of quantitative trait loci, using selected sib pairs.

The interval-mapping procedure of Fulker and Cardon for analysis of a quantitative-trait loci (QTL) is extended for application to selected samples of sib pairs. Phenotypic selection of sib pairs, which is known to yield striking increases in power when a single marker is used, provides further increases in power when the interval-mapping approach is used. The greatest benefits of the combined approach are apparent with coarse maps, where QTLs of relatively modest (15%-20%) heritability can be detected with widely spaced markers (40-60 cM apart) in reasonably sized sibling samples. Useful information concerning QTL location is afforded by interval mapping in both selected and unselected samples.     

X-linked extension of the revised Haseman-Elston algorithm for linkage analysis in sib pairs

Haseman and Elston (H-E) proposed a regression-based robust test of linkage between a marker and an autosomal quantitative trait locus, using the squared sib pair trait difference as a dependent variable and the proportion of alleles shared identical by descent by the sib pair as an independent variable. Several authors have proposed improvement of the original H-E's seminal work by using an optimal linear combination of squared sum and squared difference as the dependent variable. In this paper, we extend Haseman and Elston's sib pair method to an X-linked locus. We give a general formulation of the complete regression model and details of the regression coefficients in terms of variance components. Simulation results are presented to describe the power of this technique for a theoretical best case scenario.     

Linkage analysis of alcohol dependence using both affected and discordant sib pairs

The basic idea of affected-sib-pair (ASP) linkage analysis is to test whether the inheritance pattern of a marker deviates from Mendelian expectation in a sample of ASPs. The test depends on an assumed Mendelian control distribution of the number of marker alleles shared identical by descent (IBD), i.e., 1/4, 1/2, and 1/4 for 2, 1, and 0 allele(s) IBD, respectively. However, Mendelian transmission may not always hold, for example because of inbreeding or meiotic drive at the marker or a nearby locus. A more robust and valid approach is to incorporate discordant-sib-pairs (DSPs) as controls to avoid possible false-positive results. To be robust to deviation from Mendelian transmission, here we analyzed Collaborative Study on the Genetics of Alcoholism data by modifying the ASP LOD score method to contrast the estimated distribution of the number of allele(s) shared IBD by ASPs with that by DSPs, instead of with the expected distribution under the Mendelian assumption. This strategy assesses the difference in IBD sharing between ASPs and the IBD sharing between DSPs. Further, it works better than the conventional LOD score ASP linkage method in these data in the sense of avoiding false-positive linkage evidence.     

Mathematical assumptions versus biological reality: myths in affected sib pair linkage analysis

Affected sib pair (ASP) analysis has become common ever since it was shown that, under very specific assumptions, ASPs afford a powerful design for linkage analysis. In 2003, Vieland and Huang, on the basis of a "fundamental heterogeneity equation," proved that heterogeneity and epistasis are confounded in ASP linkage analysis. A much more serious limitation of ASP linkage analysis is the implicit assumption that randomly sampled sib pairs share half their alleles identical by descent at any locus, whereas a critical assumption underlying Vieland and Huang's proof is that of joint Hardy-Weinberg equilibrium proportions at two trait loci. These are considered as examples of mathematical assumptions that may not always reflect biological reality. More-robust sib-pair designs and appropriate methods for their analysis have long been available.     

OB gene not linked to human obesity in Mexican American affected sib pairs from Starr County,Texas

Obesity is a highly prevalent disease, which is associated with a number of chronic conditions and, as such, represents a major public health burden. Numerous studies indicate that there is a genetic component contributing to interindividual variability in obesity. The discovery of the ob gene in mice, mutations in which produce extreme obesity and non-insulin-dependent diabetes mellitus (NIDDM), provides a prime candidate gene for human obesity. We investigated linkage between the human OB gene and obesity in a sample of Mexican Americans from Starr County, Texas. Markers D7S635 and D7S1875, estimated to lie within a region approximately 290 to 400 kb proximal to the OB gene, were used to genotype 177 obese individuals distributed in 64 sibships. Obesity was defined as a body mass index (BMI) above 30 kg/m². Linkage analyses for affected sibling pairs provided no evidence for linkage in this sample. In addition, differences between siblings for weight, BMI, systolic and diastolic blood pressure, percent body fat, waist-to-hip ratio, and blood lipid measures were not significantly related to number of alleles shared identical by state (IBS) for either of the two markers. While the OB gene may be involved in the metabolic sequences leading to obesity, the present linkage results do not support the existence of common genetic variation at or near the OB locus that increases risk for human obesity. Received: 17 April 1996 / Revised: 18 June 1996     

A systematic genomewide linkage study in 353 sib pairs with schizophrenia

We undertook a genomewide linkage study in a total of 353 affected sib pairs (ASPs) with schizophrenia. Our sample consisted of 179 ASPs from the United Kingdom, 134 from Sweden, and 40 from the United States. We typed 372 microsatellite markers at approximately 10-cM intervals. Our strongest finding was a LOD score of 3.87 on chromosome 10q25.3-q26.3, with positive results being contributed by all three samples and a LOD-1 interval of 15 cM. This finding achieved genomewide significance (P<.05), on the basis of simulation studies. We also found two regions, 17p11.2-q25.1 (maximum LOD score [MLS] = 3.35) and 22q11 (MLS = 2.29), in which the evidence for linkage was highly suggestive. Linkage to all of these regions has been supported by other studies. Moreover, we found strong evidence for linkage (genomewide P<.02) to 17p11.2-q25.1 in a single pedigree with schizophrenia. In our view, the evidence is now sufficiently compelling to undertake detailed mapping studies of these three regions.