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.     

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.     

Weighting affected sib pairs by marker informativity

For the analysis of affected sib pairs (ASPs), a variety of test statistics is applied in genomewide scans with microsatellite markers. Even in multipoint analyses, these statistics might not fully exploit the power of a given sample, because they do not account for incomplete informativity of an ASP. For meta-analyses of linkage and association studies, it has been shown recently that weighting by informativity increases statistical power. With this idea in mind, the first aim of this article was to introduce a new class of tests for ASPs that are based on the mean test. To take into account how much informativity an ASP contributes, we weighted families inversely proportional to their marker informativity. The weighting scheme is obtained by use of the de Finetti representation of the distribution of identity-by-descent values. We derive the limiting distribution of the weighted mean test and demonstrate the validity of the proposed test. We show that it can be much more powerful than the classical mean test in the case of low marker informativity. In the second part of the article, we propose a Monte Carlo simulation approach for evaluating significance among ASPs. We demonstrate the validity of the simulation approach for both the classical and the weighted mean test. Finally, we illustrate the use of the weighted mean test by reanalyzing two published data sets. In both applications, the maximum LOD score of the weighted mean test is 0.6 higher than that of the classical mean test.     

p-Value simulation for affected sib pair multiple testing

A standard approach to calculation of critical values for affected sib pair multiple testing is based on: (a) fully informative markers, (b) Haldane map function assumptions leading to a Markov chain model for inheritance vectors, (c) central limit approximation to averages of sampled inheritance vectors leading to an Ornstein-Uhlenbeck process approximation, and (d) simple approximations to the maximum of such a process. Under these assumptions, assuming equispaced or close to equispaced markers, if the sample size is large, an approximation is available that is easy to calculate and performs well. However, for small sample sizes, a large number of markers, and for small p-values, there is good reason to be cautious about the use of the Gaussian approximation. We develop an algorithm for calculation of multiple testing p-values based on the standard Markov chain model, avoiding the use of Gaussian (large sample) approximation. We illustrate the use of this algorithm by demonstrating some inadequacies of the Gaussian approximation.     

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.     

Selection and subsequent analysis of sib pair data for QTL detection.

Haseman and Elston (1972) developed a robust regression method for the detection of linkage between a marker and a quantitative trait locus (QTL) using sib pair data. The principle underlying this method is that the difference in phenotypes between pairs of sibs becomes larger as they share a decreasing number of alleles at a particular QTL identical by descent (IBD) from their parents. In this case, phenotypically very different sibs will also on average share a proportion of alleles IBD at any marker linked to the QTL that is lower than the expected value of 0.5. Thus, the deviation of the proportion of marker alleles IBD from the expected value in pairs of sibs selected to be phenotypically different (i.e. discordant) can provide a test for the presence of a QTL. A simple regression method for QTL detection in sib pairs selected for high phenotypic differences is presented here. The power of the analytical method was found to be greater than the power obtained using the standard analysis when samples of sib pairs with high phenotypic differences were used. However, the use of discordant sib pairs was found to be less powerful for QTL detection than alternative selective genotyping schemes based on the phenotypic values of the sibs except with intense selection, when its advantage was only marginal. The most effective selection scheme overall was the use of sib pairs from entire families selected on the basis of high within-family variance for the trait in question. There is little effect of selection on QTL position estimates, which are in good agreement with the simulated values. However, QTL variance estimates are biased to a greater or lesser degree, depending on the selection method.     

Analysis of affected sib pairs, with covariates--with and without constraints

Covariate models have previously been developed as an extension to affected-sib-pair methods in which the covariate effects are jointly estimated with the degree of excess allele sharing. These models can estimate the differences in sib-pair allele sharing that are associated with measurable environment or genes. When there are no covariates, the pattern of identical-by-descent allele sharing in affected sib pairs is expected to fall within a small triangular region of the potential parameter space, under most genetic models. By restriction of the estimated allele sharing to this triangle, improved power is obtained in tests for genetic linkage. When the affected-sib-pair model is generalized to allow for covariates that affect allele sharing, however, new constraints and new methods for the application of constraints are required. Three generalized constraint methods are proposed and evaluated by use of simulated data. The results compare the power of the different methods, with and without covariates, for a single-gene model with age-dependent onset and for quantitative and qualitative gene-environment and gene-gene interaction models. Covariates can improve the power to detect linkage and can be particularly valuable when there are qualitative gene-environment interactions. In most situations, the best strategy is to assume that there is no dominance variance and to obtain constrained estimates for covariate models under this assumption.     

Detecting gene-gene interactions using affected sib pair analysis with covariates

Interest has recently focussed on allowing for interactions between loci as a way to increase power to detect linkage. In this paper, a simplified logistic regression method was used to perform affected sib pair analyses allowing for the inclusion of data from other loci. A systematic search of two-locus disease models was carried out to determine the situations in which this was advantageous. If IBD information is available (e.g. from a genome scan), it is unlikely that allowing for interactions will give a large lod score in the absence of linkage evidence from sinlge-locus analysis. Furthermore, allowing for interactions rarely gave a significant increase in power to detect linkage over a single-locus analysis, except for heterogeneity models with low K(P). Conversely, the availability of disease-associated genotypes may greatly increase the power both to detect linkage to a second locus and interaction between the loci. These results indicate that when only IBD information is available, two-locus analysis of genome scan data should be restricted to regions giving peaks under single-locus analysis. If disease-associated genotypes are available, it may be worth re-analysing the whole genome.     

Log-linear models for gene mapping with affected sib pair data

In genome-wide screens of genetic marker loci, non-mendelian inheritance of a marker is taken to indicate its vicinity to a disease locus. Heritable complex traits are thought to be under the influence of multiple possibly interacting susceptibility loci yet the most frequently used methods of linkage and association analysis focus on one susceptibility locus at a time. Here we introduce log-linear models for the joint analysis of multiple marker loci and interaction effects between them. Our approach focuses on affected sib pair data and identical by descent (IBD) allele sharing values observed on them. For each heterozygous parent, the IBD values at linked markers represent a sequence of dependent binary variables. We develop log-linear models for the joint distribution of these IBD values. An independence log-linear model is proposed to model the marginal means and the neighboring interaction model is advocated to account for associations between adjacent markers. Under the assumption of conditional independence, likelihood methods are applied to simulated data containing one or two susceptibility loci. It is shown that the neighboring interaction log-linear model is more efficient than the independence model, and incorporating interaction in the two-locus analysis provides increased power and accuracy for mapping of the trait loci.     

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.     

Some epistatic two-locus models of disease. I. Relative risks and identity-by-descent distributions in affected sib pairs

A two-locus disease model is presented in which a marker locus interacts epistatically with another unlinked trait to cause the disease. Such a model can lead to disease-marker associations and distortions in the sharing of marker types among affected family members. These effects are quantified. In the case of HLA-disease associations, this model is presented as an alternative to the “hitchhiking” theory of tight linkage leading to linkage disequilibrium.     

Genetic copy number variants in sib pairs both affected with schizophrenia

Background  

Schizophrenia is a complex disorder with involvement of multiple genes.     

Using identity-by-descent information in affected sib pairs to increase the efficiency of genetic association studies.

The aim of this study was to determine whether identity-by-descent (IBD) information for affected sib pairs (ASPs) can be used to select a sample of cases for a genetic case-control study which will provide more power for detecting association with loci in a known linkage region. By modeling the expected frequency of the disease allele in ASPs showing IBD sharing of 0, 1, or 2 alleles, and considering additive, recessive, and dominant disease models, we show that cases selected from IBD 2 families are best for this purpose, followed by those selected from IBD 1 families; least useful are cases selected from IBD 0 families.     

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.     

Bacteriophage P1 site-specific recombination. III. Strand exchange during recombination at lox sites

When hybrid λ-P1 phages containing either loxP or loxR sites are crossed under conditions where only the P1 lox site-specific recombination system is active, most of the crossovers occur in a region of the DNA that contains the lox sites. The remainder of the lox-mediated crossovers (4% in a P × P cross and 32% in a P × R cross) occur close to, but outside of, either loxP or loxR. These latter crossovers are not detected if one of the partners in the cross carries a deletion of loxP. We explain these results by an exchange of strands at lox sites and a migration of the resulting cross-strand junction outside of lox.     

Selection and recombination in Drosophila melanogaster

Summary Artificial selection for wing length in Drosophila melanogaster resulted in changed crossing-over frequencies between three marker genes on the 2nd chromosome, b, cn and vg.The results suggest that artificial selection is a causal agent in producing the observed changes; moreover it is suggested that the modifications in cross-over frequency are controlled by extra-nuclear factors.Research supported by C.N.R. Consiglio Nazionale delle Ricerche Roma, Grant n. 115.2298.4791.     

Genetic recombination in Coprinus: III. Inlluence of gamma-irradiation and temperature treatments on meiotic recombination

Non-lethal doses of gamma-irradiation (5 krad) increased meiotic recombination in Coprinus lagopus when treatments were given at the beginning of karyogamy. The division stage at this time was judged to be late leptotene and the duration of the sensitive period was assessed to be 3–4 h. In C. lagopus the radiation-sensitive stage is distinct from the cold-sensitive stage (pachytene). The additive effect of irradiation at early karyogamy followed by cold treatment in pachytene suggested that the two factors influenced different steps in the recombination process. On the other hand, irradiation followed by heat treatment did not significantly alter recombination frequency as compared to single treatments. It was surmised that radiation and high temperature act on the same factor(s) or at the same steps to bring about a similar net result. It was suggested that irradiation at leptotene may cause single-strand breaks in DNA which eventually participate in exchange.