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.     

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.     

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.     

Genetic copy number variants in sib pairs both affected with schizophrenia

Background  

Schizophrenia is a complex disorder with involvement of multiple genes.     

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.     

Excess of twins among affected sibling pairs with autism: implications for the etiology of autism

It is widely accepted that genes play a role in the etiology of autism. Evidence for this derives, in part, from twin data. However, despite converging evidence from gene-mapping studies, aspects of the genetic contribution remain obscure. In a sample of families selected because each had exactly two affected sibs, we observed a remarkably high proportion of affected twin pairs, both MZ and DZ. Of 166 affected sib pairs, 30 (12 MZ, 17 DZ, and 1 of unknown zygosity) were twin pairs. Deviation from expected values was statistically significant (P<10(-6) for all twins); in a similarly ascertained sample of individuals with type I diabetes, there was no deviation from expected values. We demonstrate that to ascribe the excess of twins with autism solely to ascertainment bias would require very large ascertainment factors; for example, affected twin pairs would need to be, on average, approximately 10 times more likely to be ascertained than affected non-twin sib pairs (or 7 times more likely if "stoppage" plays a role). Either risk factors (related to twinning or to fetal development) or other factors (genetic or nongenetic) in the parents may contribute to autism.     

A robust identity-by-descent procedure using affected sib pairs: multipoint mapping for complex diseases

Multipoint linkage analysis is a powerful tool to localize susceptibility genes for complex diseases. However, the conventional lod score method relies critically on the correct specification of mode of inheritance for accurate estimation of gene position. On the other hand, allele-sharing methods, as currently practiced, are designed to test the null hypothesis of no linkage rather than estimate the location of the susceptibility gene(s). In this paper, we propose an identity-by-descent (IBD)-based procedure to estimate the location of an unobserved susceptibility gene within a chromosomal region framed by multiple markers. Here we deal with the practical situation where some of the markers might not be fully informative. Rather the IBD statistic at an arbitrary within the region is imputed using the multipoint marker information. The method is robust in that no assumption about the genetic mechanism is required other than that the region contains no more than one susceptibility gene. In particular, this approach builds upon a simple representation for the expected IBD at any arbitrary locus within the region using data from affected sib pairs. With this representation, one can carry out a parametric inference procedure to locate an unobserved susceptibility gene. In addition, here we derive a sample size formula for the number of affected sib pairs needed to detect linkage with multiple markers. Throughout, the proposed method is illustrated through simulated data. We have implemented this method including exploratory and formal model-fitting procedures to locate susceptibility genes, plus sample size and power calculations in a program, GENEFINDER, which will be made available shortly.     

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.     

Genetic linkage analysis of a dichotomous trait incorporating a tightly linked quantitative trait in affected sib pairs

Many complex diseases are usually considered as dichotomous traits but are also associated with quantitative biological markers or quantitative risk factors. For such dichotomous traits, although their associated quantitative traits may not directly underly the diagnosis of the disease status, if the associated quantitative trait is also linked to the chromosomal regions linked to the dichotomous trait, then joint analysis of dichotomous and quantitative traits should be more efficient than consideration of them separately. Previous studies have focused on the situation when a dichotomous trait can be modeled by a threshold process acting on a single underlying normal liability distribution. However, for many complex disorders, including most psychiatric disorders, diagnosis is generally based on a set of binary or discrete criteria. These traits cannot be modeled on the basis of a threshold process acting on an underlying continuous trait. We propose a likelihood-based method that efficiently combines such a discrete trait and an associated quantitative trait in the analysis, using affected-sib-pair data. Our simulation studies suggest that joint analysis increases the power to detect linkage of dichotomous traits. We also apply the proposed new method to an asthma genome-scan data set and incorporate the total serum immunoglobulin E level in the analysis.     

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.     

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     

The relative efficiency of penetrance estimators for sib pairs

Here we present analytical studies to evaluate the relative efficiency of commonly used penetrance estimators using linkage designs. We investigated three different methods of estimating penetrance using sib pairs: Maximum likehood estimation (MLE) with trait information alone, MLE with both trait and marker information and the MOD score approach. Modeling sib pairs with unknown phase, we evaluated the asymptotic relative efficiency between estimators under either random sampling or single ascertainment for an autosomal dominant or recessive disease. We then provide plots of the asymptotic relative efficiency, enabling researchers to easily determine regions where the MOD score or segregation alone performs with comparable efficiency relative to joint segregation and linkage.     

Effect of genotyping error on type-I error rate of affected sib pair studies with genotyped parents

OBJECTIVE: In affected sib pair studies without genotyped parents the effect of genotyping error is generally to reduce the type I error rate and power of tests for linkage. The effect of genotyping error when parents have been genotyped is unknown. We investigated the type I error rate of the single-point Mean test for studies in which genotypes of both parents are available. METHODS: Datasets were simulated assuming no linkage and one of five models for genotyping error. In each dataset, Mendelian-inconsistent families were either excluded or regenotyped, and then the Mean test applied. RESULTS: We found that genotyping errors lead to an inflated type I error rate when inconsistent families are excluded. Depending on the genotyping-error model assumed, regenotyping inconsistent families has one of several effects. It may produce the same type I error rate as if inconsistent families are excluded; it may reduce the type I error, but still leave an anti-conservative test; or it may give a conservative test. Departures of the type I error rate from its nominal level increase with both the genotyping error rate and sample size. CONCLUSION: We recommend that markers with high error rates either be excluded from the analysis or be regenotyped in all families.     

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.     

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.