Consanguinity and the sib-pair method: an approach using identity by descent between and within individuals.

To test for linkage between a trait and a marker, one can consider identical marker alleles in related individuals, for instance, sibs. For recessive diseases, it has been shown that some information may be gained from the identity by descent (IBD) of the two alleles of an affected inbred individual at the marker locus. The aim of this paper is to extend the sib-pair method of linkage analysis to the situation of sib pairs sampled from consanguineous populations. This extension takes maximum advantage of the information provided by both the IBD pattern between sibs and allelic identity within each sib of the pair. This is possible through the use of the condensed identity coefficients. Here, we propose a new test of linkage based on a chi2. We compare the performance of this test with that of the classical chi2 test based on the distribution of sib pairs sharing 0, 1, or 2 alleles IBD. For sib pairs from first-cousin matings, the proposed test can better detect the role of a disease-susceptibility (DS) locus. Its power is shown to be greater than that of the classical test, especially for models where the DS allele may be common and incompletely penetrant; that is to say for situations that may be encountered in multifactorial diseases. A study of the impact of inbreeding on the expected proportions of sib pairs sharing 0, 1, or 2 alleles IBD is also performed here. Ignoring inbreeding, when in fact inbreeding exists, increases the rate of type I errors in tests of linkage.     

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.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees.

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

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.     

The score statistic of the LD-lod analysis: detecting linkage adaptive to linkage disequilibrium

We study the properties of a modified lod score method for testing linkage that incorporates linkage disequilibrium (LD-lod). By examination of its score statistic, we show that the LD-lod score method adaptively combines two sources of information: (a) the IBD sharing score which is informative for linkage regardless of the existence of LD and (b) the contrast between allele-specific IBD sharing scores which is informative for linkage only in the presence of LD. We also consider the connection between the LD-lod score method and the transmission-disequilibrium test (TDT) for triad data and the mean test for affected sib pair (ASP) data. We show that, for triad data, the recessive LD-lod test is asymptotically equivalent to the TDT; and for ASP data, it is an adaptive combination of the TDT and the ASP mean test. We demonstrate that the LD-lod score method has relatively good statistical efficiency in comparison with the ASP mean test and the TDT for a broad range of LD and the genetic models considered in this report. Therefore, the LD-lod score method is an interesting approach for detecting linkage when the extent of LD is unknown, such as in a genome-wide screen with a dense set of genetic markers.     

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.     

Assessing whether an allele can account in part for a linkage signal: the Genotype-IBD Sharing Test (GIST)

To fine map genes, investigators often test for disease-marker association in chromosomal regions with evidence for linkage. Given a marker allele tentatively associated with disease, one would ask if this allele, or one in linkage disequilibrium (LD) with it, could account in part for the observed linkage signal. This question can be addressed by determining if families selected on the basis of the presence of the tentatively associated allele show stronger evidence of linkage as measured by increased allele sharing identical by descent (IBD) by affected family members. However, common selection strategies can be biased for or against linkage in the marker region, even given no disease-marker association. We define unbiased selection schemes and extend the definition to allow weighted selection on the basis of all genotyped family members. For affected-sibship data, we describe three genotype-based weight variables, corresponding to dominant, recessive, and additive models. We then introduce a test for association of a family weight variable with excess IBD sharing. This test allows us to determine if the linkage signal in a region can be attributed in part to the presence of a marker allele, either because of direct involvement in disease etiology or because of LD with a predisposing genetic variant. For samples of 500 affected sib pairs, the tests are powerful in detection of genotype-IBD sharing association, even for disease models with sib relative risk as low as lambda S=1.1, or when evidence for linkage is absent because of sampling variation. This makes our method a new tool for detecting linkage as well as association, especially in regions harboring a candidate gene. We have implemented these methods in the software package GIST (Genotype-IBD Sharing Test).     

The linkage information content value of polymorphism genetic markers in model-free linkage analysis

Guo and Elston [Hum Hered 1999;49:112-118] developed a linkage information content (LIC) value to measure the informativeness of a marker for identity-by-descent (IBD) sharing status of relative pairs. LIC values were derived for five types of relative pairs: full sib, half sib, grandparent-grandchild, first cousin and avuncular. In this paper, we give corrected LIC values for full sib, grandparent-grandchild, first cousin and avuncular pairs, and indicate the availability of a computer program to calculate them.     

Statistical tests for detection of misspecified relationships by use of genome-screen data

Misspecified relationships can have serious consequences for linkage studies, resulting in either reduced power or false-positive evidence for linkage. If some individuals in the pedigree are untyped, then Mendelian errors may not be observed. Previous approaches to detection of misspecified relationships by use of genotype data were developed for sib and half-sib pairs. We extend the likelihood calculations of G?ring and Ott and Boehnke and Cox to more-general relative pairs, for which identity-by-descent (IBD) status is no longer a Markov chain, and we propose a likelihood-ratio test. We also extend the identity-by-state (IBS)-based test of Ehm and Wagner to nonsib relative pairs. The likelihood-ratio test has high power, but its drawbacks include the need to construct and apply a separate Markov chain for each possible alternative relationship and the need for simulation to assess significance. The IBS-based test is simpler but has lower power. We propose two new test statistics-conditional expected IBD (EIBD) and adjusted IBS (AIBS)-designed to retain the simplicity of IBS while increasing power by taking into account chance sharing. In simulations, the power of EIBD is generally close to that of the likelihood-ratio test. The power of AIBS is higher than that of IBS, in all cases considered. We suggest a strategy of initial screening by use of EIBD and AIBS, followed by application of the likelihood-ratio test to only a subset of relative pairs, identified by use of EIBD and AIBS. We apply the methods to a Genetic Analysis Workshop 11 data set from the Collaborative Study on the Genetics of Alcoholism.     

A unified Haseman-Elston method for testing linkage with quantitative traits

The Haseman and Elston (H-E) method uses a simple linear regression to model the squared trait difference of sib pairs with the shared allele identical by descent (IBD) at marker locus for linkage testing. Under this setting, the squared mean-corrected trait sum is also linearly related to the IBD sharing. However, the resulting slope estimate for either model is not efficient. In this report, we propose a simple linkage test that optimally uses information from the estimates of both models. We also demonstrate that the new test is more powerful than both the traditional one and the recently revisited H-E methods.     

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.     

Linkage detection adaptive to linkage disequilibrium: the disequilibrium maximum-likelihood-binomial test for affected-sibship data

It has been demonstrated in the literature that the transmission/disequilibrium test (TDT) has higher power than the affected-sib-pair (ASP) mean test when linkage disequilibrium (LD) is strong but that the mean test has higher power when LD is weak. Thus, for ASP data, it seems clear that the TDT should be used when LD is strong but that the mean test or other linkage tests should be used when LD is weak or absent. However, in practice, it may be difficult to follow such a guideline, because the extent of LD is often unknown. Even with a highly dense genetic-marker map, in which some markers should be located near the disease-predisposing mutation, strong LD is not inevitable. Besides the genetic distance, LD is also affected by many factors, such as the allelic heterogeneity at the disease locus, the initial LD, the allelic frequencies at both disease locus and marker locus, and the age of the mutation. Therefore, it is of interest to develop methods that are adaptive to the extent of LD. In this report, we propose a disequilibrium maximum-binomial-likelihood (DMLB) test that incorporates LD in the maximum-binomial-likelihood (MLB) test. Examination of the corresponding score statistics shows that this method adaptively combines two sources of information: (a) the identity-by-descent (IBD) sharing score, which is informative for linkage regardless of the existence of LD, and (b) the contrast between allele-specific IBD sharing score, which is informative for linkage only in the presence of LD. For ASP data, the proposed test has higher power than either the TDT or the mean test when the extent of LD ranges from moderate to strong. Only when LD is very weak or absent is the DMLB slightly less powerful than the mean test; in such cases, the TDT has essentially no power to detect linkage. Therefore, the DMLB test is an interesting approach to linkage detection when the extent of LD is unknown.     

Linkage analysis for diseases with variable age of onset

We present a method for the multivariate linkage analysis of the age of onset of a disease. The approach allows the incorporation of covariates for the study of gene by environment interactions. It is applicable to general pedigrees. The likelihood of the data is expressed as a function of the number of alleles identical by descent at a marker, the censored ages of onset and disease status, and environmental exposures. In a simulation study, we compare the power to detect linkage under different sampling schemes for either a dominant or recessive trait when approximately 10% of individuals are gene carriers. The majority of the linkage information from a sample of randomly selected sib pairs was retained when the analyses were limited to sibships with one sibling having early-onset disease (<59 years old). Incorporating parental phenotypes could improve the power to detect the gene. When the sample consists of affected sib pairs (ASPs) having variable age of onset, the likelihood ratio (LR) test had higher power than the means (t(2)) test for detecting a locus with a large genetic relative risk (R(g) = 20). However, the power of the two tests was similar when ASPs are selected so that the proband has an early onset of disease. Lastly, the LR test had more power than the t(2) test to detect linkage in the presence of gene by environment interactions.     

A genomic screen of autism: evidence for a multilocus etiology.

We have conducted a genome screen of autism, by linkage analysis in an initial set of 90 multiplex sibships, with parents, containing 97 independent affected sib pairs (ASPs), with follow-up in 49 additional multiplex sibships, containing 50 ASPs. In total, 519 markers were genotyped, including 362 for the initial screen, and an additional 157 were genotyped in the follow-up. As a control, we also included in the analysis unaffected sibs, which provided 51 discordant sib pairs (DSPs) for the initial screen and 29 for the follow-up. In the initial phase of the work, we observed increased identity by descent (IBD) in the ASPs (sharing of 51.6%) compared with the DSPs (sharing of 50.8%). The excess sharing in the ASPs could not be attributed to the effect of a small number of loci but, rather, was due to the modest increase in the entire distribution of IBD. These results are most compatible with a model specifying a large number of loci (perhaps >/=15) and are less compatible with models specifying 相似文献   

Combined linkage and association sib-pair analysis for quantitative traits.

An extension to current maximum-likelihood variance-components procedures for mapping quantitative-trait loci in sib pairs that allows a simultaneous test of allelic association is proposed. The method involves modeling of the allelic means for a test of association, with simultaneous modeling of the sib-pair covariance structure for a test of linkage. By partitioning of the mean effect of a locus into between- and within-sibship components, the method controls for spurious associations due to population stratification and admixture. The power and efficacy of the method are illustrated through simulation of various models of both real and spurious association.     

Construction of a confidence set of markers for the location of a disease gene using affected sib pair data

We have previously proposed a confidence set approach for finding tightly linked genomic regions under the setting of parametric linkage analysis. In this article, we extend the confidence set approach to nonparametric linkage analysis of affected sib pair (ASP) data based on their identity-by-descent (IBD) information. Two well-known statistics in nonparametric linkage analysis, the Two-IBD test (proportion of ASPs sharing two alleles IBD), and the Mean test (average number of alleles shared IBD in the ASPs), are used for constructing confidence sets. Some numerical analyses as well as a simulation study were carried out to demonstrate the utility of the methods. Our results show that the fundamental advantages of the confidence set approach in parametric linkage analysis are retained when the method is generalized to nonparametric analysis. Our study on the accuracy of confidence sets, in terms of choice of tests, underlying disease incidence data, and amount of data available, leads us to conclude, among other things, that the Mean test outperforms the Two-IBD test in most situations, with the reverse being true only for traits with small additive variance. Although we describe how to construct confidence sets based on only two familiar tests, one can construct confidence sets similarly using other allele sharing statistics.     

Effects of stratification in the analysis of affected-sib-pair data: benefits and costs

The benefits and costs of stratification of affected-sib-pair (ASP) data were examined in three situations: (1) when there is no difference in identity-by-descent (IBD) allele sharing between stratified and unstratified ASP data sets; (2) when there is an increase in IBD allele sharing in one of the stratified groups; and (3) when the data are stratified on the basis of IBD allele-sharing status at one locus, and the stratified ASPs are then analyzed for linkage at a second locus. When there is no difference in IBD sharing between strata, a penalty is always paid for stratifying the data. The loss of power to detect linkage in the stratified ASP data sets is the result of multiple testing and the smaller sample size within individual strata. In the case in which etiologic heterogeneity (i.e., severity of phenotype, age at onset) represents genetic heterogeneity, the power to detect linkage can be increased by stratifying the ASP data. This benefit is obtained when there is sufficient IBD allele sharing and sample sizes. Once linkage has been established for a given locus, data can be stratified on the basis of IBD status at this locus and can be tested for linkage at a second locus. When the relative risk is in the vicinity of 1, the power to detect linkage at the second locus is always greater for the unstratified ASP data set. Even for values of the relative risk that diverge sufficiently from 1, with adequate sample sizes and IBD allele sharing, the benefits of stratifying ASP data are minimal.     

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 discordant sib pairs to map loci for qualitative traits with high sibling recurrence risk.

A common approach for detecting genetic linkage using siblings is to collect affected sib pairs (ASPs) and to identify markers where allele sharing exceeds expectation. Alternatively, markers can be analyzed in discordant sib pairs (DSPs) for allele sharing below expectation. Relative to the ASP approach, according to Risch, the power of the DSP approach increases with sibling recurrence risk, the two approaches being equally effective at 50% recurrence risk. However, with many diseases associated with more moderate sibling recurrence risk, less emphasis has been placed on the use of DSPs and the development of the underlying theory. In this paper, we expand the work of Risch to provide a more general foundation for DSP studies, since power can be quite high under the appropriate conditions. For example, in some highly affected populations, such as the diabetes-prone Pima Indians, sibling recurrence risk can be very large and, thus, DSPs ideal. Similarly, as we show through simulation, DSPs are preferable for diabetic nephropathy due to a 70% recurrence rate among siblings with insulin-dependent diabetes mellitus. Following the diabetic nephropathy example, we consider more systematically the situations in which DSPs can provide an efficient alternative to ASPs.