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.     

Detecting heterogeneity with the affected-pedigree-member (APM) method

We have developed a novel test of heterogeneity based on the APM method. We present tests of this method on both empiric and simulated data. © 1993 Wiley-Liss, Inc.     

A novel polylocus method for linkage analysis using the lod-score or affected sib-pair method

A novel approach to combining data from multiple linked loci is proposed that can provide substantial increases in power over normal two-point linkage analysis or sib-pair analysis, with a substantial saving in computing time over traditional multipoint methods. © 1993 Wiley-Liss, Inc.     

Two-locus developments of the weighted pairwise correlation method for linkage analysis

Different studies of complex traits assumed to be influenced by two unliked loci found that two-locus linkage analysis is more powerful than the classical one-locus strategy. The Weighted Pairwise Correlation (WPC) approach is a nonparametric method for linkage analysis that has the advantage to analyze any kind of phenotypes and to consider extended pairs of relatives. In this report, we propose different two-locus extensions of the WPC method based on an additive or a multiplicative effect of two unlinked marker loci on the phenotype. Both methods and their corresponding statistics are easily derived from the classical WPC approach. Compared to the additive model, the multiplicative approach, which can be understood as a statistical interaction effect of the two markers, does not need to specify any additional parameter and allows one to test both the global effect of the two markers (T_AB test) and the effect of one marker, e.g., B, taking into account the effect of the other, A (T_AB/A test). When compared to classical one-locus tests by means of simulations, two-locus tests have comparable 0.05 type I error and are more powerful. In particular, tests based on the multiplicative approach appear to be quite interesting in addition to single locus tests to detect the combined role of two markers (T_AB), or to investigate the role of a marker taking into account a known linked marker (T_AB/A), especially when these markers have complex effects on the phenotype (e.g., statistical interaction). Genet. Epidemiol. 15:491–510,1998. © 1998 Wiley-Liss, Inc.     

Genetic epidemiology of bilateral breast cancer: a linkage analysis using the affected-pedigree-member method

We used the affected-pedigree-member (APM) method to conduct linkage analyses on 19 pedigrees in which the probands had premenopausal bilateral breast cancer. This method analyzes all affected pairs of relatives, as opposed to siblings only, and incorporates into the analyses information on the frequency of marker alleles. Fourteen codominant marker systems were evaluated in two separate analyses. In the first, only premenopausal cases of breast cancer were coded as affected because we assumed that postmenopausal cases were due to a different etiology. In the second analysis, all cases of breast cancer were coded as affected, irrespective of menopausal status. In the premenopausal-cases-only analysis, we observed evidence suggestive of nonindependent segregation for C3 and ESD. In the all-cases analysis, we observed much weaker evidence for C3 and ESD and noted a suggestion of nonindependent segregation for AMY2 and PGM1.     

Genetic analysis workshop III: Multipoint linkage analysis

It is possible to obtain an invalid set of estimates for the pairwise recombination values from using two-point linkage analysis. Development of a multipoint linkage analysis which estimates the joint recombination events in a multilocus system is outlined.     

The method of sib-pair linkage analysis in context of case-control design

We used sib-pair linkage analysis as part of an epidemiologic approach to solving Problem 2 of the GAW10 data set of nuclear families. We recoded the quantitative trait Q1 into a dichotomous trait using Q1 ≥ 40 as the cut-point. In a case-control design of sib-pair analysis, the affected siblings of the proband were the case subjects and the unaffected siblings were the control subjects. Case and control subjects were compared with respect to the number of alleles at one or more loci (0,1,2) that were identical-by-descent (IBD) with those of the proband. Odds ratios (Ors) and 95% confidence intervals (95% CI) were then computed with subjects sharing no alleles (share-0) serving as the reference group. Significantly high ORs were taken as indication of linkage between a marker locus and a suspected disease-susceptibility locus. The case-control sib-pair analysis identified marker D5G15 as associated with disease susceptibility (OR of sharing two alleles [share-2] = 7.7 [95% CI 2.5-23.9]). Our results were consistent with the results from Kruglyak and Lander's method of complete multipoint sib-pair analysis for linkage. For the marker (D5G15) identified through sib-pair analysis, we examined the effects of other covariates and evaluated gene-environment interaction using conditional logistic regression. © 1997 Wiley-Liss, Inc.     

Path analysis and sib-pair linkage

When the distance between linked loci is expressed in terms of the correlation between the identity-by-descent (idb) values of the loci, then a path model may be used to order loci with data on sib-pairs and their parents. The relationship between the recombination fraction and the correlation coefficient is developed and a method for fitting a covariance matrix predicted by a specific ordering of loci to an observed covariance matrix is proposed. © 1993 Wiley-Liss. Inc.     

Introduction of the IBD information into the weighted pairwise correlation method for linkage analysis

The Weighted Pairwise Correlation (WPC) approach is a non‐parametric method of linkage analysis that allows analysis of any kind of phenotypes (quantitative, binary, binary with age of onset) and to consider all pairs of relatives in a pedigree. The principle of this method is to test whether two relatives having close phenotypes also resemble at the marker locus more than expected under the null hypothesis of no linkage. So far, this marker resemblance was estimated by the proportion of alleles shared Identical By State (IBS) by the two relatives. Here, we propose a method to incorporate the Identical By Descent (IBD) information into the WPC approach. For any kind of relative pairs, the computation of the proportion of alleles shared IBD is based on the identification of the closest couple of ancestors, denoted as the reference couple. The IBD information is obtained for pairs of relatives having the same reference couple using individual genotypic vectors derived from this couple. This reconstruction of the IBD information is performed rapidly even in large pedigrees. Simulation studies conducted under various genetic models demonstrate that the use of IBD instead of IBS information leads to a large increase of power, especially in the situation of poorly informative markers. Genet. Epidemiol. 17:35–50, 1999. © 1999 Wiley‐Liss, Inc.     

A general method for linkage disequilibrium correction for multipoint linkage and association

Lately, many different methods of linkage, association or joint analysis for family data have been invented and refined. Common to most of those is that they require a map of markers that are in linkage equilibrium. However, at the present day, high-density single nucleotide polymorphisms (SNPs) maps are both more inexpensive to create and they have lower genotyping error. When marker data is incomplete, the crucial and computationally most demanding moment in the analysis is to calculate the inheritance distribution at a certain position on the chromosome. Recently, different ways of adjusting traditional methods of linkage analysis to denser maps of SNPs in linkage disequilibrium (LD) have been proposed. We describe a hidden Markov model which generalizes the Lander-Green algorithm. It combines Markov chain for inheritance vectors with a Markov chain modelling founder haplotypes and in this way takes account for LD between SNPs. It can be applied to association, linkage or combined association and linkage analysis, general phenotypes and arbitrary score functions. We also define a joint likelihood for linkage and association that extends an idea of Kong and Cox (1997 Am. J. Hum. Genet. 61: 1179-1188) for pure linkage analysis.     

Screening for linkage using a multipoint identity-by-descent method

The multipoint identity-by-descent method (MIM) was used to analyze simulated data for quantitative traits from GAW9. A two-stage method of implementation was used. First, polymorphic markers spaced 6-12 cM apart were used to identify chromosomes of interest for each trait Q1-Q4; and second, for each of these chromosomes, markers spaced 2 cM apart were used to confirm the linkage detected and refine the region for the susceptibility loci. MIM performed well at both levels of mapping, correctly detecting major genes for trait Q3 on chromosome 2, trait Q2 on chromosome 1, and trait Q4 on chromosome 5. © 1995 Wiley-Liss, Inc.     

Evidence for linkage between Wilson disease and esterase D in three kindreds: detection of linkage for an autosomal recessive disorder by the family study method

Wilson disease (WD) is an inherited disorder of copper metabolism that affects the brain, liver, and other organs. Our group recently reported close linkage between the locus for WD and a polymorphic red cell enzyme, esterase D (EsD), in a large inbred Israeli-Arab lineage. We have subsequently studied two unrelated Druze kindreds in order to confirm this linkage and more precisely define the distance between the two loci. The maximum likelihood estimate of recombination was determined to be zero with lod scores of 1.48 and 1.06 in each Druze family, respectively. The combined maximum lod score based on pooled results from the Israeli-Arab and Druze kindreds is 5.49 at theta = 0.03. WD is one of a few autosomal recessive disorders that has been mapped by classical family study methods. In this paper, the merits for using large, inbred families in linkage studies of rare recessive disorders are discussed. Major considerations for pedigree selection are size and number of constituent nuclear families, number and distribution of affected individuals, and pedigree structure that may provide information for determination of phase between the disease and marker loci.     

Construction of human linkage maps: Likelihood calculations for multilocus linkage analysis

Methods are given for efficient calculation of the likelihood for multilocus linkage in families comprised of grandparents, parents, and children. Such families are being used in large-scale cooperative efforts to build a detailed linkage map of the human genome. The methods are illustrated by an application to loci on chromosome 13.     

Genetic analysis workshop III: Multilocus linkage analysis using PAP

Two linkage groups were identified through pairwise linkage analysis using PAP. Three-locus analysis confirmed the suggested order of the loci within the linkage groups and was used to assess the strength of the conclusions. Strategies for improving the efficiency of linkage analysis are discussed.     

Efficient simulation of P values for linkage analysis

In many genetic linkage analyses, the P value is obtained through simulation since the underlying distribution of the test statistic is complex and unknown. However, this can be very computationally intensive. A "bootstrap/replicate pool" approach has been suggested that generates P values more efficiently in terms of computation by resampling sums from a small set of simulated replicates for each pedigree. The replicate pool idea has been successfully applied, but, to our knowledge, has never been theoretically studied. An entirely different method for increasing the computational efficiency of P value simulation is Besag and Clifford's sequential sampling method. We propose an algorithm which combines Besag and Clifford's method with the replicate pool method to efficiently estimate P values for linkage studies. We derive variance expressions for the P value estimates from the replicate pool method and from our proposed hybrid method, and use these to show that the hybrid estimator has a substantial advantage over the other methods in most situations.     

Two-locus approach of segregation and linkage analysis in the study of complex traits

A two-locus segregation and linkage-analysis approach was used to characterize the genetic control of a complex trait (Q1) and to localize the genes that have detectable effects. The results suggested that a two-locus Mendelian model fit the data significantly better than a one-locus model. The linkage results based on the most parsimonious two-locus model revealed linkage of Q1 to two areas (MG2 and MG3), while there was less evidence for linkage using one-locus models. Results also suggested that the subphenotypes (Q2 and Q3) provided useful information for further analysis of Q1 using two-locus models. © 1995 Wiley-Liss, Inc.     

A brute force dichotomization approach to quantitative trait linkage analysis

The effect of dichotomizing a continuous phenotype in linkage analysis of a simulated oligogenic trait is explored. We conclude that dichotomization does not in itself preclude the detection of loci which account for as little as 16% of the genetic variance of the disease. The effects of inclusion of known covariates and quantitative trait linkage analysis are also discussed. © 1995 Wiley-Liss, Inc.     

The Maximum-Likelihood-Binomial method revisited: a robust approach for model-free linkage analysis of quantitative traits in large sibships

Model‐free linkage analysis methods, based on identity‐by‐descent allele sharing, are commonly used for complex trait analysis. The Maximum‐Likelihood‐Binomial (MLB) approach, which is based on the hypothesis that parental alleles are binomially distributed among affected sibs, is particularly popular. An extension of this method to quantitative traits (QT) has been proposed (MLB‐QTL), based on the introduction of a latent binary variable capturing information about the linkage between the QT and the marker. Interestingly, the MLB‐QTL method does not require the decomposition of sibships into constituent sibpairs and requires no prior assumption about the distribution of the QT. We propose a new formulation of the MLB method for quantitative traits (nMLB‐QTL) that explicitly takes advantage of the independence of paternal and maternal allele transmission under the null hypothesis of no linkage. Simulation studies under H₀ showed that the nMLB‐QTL method generated very consistent type I errors. Furthermore, simulations under the alternative hypothesis showed that the nMLB‐QTL method was slightly, but systematically more powerful than the MLB‐QTL method, whatever the genetic model, residual correlation, ascertainment strategy and sibship size considered. Finally, the power of the nMLB‐QTL method is illustrated by a chromosome‐wide linkage scan for a quantitative endophenotype of leprosy infection. Overall, the nMLB‐QTL method is a robust, powerful, and flexible approach for detecting linkage with quantitative phenotypes, particularly in studies of non Gaussian phenotypes in large sibships. Genet. Epidemiol. 35:46–56, 2011. © 2010 Wiley‐Liss, Inc.     

Score test for age at onset genetic linkage analysis in selected sibling pairs

A new score statistic is derived, which uses information from registries (age‐specific incidences) and family studies (sib–sib marginal correlation) to weight affected sibling pairs according to their age at onset. Age at onset of sibling pairs is modelled by a gamma frailty model. From this model we derive a bivariate survival function, which depends on the marginal survival and on the marginal correlation. The score statistic for linkage is a classical nonparametric linkage (NPL) statistic where the identical by descent sharing is weighted by a particular function of the age at onset data. Since the statistic is based on survival models, it can also be applied to discordant and healthy sibling pairs. Simulation studies show that the proposed method is robust and more powerful than standard NPL methods. As illustration we apply the new score statistic to data from a breast cancer study. Copyright © 2009 John Wiley & Sons, Ltd.     

Genetic Analysis Workshop II: results of incorporating a linkage disequilibrium parameter

The corporation of a linkage disequilibrium parameter, delta, into linkage analysis is illustrated for data from Genetic Analysis Workshop II. Points from a joint likelihood surface are calculated and displayed on a recombination fraction-linkage disequilibrium grid using a simple modification of LIPED. The approach is shown to increase the power of linkage analysis and the power of tests for heterogeneity of linkage for the simulated examples.