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The left ventricular outflow tract (LVOTO) malformations, aortic valve stenosis (AVS), coarctation of the aorta (COA), and hypoplastic left heart (HLH) constitute a mechanistically defined subgroup of congenital heart defects that have substantial evidence for a genetic component. Evidence from echocardiography studies has shown that bicuspid aortic valve (BAV) is found frequently in relatives of children with LVOTO defects. However, formal inheritance analysis has not been performed. We ascertained 124 families by an index case with AVS, COA, or HLH. A total of 413 relatives were enrolled in the study, of which 351 had detailed echocardiography exams for structural heart defects and measurements of a variety of aortic arch, left ventricle, and valve structures. LVOTO malformations were noted in 30 relatives (18 BAV, 5 HLH, 3 COA, and 3 AVS), along with significant congenital heart defects (CHD) in 2 others (32/413; 7.7%). Relative risk for first-degree relatives in this group was 36.9, with a heritability of 0.71–0.90. Formal segregation analysis suggests that one or more minor loci with rare dominant alleles may be operative in a subset of families. Multiplex relative risk analysis, which estimates number of loci, had the highest maximum likelihood score in a model with 2 loci (range of 1–6 in the lod-1 support interval). Heritability of several aortic arch measurements and aortic valve was significant. These data support a complex but most likely oligogenic pattern of inheritance. A combination of linkage and association study designs is likely to enable LVOTO risk gene identification. This data can also provide families with important information for screening asymptomatic relatives for potentially harmful cardiac defects.

Objective. Left ventricular outflow tract obstructive (LVOTO) malformations are a leading cause of infant mortality from birth defects. Genetic mechanisms are likely, and there may be a higher rate of asymptomatic LVOTO anomalies in relatives of affected children. This study sought to define the incidence of cardiac anomalies in first-degree relatives of children with congenital aortic valve stenosis (AVS), coarctation of the aorta (CoA), and hypoplastic left heart syndrome (HLHS). Methods. A total of 113 probands with a nonsyndromic LVOTO malformation of AVS (n = 25), BAV (n = 3), CoA (n = 52), HLHS (n = 30), and aortic hypoplasia with mitral valve atresia (n = 2) were ascertained through chart review or enrolled at the time of diagnosis. Echocardiography was performed on 282 asymptomatic first-degree relatives. Results. Four studies had poor acoustic windows, leaving 278 studies for analysis. BAV were found in 13 (4.68%) first-degree relatives. The relative risk of BAV in the relatives was 5.05 (95% confidence interval: 2.2–11.7), and the broad sense heritability was 0.49, based on a general population frequency of 0.9%. BAV was more common in multiplex families compared with sporadic cases. An additional 32 relatives had anomalies of the aorta, aortic valve, left ventricle, or mitral valve. Conclusions. The presence of an LVOTO lesion greatly increases the risk of identifying BAV in a parent or sibling, providing additional support for a complex genetic cause. The parents and siblings of affected patients should be screened by echocardiography as the presence of an asymptomatic BAV may carry a significant long-term health risk.

Genotyping errors can create a problem for the analysis of case-parents data because some families will exhibit genotypes that are inconsistent with Mendelian inheritance. The problem with correcting Mendelian inconsistent genotype errors by regenotyping or removing families in which they occur is that the remaining unidentified genotype errors can produce excess type I (false positive) error for some family-based tests for association. We address this problem by developing a likelihood ratio test (LRT) for association in a case-parents design that incorporates nuisance parameters for a general genotype error model. We extend the likelihood approach for a single SNP to include short haplotypes consisting of 2 or 3 SNPs. The extension to haplotypes is based on assumptions of random mating, multiplicative penetrances, and at most a single genotype error per family. For a single SNP, we found, using Monte Carlo simulation, that type I error rate can be controlled for a number of genotype error models at different error rates. Simulation results suggest the same is true for 2 and 3 SNPs. In all cases, power declined with increasing genotyping error rates. In the absence of genotyping errors, power was similar whether nuisance parameters for genotype error were included in the LRT or not. The LRT developed here does not require prior specification of a particular model for genotype errors and it can be readily computed using the EM algorithm. Consequently, this test may be generally useful as a test of association with case-parents data in which Mendelian inconsistent families are observed. Genet Epidemiol 26:142–154, 2004. Published 2004 Wiley-Liss, Inc.

In studies of complex diseases, a common paradigm is to conduct association analysis at markers in regions identified by linkage analysis, to attempt to narrow the region of interest. Family-based tests for association based on parental transmissions to affected offspring are often used in fine-mapping studies. However, for diseases with late onset, parental genotypes are often missing. Without parental genotypes, family-based tests either compare allele frequencies in affected individuals with those in their unaffected siblings or use siblings to infer missing parental genotypes. An example of the latter approach is the score test implemented in the computer program TRANSMIT. The inference of missing parental genotypes in TRANSMIT assumes that transmissions from parents to affected siblings are independent, which is appropriate when there is no linkage. However, using computer simulations, we show that, when the marker and disease locus are linked and the data set consists of families with multiple affected siblings, this assumption leads to a bias in the score statistic under the null hypothesis of no association between the marker and disease alleles. This bias leads to an inflated type I error rate for the score test in regions of linkage. We present a novel test for association in the presence of linkage (APL) that correctly infers missing parental genotypes in regions of linkage by estimating identity-by-descent parameters, to adjust for correlation between parental transmissions to affected siblings. In simulated data, we demonstrate the validity of the APL test under the null hypothesis of no association and show that the test can be more powerful than the pedigree disequilibrium test and family-based association test. As an example, we compare the performance of the tests in a candidate-gene study in families with Parkinson disease.

We investigated the effect of multiple susceptibility alleles at a single disease locus on the statistical power of a likelihood ratio test to detect association between alleles at a marker locus and a disease phenotype in a case-control design. Using simplifying assumptions to obtain the joint frequency distribution of marker and disease locus alleles, we present numerical results that illustrate the impact of historical variation of initial associations between marker alleles and susceptibility alleles on the power of a likelihood ratio test for association. Our results show that an increase in the number of susceptibility alleles produces a decrease in power of the likelihood ratio test. The decrease in power in the presence of multiple susceptibility alleles, however, is less for markers with multiple alleles than for markers with two alleles. We investigate the implications of this observation for tests of association based on haplotypes made up of tightly linked single-nucleotide polymorphisms (SNPs). Our results suggest that an analysis based on haplotypes can be advantageous over an analysis based on individual SNPs in the presence of multiple susceptibility alleles, particularly when linkage disequilibria between SNPs is weak. The results provide motivation for further development of statistical methods based on haplotypes for assessing the potential for association methods to identify and locate complex disease genes.

Family-based tests of association are now often used when trying to fine-map a disease susceptibility locus. Recently, several tests of linkage and association have been proposed that use nuclear families with multiple affected and unaffected sibs rather than just case-parent triads. In this paper we propose a test that generalizes these previous tests. Formulae are derived to calculate the power of the test for a randomly mating population. These power calculations are used to determine conditions under which it is advantageous to include unaffected sibs in the analysis.

The potential of association studies for fine-mapping loci with common disease susceptibility alleles for complex genetic diseases in outbred populations is unclear. For a battery of tightly linked anonymous genetic markers spanning a candidate region centered around a disease locus, simulation methods based on a coalescent process with mutation, recombination, and genetic drift were used to study the spatial distribution of markers with large noncentrality parameters in a case-control study design. Simulations with a disease allele at intermediate frequency, presumably representing an old mutation, tend to exhibit the largest noncentrality parameter values at markers near the disease locus. In contrast, simulations with a disease allele at low frequency, presumably representing a young mutation, often exhibit the largest noncentrality parameter values at markers scattered over the candidate region. In the former case, sample sizes or marker densities sufficient to detect association are likely to lead to useful localization, whereas, in the latter case, localization of the disease locus within the candidate region is much less likely, regardless of the sample size or density of the map. The simulations suggest that for a single marker analysis, the simple strategy of choosing the marker with smallest associated P value to begin a laboratory search for the disease locus performs adequately for a common disease allele.

Tests of linkage and association between a disease and either a candidate gene or marker allele can be based on sibships with at least one affected and one unaffected sibling. However, specialized techniques are required to account for within-sibship correlation if some sibships contain more than one affected or more than one unaffected sib. In this paper, we propose Within Sibship Paired Resampling (WSPR), a technique that is designed to test the null hypothesis of no linkage or no association, even when sibships contain variable numbers of sibs. One repeatedly generates data subsets based on randomly sampling one affected and one unaffected sibling from each sibship, and each subset is analyzed individually. Then, evidence is combined by averaging results across these resampled data sets, applying a variance expression that implicitly accounts for the correlation among siblings. While the general WSPR procedure allows for numerous testing strategies, we describe two in detail. Simulation results for scenarios with varying degrees of population stratification demonstrate good power for the WSPR testing methods compared to the sib TDT (S-TDT) and the sibship disequilibrium test (SDT).

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures

Summary One strategy for localization of a quantitative-trait locus (QTL) is to test whether the distribution of a quantitative trait depends on the number of copies of a specific genetic-marker allele that an individual possesses. This approach tests for association between alleles at the marker and the QTL, and it assumes that association is a consequence of the marker being physically close to the QTL. However, problems can occur when data are not from a homogeneous population, since associations can arise irrespective of a genetic marker being in physical proximity to the QTL—that is, no information is gained regarding localization. Methods to address this problem have recently been proposed. These proposed methods use family data for indirect stratification of a population, thereby removing the effect of associations that are due to unknown population substructure. They are, however, restricted in terms of the number of children per family that can be used in the analysis. Here we introduce tests that can be used on family data with parent and child genotypes, with child genotypes only, or with a combination of these types of families, without size restrictions. Furthermore, equations that allow one to determine the sample size needed to achieve desired power are derived. By means of simulation, we demonstrate that the existing tests have an elevated false-positive rate when the size restrictions are not followed and that a good deal of information is lost as a result of adherence to the size restrictions. Finally, we introduce permutation procedures that are recommended for small samples but that can also be used for extensions of the tests to multiallelic markers and to the simultaneous use of more than one marker.

Advances in marker technology have made a dense marker map a reality. If each marker is considered separately, and separate tests for association with a disease gene are performed, then multiple testing becomes an issue. A common solution uses a Bonferroni correction to account for multiple tests performed. However, with dense marker maps, neighboring markers are tightly linked and may have associated alleles; thus tests at nearby marker loci may not be independent. When alleles at different marker loci are associated, the Bonferroni correction may lead to a conservative test, and hence a power loss. As an alternative, for tests of association that use family data, we propose a Monte Carlo procedure that provides a global assessment of significance. We examine the case of tightly linked markers with varying amounts of association between them. Using computer simulations, we study a family-based test for association (the transmission/disequilibrium test), and compare its power when either the Bonferroni or Monte Carlo procedure is used to determine significance. Our results show that when the alleles at different marker loci are not associated, using either procedure results in tests with similar power. However, when alleles at linked markers are associated, the test using the Monte Carlo procedure is more powerful than the test using the Bonferroni procedure. This proposed Monte Carlo procedure can be applied whenever it is suspected that markers examined have high amounts of association, or as a general approach to ensure appropriate significance levels and optimal power.

One strategy for mapping disease loci using marker-disease associations is to test for association with case-control samples and follow up a positive result with a family-based test. Using a family-based test in the second stage can help provide protection against false-positive results that can result from use of inappropriate controls and provides assurance that association identified in the first stage is occurring between linked loci. It is crucial for this two-stage strategy that the first stage be as powerful as possible to detect association since only positive results are tested in the second stage. In certain situations, the power of the first-stage test can be increased by combining the case-control and family data. However, this introduces correlation between the first- and second-stage tests, and treating them as independent tests causes a bias. Here we propose a Monte Carlo method that accounts for the correlation and provides the correct significance level for the second-stage test. We also discuss the use of a two-stage procedure when doing a genome scan for the data presented in the Genetic Analysis Workshop 9 study.

SummaryThe transmission/disequilibrium test (TDT) developed by Spielman et al. can be a powerful family-based test of linkage and, in some cases, a test of association as well as linkage. It has recently been extended in several ways; these include allowance for implementation with quantitative traits, allowance for multiple alleles, and, in the case of dichotomous traits, allowance for testing in the absence of parental data. In this article, these three extensions are combined, and two procedures are developed that offer valid joint tests of linkage and (in the case of certain sibling configurations) association with quantitative traits, with use of data from siblings only, and that can accommodate biallelic or multiallelic loci. The first procedure uses a mixed-effects (i.e., random and fixed effects) analysis of variance in which sibship is the random factor, marker genotype is the fixed factor, and the continuous phenotype is the dependent variable. Covariates can easily be accommodated, and the procedure can be implemented in commonly available statistical software. The second procedure is a permutation-based procedure. Selected power studies are conducted to illustrate the relative power of each test under a variety of circumstances.

A two-stage approach was used to analyze Problem 2 simulated data from Genetic Analysis Workshop 11. In the first stage, we tested for linkage with the Haseman-Elston test in SIBPAL. Markers that were significant in the first stage were followed up with two types of association tests. These association tests differ in the type of family information used: 1) parental transmissions to affected children or 2) differences in marker allele frequencies between affected and unaffected siblings. We also explored how the conclusions changed when different sampling strategies were used. Of particular interest was whether the entire data set should be used to test for both linkage and association or whether the data set should be halved to allow for replication of the initial association results.

SummaryPopulation-based tests of association have used data from either case-control studies or studies based on trios (affected child and parents). Case-control studies are more prone to false-positive results caused by inappropriate controls, which can occur if, for example, there is population admixture or stratification. An advantage of family-based tests is that cases and controls are well matched, but parental data may not always be available, especially for late-onset diseases. Three recent family-based tests of association and linkage utilize unaffected siblings as surrogates for untyped parents. In this paper, we propose an extension of one of these tests. We describe and compare the four tests in the context of a complex disease for both biallelic and multiallelic markers, as well as for sibships of different sizes. We also examine the consequences of having some parental data in the sample.

During the last decade new methods for mapping quantitative trait loci (QTLs) have helped geneticists uncover disease-associated genes. Genetic dissection of complex multigenic diseases such as cancer is being accomplished in part by mapping QTLs in experimental crosses of mice [1]. With the recent construction of dense genetic linkage maps for the mouse, mapping of quantitative trait loci has become practical [2]. Over 6000 polymorphic simple sequence length repeat markers (microsatellite markers) have been mapped in the mouse genome [3], and new analytical approaches to linkage analysis have made QTL mapping a powerful technique for identifying cancer genes [4-7]. In this overview we discuss the design of QTL mapping studies and some of the findings from studies on the mapping of murine lung tumor susceptibility loci.

Summary The transmission/disequilibrium test (TDT) originally was introduced to test for linkage between a genetic marker and a disease-susceptibility locus, in the presence of association. Recently, the TDT has been used to test for association in the presence of linkage. The motivation for this is that linkage analysis typically identifies large candidate regions, and further refinement is necessary before a search for the disease gene is begun, on the molecular level. Evidence of association and linkage may indicate which markers in the region are closest to a disease locus. As a test of linkage, transmissions from heterozygous parents to all of their affected children can be included in the TDT; however, the TDT is a valid x 2 test of association only if transmissions to unrelated affected children are used in the analysis. If the sample contains independent nuclear families with multiple affected children, then one procedure that has been used to test for association is to select randomly a single affected child from each sibship and to apply the TDT to those data. As an alternative, we propose two statistics that use data from all of the affected children. The statistics give valid x 2 tests of the null hypothesis of no association or no linkage and generally are more powerful than the TDT with a single, randomly chosen, affected child from each family.

A permutation test is proposed for assessing affection status models. The test uses marker data from regions with prior evidence of linkage to susceptibility genes, and three different test statistics are examined. We applied the test to the GAW10 data and found no evidence on chromosome 18 to reject the affection status model that groups individuals diagnosed with either bipolar I, bipolar II or unipolar. The chromosome 5 data gave similar results, and further suggested that individuals diagnosed with unipolar-single episode not be included as affected. A preliminary power study suggested that one of the proposed statistics, S, is to be preferred in certain circumstances.

To the Editor: Recently, we proposed the pedigree disequilibrium test (PDT) as a test for allelic association and linkage (linkage disequilibrium) in general pedigrees (Martin et al. 2000). We have discovered that, in certain cases in extended pedigrees, the PDT can be biased under the null hypothesis. In this letter we describe the nature of the bias and illustrate a model in which the bias arises. We offer two alternative modifications to the PDT statistic, both of which result in valid tests of linkage disequilibrium over all genetic models and family structures. In constructing the PDT statistic, we considered two types of families within a pedigree. Informative nuclear families are those in which there is at least one affected individual, with both parents genotyped at the marker and at least one parent heterozygous. Informative discordant sibships have at least one affected and one unaffected sibling with different marker genotypes. For a marker locus with two alleles, M1 and M2, we defined the random variables XTj, for the jth triad (affected individual and both parents) in the pedigree, and XSj, for the jth discordant sib pair (DSP) in the pedigree: XTj = (no. of M1 transmitted) − (no. of M1 not transmitted) and XSj = (no. of M1 in affected sib) − (no. of M1 in unaffected sib), respectively. In our previous study (Martin et al. 2000), we defined a measure of association (D) for a pedigree containing nT triads from informative nuclear families and nS DSPs from informative discordant sibships: Let Di be the measure of association in the ith pedigree in a sample of N independent pedigrees. The PDT statistic is given by . The critical assumption is that the T is asymptotically normal, with mean 0 and variance 1, under the null hypothesis of no linkage disequilibrium. The difficulty that can be encountered is that, for some cases under the null hypothesis, the expected value of T may actually be different from 0, a situation that results in an inflated type I error. This is best illustrated by an example. Consider a fully penetrant dominant disease locus (with alleles d1 and d2) with no phenocopies, so that there is probability 1 that an individual with at least one copy of the disease allele is affected. Furthermore, assume that the disease allele (d1) is rare so that in any pedigree there is, at most, one segregating copy of the disease allele. Suppose that we have sampled extended three-generation pedigrees with the structure shown in figure 1. Only families in which the grandparent (GP2), parent (P2), and offspring (O) are all affected can lead to bias. Otherwise there will be, at most, one informative triad. Disease-locus genotypes are fully specified, given the affection status (see fig. 1). Figure 1 Pedigrees illustrating PDT bias. Black circles denote affected individuals and white squares denote unaffected individuals. Disease- and marker-locus genotypes are shown for each individual. Values of quantities from equation (1) are given for each pedigree. ... Suppose that there is a marker locus fully linked to the disease locus (i.e., there is no recombination) but that there is no allelic association between the alleles at the two loci. This is the null hypothesis for the PDT. Furthermore, suppose that the marker locus has two alleles, with one allele—say, M1—being rare so that only one founder is heterozygous at the marker (families with no heterozygotes are not informative and therefore are not considered) and all three of the founders (GP1, GP2, and P1) are equally likely to be the heterozygote. The possible transmission patterns and the calculation of relevant quantities are shown in figure 1. For each pedigree we give the value of D, XT, and nT. Each of the six pedigrees in figure 1 is equally likely under the null hypothesis for the model given. Taking the expectation of D over these pedigrees yields E(D)=- 1/6. Therefore, in this example, it is not the case that E(T)=0. From this example we can see that the problem arises when a grandparent is heterozygous: even though heterozygous grandparents are equally likely to transmit M1 or M2, the weights in the average (eq. [1]) differ depending on which allele is transmitted. If M1 is transmitted, then the average is over nT=2. If M2 is transmitted, then the average is over nT=1. Thus, there is a bias toward concluding that the more common allele is transmitted more often, even under the null hypothesis of equal transmission. One can construct an unbiased test by requiring that the weights used in the average be independent of marker genotype. One alternative, hereafter referred to as the “PDT-avg,” is to average over all phenotypically informative units. Specifically, let nT be the number of fully genotyped family triads, irrespective of heterozygosity, and let nS be the number of DSPs, without requiring that they come from an informative sibship. For the example in figure 1, the PDT-avg is calculated by setting all nT=2, and this gives E(D)=0. A second alternative, hereafter referred to as the “PDT-sum,” is to use the sum from equation (1) and not use averages at all. This also gives E(D)=0 for the example in figure 1, since all nT=1 for the PDT-sum. (Software for the calculation of the PDT-avg and the PDT-sum statistics can be obtained from the Duke Center for Human Genetics Web site.) Approaches based on sums of random variables within pedigrees have also been proposed elsewhere (Martin et al. 1997; Teng and Risch 1999; Abecasis et al. 2000; Rabinowitz and Laird 2000). Intuitively, basing a statistic on the sum gives more weight to families with a greater number of phenotypically informative units, whereas averaging gives all families equal weight. To compare these alternative tests to the original form of the PDT (“PDT-old”), we estimated type I error and power for the tests, using simulations (table 1). The same genetic models (i.e., 1–6) used by Martin et al. (2000) were used in these simulations, and marker- and disease-allele frequencies were set at .3. To simulate the null hypothesis, we simulated a lack of allelic association between the marker and disease loci but did not allow recombination. For each estimate, 5,000 replicate samples of 250 extended pedigrees of the structure used by Martin et al. (2000) were simulated. These simulations differ from those of Martin et al. (2000). In that study, ascertainment was assumed to be random with respect to affection status. In an attempt to simulate the ascertainment of extended pedigrees more realistically, the simulations in the present study produce pedigrees that are conditional on having at least one affected cousin pair. Table 1 Estimates of Type 1 Error and Power for PDTs for Various Genetic Models, Based on 5,000 Replicate Simulations[Note] The results show that, for the cases examined, all tests have type I error levels close to the nominal level of .05 and thus are valid for these models. As we reported in our previous article (Martin et al. 2000), there is little bias reflected in the test when the original form of the statistic is used, although the estimates of type I error are larger than those for the PDT-avg and the PDT-sum, for each model. Part of the reason that there is little bias in these simulations is our choice of allele frequency for the marker. It can be shown that there is no bias when the frequencies of the marker alleles are .5. In these simulations, we used frequencies of .3 and .7, so there was less bias than expected for cases with more-extreme allele frequencies. An additional reason that little bias was seen is that we did not use grandparental genotypes in the calculation of the test statistic. It is possible to show that, when there are only two generations in the pedigree, there will be little bias as long as the genetic effect is not large. In these simulations, the genetic effect was low (i.e., the penetrances are all similar) for each of the models considered. It is noteworthy that, if grandparental genotypes were used, there could be bias even if there were no genetic effect due to this locus (i.e., even if penetrances were equal). The results in table 1 demonstrate that the new tests can be more powerful than the original test. For these simulations we found that power is similar for the PDT-avg and the PDT-sum, but this will not always be the case. The PDT-sum gives more weight to families of larger size, whereas the PDT-avg gives all families equal weight. Thus, if pedigrees contain a similar number of phenotypically informative family units, then the values of the statistics will be similar. Differences will be most apparent when families are of different sizes. Exploratory simulations (not shown) have demonstrated that, in many cases, the PDT-sum can be more powerful than the PDT-avg; however, neither test is uniformly more powerful over all genetic models. In summary, we have identified examples in which the original form of the PDT can be biased. There is no bias when the original form of the statistic is used in nuclear families (with or without parents) or when the marker-allele frequencies are .5. The bias is evident only when there are multiple generations contributing to the statistic, when the genetic effect due to the locus is strong, and when marker-allele frequencies are extreme. We have proposed two alternative statistics that not only remove the bias but also result in tests that can be more powerful than the original test. These tests provide valid alternatives for assessment of linkage disequilibrium in general pedigrees.

Family-based tests of linkage disequilibrium are usually based on nuclear family data including affected individuals and their parents or their unaffected siblings. A problem with these tests is that they are not valid tests of association when data from related nuclear families from larger pedigrees are used. One way to ensure validity when testing for association is to select a single nuclear family from each extended pedigree in the sample. When data are available for larger pedigrees, it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this paper we present such a test: the Pedigree Disequilibrium Test (PDT). The PDT can use data from related nuclear families from extended pedigrees and remains valid when there is population substructure. Power simulations demonstrate that, when extended pedigree data are available, gains in power can be obtained by using the PDT rather than existing methods that only use a subset of the data. The PDT can also be more powerful than current methods when the data consist of a sample of independent nuclear families or sibships.

SummaryA population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus ofDrosophila melanogasterare found to fit the proposed model slightly better than a similar model without subdivision.

This unit describes the statistical techniques necessary for performing family-based association studies (such as the TDT) for genetic polymorphisms. Such studies have become increasingly important in the identification of genes that confer an increased risk to disease, particularly for common diseases with a complex etiology. The family-based approach avoids some of the problems often encountered when applying the traditional case-control design to genetic studies. The unit includes the Sib TDT (S-TDT) method, which allows application of the principle of the TDT to sibships without parental data, and several related tests. Curr. Protoc. Hum. Genet. 58:1.12.1-1.12.24. © 2008 by John Wiley & Sons, Inc. Keywords: genetic association; genetic linkage; linkage disequilibrium; TDT

HapMap provides linkage disequilibrium (LD) information on a sample of 3.7 million SNPs that can be used for tag SNP selection in whole-genome association studies. HapMap can also be used for tag SNP selection in candidate genes, although its performance has yet to be evaluated against gene resequencing data, where there is near-complete SNP ascertainment. The Environmental Genome Project (EGP) is the largest gene resequencing effort to date with over 500 resequenced genes. We used HapMap data to select tag SNPs and calculated the proportions of common SNPs (MAFor=0.05) tagged (rho2or=0.8) for each of 127 EGP Panel 2 genes where individual ethnic information was available. Median gene-tagging proportions are 50, 80 and 74% for African, Asian, and European groups, respectively. These low gene-tagging proportions may be problematic for some candidate gene studies. In addition, although HapMap targeted nonsynonymous SNPs (nsSNPs), we estimate only approximately 30% of nonsynonymous SNPs in EGP are in high LD with any HapMap SNP. We show that gene-tagging proportions can be improved by adding a relatively small number of tag SNPs that were selected based on resequencing data. We also demonstrate that ethnic-mixed data can be used to improve HapMap gene-tagging proportions, but are not as efficient as ethnic-specific data. Finally, we generalized the greedy algorithm proposed by Carlson et al (2004) to select tag SNPs for multiple populations and implemented the algorithm into a freely available software package mPopTag.

One of the goals of the International HapMap Project is the identification of common haplotypes in genes. However, HapMap uses an incomplete catalogue of single nucleotide polymorphisms (SNPs) and might miss some common haplotypes. We examined this issue using data from the Environmental Genome Project (EGP) which resequenced 335 genes in 90 people, and thus, has a nearly complete catalogue of gene SNPs. The EGP identified a total of 45,243 SNPs, of which 10,780 were common SNPs (minor allele frequency ≥0.1). Using EGP common SNP genotype data, we identified 1,459 haplotypes with frequency ≥0.05 and we use these as “benchmark” haplotypes. HapMap release 16 had genotype information for 1,573 of 10,780 (15%) EGP common SNPs. Using these SNPs, we identified common HapMap haplotypes (frequency ≥0.05) in each of the four HapMap ethnic groups. To compare common HapMap haplotypes to EGP benchmark haplotypes, we collapsed benchmark haplotypes to the set of 1,573 SNPs. Ninety-eight percent of the collapsed benchmark haplotypes could be found as common HapMap haplotypes in one or more of the four HapMap ethnic groups. However, collapsing benchmark haplotypes to the set of SNPs available in HapMap resulted in a loss of haplotype information: 545 of 1,459 (37%) benchmark haplotypes were uniquely identified, and only 25% of genes had all their benchmark haplotypes uniquely identified. We resampled the EGP data to examine the effect of increasing the number of HapMap SNPs to 5 million, and estimate that ∼40% of common SNPs in genes will be sampled and that half of the genes will have sufficient SNPs to identify all common haplotypes. This inability to distinguish common haplotypes of genes may result in loss of power when examining haplotype-disease association. (Cancer Epidemiol Biomarkers Prev 2006;15(1):133–7)

The pedigree disequilibrium test (PDT) has been proposed recently as a test for association in general pedigrees [Martin et al., Am J Hum Genet 67:146-54, 2000]. The Genetic Analysis Workshop (GAW) 12 simulated data, with many extended pedigrees, is an example the type of data to which the PDT is ideally suited. In replicate 42 from the general population the PDT correctly identifies candidate genes 1, 2, and 6 as containing single nucleotide polymorphisms (SNPs) that are significantly associated with the disease. We also applied the truncated product method (TPM) [Zaykin et al., Genet Epidemiol, in press] to combine p-values in overlapping windows across the genes. Our results show that the TPM is helpful in identifying significant SNPs as well as removing spurious false positives. Our results indicate that, using the PDT, functional disease-associated SNPs can be successfully identified with a dense map of moderately polymorphic SNPs.

Summary: Genetic association studies increasingly rely on the use of linkage disequilibrium (LD) tag SNPs to reduce genotyping costs. We developed a software package TAGster to select, evaluate and visualize LD tag SNPs both for single and multiple populations. We implement several strategies to improve the efficiency of current LD tag SNP selection algorithms: (1) we modify the tag SNP selection procedure of Carlson et al. to improve selection efficiency and further generalize it to multiple populations. (2) We propose a redundant SNP elimination step to speed up the exhaustive tag SNP search algorithm proposed by Qin et al. (3) We present an additional multiple population tag SNP selection algorithm based on the framework of Howie et al., but using our modified exhaustive search procedure. We evaluate these methods using resequenced candidate gene data from the Environmental Genome Project and show improvements in both computational and tagging efficiency.Availability: The software Package TAGster is freely available at http://www.niehs.nih.gov/research/resources/software/tagster/Contact: taylor@niehs.nih.govSupplementary information: Additional information, including a tutorial, detailed algorithm and detailed evaluation results, is also available from TAGster web site (see above).

SummaryRecent admixture between genetically differentiated populations can result in high levels of association between alleles at loci that are ≤10 cM apart. The transmission/disequilibrium test (TDT) proposed by Spielman et al. (1993) can be a powerful test of linkage between disease and marker loci in the presence of association and therefore could be a useful test of linkage in admixed populations. The degree of association between alleles at two loci depends on the differences in allele frequencies, at the two loci, in the founding populations; therefore, the choice of marker is important. For a multiallelic marker, one strategy that may improve the power of the TDT is to group marker alleles within a locus, on the basis of information about the founding populations and the admixed population, thereby collapsing the marker into one with fewer alleles. We have examined the consequences of collapsing a microsatellite into a two-allele marker, when two founding populations are assumed for the admixed population, and have found that if there is random mating in the admixed population, then typically there is a collapsing for which the power of the TDT is greater than that for the original microsatellite marker. A method is presented for finding the optimal collapsing that has minimal dependence on the disease and that uses estimates either of marker allele frequencies in the two founding populations or of marker allele frequencies in the current, admixed population and in one of the founding populations. Furthermore, this optimal collapsing is not always the collapsing with the largest difference in allele frequencies in the founding populations. To demonstrate this strategy, we considered a recent data set, published previously, that provides frequency estimates for 30 microsatellites in 13 populations.

Human cytochrome P4502E1 (CYP2E1) is inducible by ethanol and is involved in metabolism of many known carcinogens including N-nitrosodimethylamine, butadiene, benzene, and carbon tetrachloride. A 50-fold variability in CYP2E1 enzyme activity in humans has been observed but it is unknown whether the basis for this variation is genetic or environmental. Recently, two restriction fragment length polymorphisms (RFLPs) within the CYP2E1 gene have been suggested as genetic markers of risk for cancer. The first was a Rsa I polymorphism in the 5' regulatory region that appeared to alter transcriptional activation of the gene and the second was a Dra I polymorphism located approximately 7000 bp downstream in an intron. Rare alleles at each of these loci have been associated with a reduced risk for lung cancer in Japanese and Swedish populations. We have used a polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method to determine the genotype frequency for each of these CYP2E1 RFLPs in 695 individuals of Taiwanese, African-American or European-American background. Genotype and allele frequencies for Taiwanese were significantly different from those of African-Americans and European-Americans at either Rsa I or Dra I sites (p0.0001). Allele frequencies for African-Americans and European-Americans were significantly different at the Rsa I site (p = 0.03). The rare alleles (c2 and C) occurred at frequencies of 0.28 and 0.24 in Taiwanese, 0.01 and 0.08 in African-Americans, and 0.04 and 0.11 in European-Americans. In addition, we describe three haplotypes common to all three population samples and a fourth haplotype that was only detected in the Taiwanese population sample. This fourth haplotype may have been caused by a recombination event between these markers.(ABSTRACT TRUNCATED AT 250 WORDS)

A statistical test for detecting genetic differentiation of subpopulations is described that uses molecular variation in samples of DNA sequences from two or more localities. The statistical significance of the test is determined with Monte Carlo simulations. The power of the test to detect genetic differentiation in a selectively neutral Wright-Fisher island model depends on both sample size and the rates of migration, mutation, and recombination. It is found that the power of the test is substantial with samples of size 50, when 4Nm less than 10, where N is the subpopulation size and m is the fraction of migrants in each subpopulation each generation. More powerful tests are obtained with genes with recombination than with genes without recombination.

A general scheme is proposed which relates the carcinogenic responses to the amount of DNA-carcinogen adduct formed instead of applied dose. Based on the present understanding of the mechanism of carcinogenesis, we believe this to be a more rational approach to the low-dose extrapolation problem. In addition to specifying the low-dose extrapolation routine, it is necessary in this scheme to construct a pharmacokinetic model relating exposure concentration to the amount of DNA-chemical adduct formed. Two pharmacokinetic models are constructed for vinyl chloride. Low-dose risk estimates are determined from dose-response functions corresponding to the probit and multistage models. The estimates obtained using the probit model vary considerably when the pharmacokinetics parameters are changed whereas for the multistage model the low-dose estimates have less variability, varying in general by no more than one order of magnitude. This is not unexpected since the probit dose-response function is very “flat” in the low-dose region whereas the multistage dose-response function is analytic. In some cases a detailed pharmacokinetic study of the carcinogen may be as important as the bioassay study for lowdose and across-species extrapolation. However, it is important to realize that even though the incorporation of pharmacokinetics into the low-dose estimation process better reflects reality, it does not help in resolving the issue of which underlying model to use for the low-dose extrapolation, e.g., probit versus multistage.

An estimate of the average number of evolutionarily acceptable substitutions per nucleotide since the most recent common ancestor of a pair of homologous sequences is found which uses nucleotide sequence data. The estimate is derived assuming a Poisson-like model for the evolutionary process. A method is also suggested for analyzing nucleotide sequence data in M homologous sequences (M ⩾ 3). A simulation study is reported showing that the estimates are satisfactory providing there is sufficient homology between the sequences. To demonstrate the methods a numerical example using some β-globin data is presented.

A selectively neutral m-loci model with recombination is studied. A general method is developed to calculate the variance of the number of segregating sites in samples of arbitrary size and the m-loci homozygosity. The method is based on properties of the genealogy of the sample rather than diffusion approximations. To demonstrate the scope of the method several calculations are presented.

For eachN≧1, let {XN(t, x), t≧0} be a discrete-time stochastic process withXN(0) =x. LetFN(y)= E(XN(t +1) |XN(t) =y), and defineYN(t,x) =FN(YN(t –1,x)),t≧1 andYN(0,x) =x. Assume that in a neighborhood of the originFN(y)= mNy(l +O(y)) wheremN> 1, and define forδ> 0 andx> 0, υN(δ,x) = inf{t:xmtN>δ}. Conditions are given under which, forθ> 0 and ε> 0, there exist constantsδ> 0 andLThis result together with a result of Kurtz (1970), (1971) shows that, under appropriate conditions, the time needed for the stochastic process {XN(t, 1/N),t≧0} to escape aδ-neighborhood of the origin is of order logΝδ/logmN. To illustrate the results the Wright-Fisher model with selection is considered.

How often will a store with two elevators be without service assuming that repairs are quick? In this note it is shown that, under very mild assumptions on the operating- and repair-time distributions, the times when the building is without service are asymptotically Poisson.

Statistical properties of the amount of divergence of genes in multigene families are studied. The model considered is an infinite-site neutral model with unbiased intrachromosomal conversion, unbiased interchromosomal conversion, and recombination. By considering the time back to the most recent common ancestor of two genes, both the probability of identity and the moments of S, the number of sites that differ between two sampled genes, are obtained. We find that if recombination rates are large or conversion is always interchromosomal, then the expectation of S is 4N mu n where N is the population size, mu is the rate of mutation per generation per gene and n is the number of genes in the gene family, as the conversion rates approach zero, the moments of divergence do not approach the moments of divergence with conversion rates equal to zero, and it is possible for a decrease in the rate of intrachromosomal conversion to result in a higher probability of identity, but a greater mean divergence of the two genes.

The DA process has the advantages of clear solution scrubbing, high SO2 removal efficiency, low liquid to gas ratio and reliability.

Efforts in estimating carcinogenic risk in humans from long-term exposure to chemical carcinogens have centered on the problem of low-dose extrapolation. For chemicals with metabolites that interact with DNA, it may be more meaningful to relate tumor response to the concentration of the DNA adducts in the target organ rather than to the applied dose. Many data suggest that the relation between tumor response and concentration of DNA adducts in the target organ may be linear. This implies that the nonlinearities of the dose-response curve for tumor induction may be due to the kinetic processes involved in the formation of carcinogen metabolite--DNA adducts. Of particular importance is the possibility that the kinetic processes may show a nonlinear "hockey-stick" like behavior which results from saturation of detoxification or DNA repair processes. The mathematical models typically used for low-dose extrapolation are shown potentially to overestimate risk by several orders of magnitude when nonlinear kinetics are present.

A numerical method is developed for solving a nonstandard singular system of second-order differential equations arising from a problem in population genetics concerning the coalescent process for a sample from a population undergoing selection. The nonstandard feature of the system is that there are terms in the equations that approach infinity as one approaches the boundary. The numerical recipe is patterned after the LU decomposition for tridiagonal matrices. Although there is no analytic proof that this method leads to the correct solution, various examples are presented that suggest that the method works. This method allows one to calculate the expected number of segregating sites in a random sample of n genes from a population whose evolution is described by a model which is not selectively neutral.

The statistical properties of the process describing the genealogical history of a random sample of genes at a selectively neutral locus which is linked to a locus at which natural selection operates are investigated. It is found that the equations describing this process are simple modifications of the equations describing the process assuming that the two loci are completely linked. Thus, the statistical properties of the genealogical process for a random sample at a neutral locus linked to a locus with selection follow from the results obtained for the selected locus. Sequence data from the alcohol dehydrogenase (Adh) region of Drosophila melanogaster are examined and compared to predictions based on the theory. It is found that the spatial distribution of nucleotide differences between Fast and Slow alleles of Adh is very similar to the spatial distribution predicted if balancing selection operates to maintain the allozyme variation at the Adh locus. The spatial distribution of nucleotide differences between different Slow alleles of Adh do not match the predictions of this simple model very well.

Within-population variation at the DNA level will rarely be studied by sequencing of loci of randomly chosen individuals. Instead, individuals will usually be chosen for sequencing based on some knowledge of their genotype. Data collected in this way require new sampling theory. Motivated by these observations, we have examined the sampling properties of a finite population model with two mutation processes and with no selection or recombination. One mutation process generates new alleles according to an infinite-alleles model, and the other generates polymorphisms at sites according to an infinite-sites model. A sample of n genes is considered. The stationary distribution of the number of segregating sites in a subsample from one of the allelic classes in the sample conditional on the allelic configuration of the sample is studied. A recursive scheme is developed to compute the moments of this distribution, and it is shown that the distribution is functionally independent of the number of additional alleles in the sample and their respective frequencies in the sample. For the case in which the sample contains only two alleles, the distribution of the number of segregating sites in a subsample containing both alleles conditional on the sample frequencies of the alleles is studied. The results are applied to the analysis of DNA sequences of two alleles found at the Adh locus of Drosophila melanogaster. No significant departure from the neutral model is detected.

The method proposed by Kaplan and Langley for estimating the extent of sequence divergence between related DNA's using restriction endonuclease maps is modified so that the estimates are easier to compute. In the two-species case, these modifications lead via a maximum likelihood approach to an estimate which is closely related to one recently suggested by Nei and Li (1979) and Gotoh et al. (1979). Simulation studies show that the modified estimates are comparable to those of Kaplan and Langley, providing that there is sufficient homology in the DNA segments of the related species. The M-species case, M greater than or equal to 3, is also discussed.

The behavior of the frequency spectrum of sites of transposable elements for the model proposed by Langley, Brookfield, and Kaplan ((1983) Genetics 104) is studied when some of the sites have weak additive selection against the host. In particular, it is shown that under certain conditions, the expected homozygosity at equilibrium will always be larger when there is variation in selection between sites than when such variation is absent.

A model of the evolution of a transposable element family in a Mendelian host population is proposed that incorporates heritable phenotypic mutations in the elements. The temporal behavior of the numbers of mutant and wild-type elements is studied, and the expected extinction time of the transposable element family is examined. Our results indicate that, if the mutant can be transposed equally well in the presence of the wild type, then it can be expected to be found in preponderance, whereas elements, such as retroviruses, where the transposing genome and its phenotypic expression are coupled, may be characterized by a low mutant frequency.

Statistical properties of the amount of divergence of members of a transposable element family are studied. The analysis is based on the model proposed by Langley et al. [5], describing the evolution of a family of selectively neutral transposable elements in a finite haploid population of size 2N. By considering the time back to the most recent common ancestor of two copies, both the probability of identity and the moments of the number of sites that differ between two sampled copies are obtained. Our analytic results are consistent with the numerical results of Ohta [8] for a similar model. The effects of gene conversion are also examined. In agreement with Slatkin [9], we find that gene conversion has a minimal effect on the probability of identity providing that the rate of deletion is sufficiently large.

SummaryA population genetics model of the role of asymmetric pairing and unequal exchange in the stabilization of transposable element copy number in natural populations is proposed and analysed. Monte Carlo simulations indicate that the approximations incorporated into the analysis are robust in the relevant parameter ranges. Given several simple assumptions concerning transposition and excision, equal and unequal exchange, and chromosome structure, predictions of the relative numbers of transposable elements in various regions of theDrosophila melanogastergenome are compared to the observed distribution ofroo/B104elements across chromosomal regions with differing rates of exchange, and betweenXchromosomes and autosomes. There is no indication of an accumulation of elements in the distal regions of chromosomes, which is expected if unequal exchange is reduced concomitantly with normal crossing over in the distal regions. There is, however, an indication of an excess of elements relative to physical length in the proximal regions of the chromosomes, which also have restricted crossing over. This observation is qualitatively consistent with the model's predictions. The observed distribution of elements between the mid-sections of theXchromosomes and autosomes is consistent with the predictions of one of two models of unequal exchange.

A new estimate of the sequence divergence of mitochondrial DNA in related species using restriction enzyme maps is constructed. The estimate is derived assuming a simple Posisson-like model for the evolutionary process and is chosen to maximize an expression which is a reasonable approximation to the true likelihood of the restriction map data. Using this estimate, four sets of mitochondrial DNA data are analyzed and discussed.

The number of selectively neutral polymorphic sites in a random sample of genes can be affected by ancestral selectively favored substitutions at linked loci. The degree to which this happens depends on when in the history of the sample the selected substitutions happen, the strength of selection and the amount of crossing over between the sampled locus and the loci at which the selected substitutions occur. This phenomenon is commonly called hitchhiking. Using the coalescent process for a random sample of genes from a selectively neutral locus that is linked to a locus at which selection is taking place, a stochastic, finite population model is developed that describes the steady state effect of hitchhiking on the distribution of the number of selectively neutral polymorphic sites in a random sample. A prediction of the model is that, in regions of low crossing over, strongly selected substitutions in the history of the sample can substantially reduce the number of polymorphic sites in a random sample of genes from that expected under a neutral model.

Transposable elements are DNA sequences, found throughout eukaryotes, that transpose replicatively and cause numerous genetic and developmental effects on their hosts. A model of the evolution of transposable elements in Mendelian populations is proposed. From its analysis, formulas for the mean copy number and frequency spectrum are obtained.