Mapping quantitative trait loci with extreme discordant sib pairs: sampling considerations.

Elsewhere we have proposed the use of extreme discordant sib pairs (EDSPs) for mapping quantitative trait loci in humans. Here we present sample sizes necessary to achieve a given level of power with this study design, as well as the number of sibs that need to be screened to obtain the required sample. Further, we present simple formulas for adjusting sample sizes to account for variable significance levels and power, as well as the density and informativeness of linkage markers in a multipoint sib-pair analysis. We conclude that with EDSPs, the most powerful study design, the smallest genetic effect detectable with a realistic sample size is approximately 10% of the variance of the trait.     

A two-stage variable-stringency semiparametric method for mapping quantitative-trait loci with the use of genomewide-scan data on sib pairs

Genomewide scans for mapping loci have proved to be extremely powerful and popular. We present a semiparametric method of mapping a quantitative-trait locus (QTL) or QTLs with the use of sib-pair data generated from a two-stage genomic scan. In a two-stage genomic scan, either the entire genome or a large portion of the genome is saturated with low-density markers at the first stage. At the second stage, the intervals that are identified as probable locations of the trait loci, by means of analysis of data from the first stage, are then saturated with higher-density markers. These data are then analyzed for fine mapping of the loci. Our statistical strategy for analysis of data from the first stage is a low-stringency method based on the rank correlation of squared trait-difference values of the sib pairs and the estimated identity-by-descent scores at the marker loci. We suggest the use of a low-stringency method at the first stage, to save on computational time and to avoid missing any marker interval that may contain the trait loci. For analysis of data from the second stage, we have developed a high-stringency nonparametric-regression approach, using the kernel-smoothing technique. Through extensive simulations, we show that this approach is more powerful than is a currently used method for mapping QTLs by use of sib pairs, particularly in the presence of dominance and epistatic effects at the trait loci.     

A linkage strategy for detection of human quantitative-trait loci. I. Generalized relative risk ratios and power of sib pairs with extreme trait values.

We generalize the concept of the relative risk ratio (lambda) to the case of quantitative traits, to take into account the various trait outcomes of a relative pair. Formulas are derived to express the expected proportions of genes shared identical by descent by a sib pair, in terms of the generalized lambda's for sib pairs (lambda S), parent-offspring pairs (lambda O), and monozygotic twins (lambda M) and in terms of the recombination fraction, with the assumption of no residual correlations. If residual correlations are nonzero among relative pairs, we assume that they are the same among sib pairs, parent-offspring pairs, and monozygotic twins, and we employ a slightly different definition for the generalized lambda so that the same set of formulas still hold. The power (or, the sample size necessary) to detect quantitative-trait loci (QTLs) by use of extreme sib pairs (ESPs) is shown to be a function of the three generalized lambda's. Since lambda M can be derived by use of values of lambda S and lambda O, estimates of the latter two lambda's will suffice for the analysis of power and the necessary sample sizes of ESPs, for a QTL linkage study.     

A linkage strategy for detection of human quantitative-trait loci. II. Optimization of study designs based on extreme sib pairs and generalized relative risk ratios.

We are concerned here with practical issues in the application of extreme sib-pair (ESP) methods to quantitative traits. Two important factors-namely, the way extreme trait values are defined and the proportions in which different types of ESPs are pooled, in the analysis-are shown to determine the power and the cost effectiveness of a study design. We found that, in general, combining reasonable numbers of both extremely discordant and extremely concordant sib pairs that were available in the sample is more powerful and more cost effective than pursuing only a single type of ESP. We also found that dividing trait values with a less extreme threshold at one end or at both ends of the trait distribution leads to more cost-effective designs. The notion of generalized relative risk ratios (the lambda methods, as described in the first part of this series of two articles) is used to calculate the power and sample size for various choices of polychotomization of trait values and for the combination of different types of ESPs. A balance then can be struck among these choices, to attain an optimum design.     

The power of interval mapping of quantitative trait loci, using selected sib pairs.

The interval-mapping procedure of Fulker and Cardon for analysis of a quantitative-trait loci (QTL) is extended for application to selected samples of sib pairs. Phenotypic selection of sib pairs, which is known to yield striking increases in power when a single marker is used, provides further increases in power when the interval-mapping approach is used. The greatest benefits of the combined approach are apparent with coarse maps, where QTLs of relatively modest (15%-20%) heritability can be detected with widely spaced markers (40-60 cM apart) in reasonably sized sibling samples. Useful information concerning QTL location is afforded by interval mapping in both selected and unselected samples.     

Linkage analysis of extremely discordant and concordant sibling pairs identifies quantitative-trait loci that influence variation in the human personality trait neuroticism

Several theoretical studies have suggested that large samples of randomly ascertained siblings can be used to ascertain phenotypically extreme individuals and thereby increase power to detect genetic linkage in complex traits. Here, we report a genetic linkage scan using extremely discordant and concordant sibling pairs, selected from 34,580 sibling pairs in the southwest of England who completed a personality questionnaire. We performed a genomewide scan for quantitative-trait loci (QTLs) that influence variation in the personality trait of neuroticism, or emotional stability, and we established genomewide empirical significance thresholds by simulation. The maximum pointwise P values, expressed as the negative logarithm (base 10), were found on 1q (3.95), 4q (3.84), 7p (3.90), 12q (4.74), and 13q (3.81). These five loci met or exceeded the 5% genomewide significance threshold of 3.8 (negative logarithm of the P value). QTLs on chromosomes 1, 12, and 13 are likely to be female specific. One locus, on chromosome 1, is syntenic with that reported from QTL mapping of rodent emotionality, an animal model of neuroticism, suggesting that some animal and human QTLs influencing emotional stability may be homologous.     

Multipoint interval mapping of quantitative trait loci, using sib pairs.

The sib-pair interval-mapping procedure of Fulker and Cardon is extended to take account of all available marker information on a chromosome simultaneously. The method provides a computationally fast multipoint analysis of sib-pair data, using a modified Haseman-Elston approach. It gives results very similar to those of the earlier interval-mapping procedure when marker information is relatively uniform and a coarse map is used. However, there is a substantial improvement over the original method when markers differ in information content and/or when a dense map is employed. The method is illustrated by using simulated sib-pair data.     

Anxiety and depression in twin and sib pairs extremely discordant and concordant for neuroticism: prodromus to a linkage study.

Multivariate modelling of anxiety and depression data in twins has suggested that the two phenotypes are largely underpinned by one genetic factor, while other studies have indicated a relationship between these disorders and the neuroticism personality trait. As part of a study to identify quantitative trait loci for anxiety and depression, questionnaire responses and interviews of 15,027 Australian twins and 11,389 of their family members conducted during the past 20 years were reviewed to identify individuals with neuroticism, anxiety and depression scores in the upper or lower deciles of the population. This information was then used to identify extreme discordant and concordant (EDAC) sib pairs. 1373 high-scoring and 1571 low-scoring subjects (2357 sib pairs) were selected for participation, and extremely high participation rates were achieved, with over 90% of contactable prospective participants completing the interview phase, and over 90% of these providing blood or buccal samples. Participation bias arising from the nature of the selection variables was minimal, with only a small difference between rates of interview participation among prospective participants with high and low selection scores (89.4% vs 91.6%). The interview permitted the diagnosis of depression and several anxiety disorders (OCD, agoraphobia, panic disorder, generalised anxiety disorder) in this sample according to DSM-IV criteria. The methodology for selection of prospective subjects was demonstrated to be extremely successful, with highly significant differences in depression and anxiety disorder prevalence rates between individuals in the two selection groups. The success of this EDAC sampling scheme will enhance the power for QTL linkage and association analysis in this sample.     

On the use of concordant pairs in matched case-control studies

A new estimator of the common odds ratio in one-to-one matched case-control studies is proposed. The connection between this estimator and the James-Stein estimating procedure is highlighted through the argument of estimating functions. Comparisons are made between this estimator, the conditional maximum likelihood estimator, and the estimator ignoring the matching in terms of finite sample bias, mean squared error, coverage probability, and length of confidence interval. In many situations, the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching. The extension to multiple risk factors is also outlined.     

Cost-effective sib-pair designs in the mapping of quantitative-trait loci.

The extreme discordant-sib-pair design has been found to be the most powerful, across most genetic models. In this paper, we address two of the most frequently asked questions related to this design. First, under the extreme discordant-sib-pair design, a large number of people have to be screened for the phenotype of interest, before the desired number of discordant sibs can be collected for genotyping and linkage analysis. When the phenotyping cost is not negligible compared with the genotyping cost, such methods might not be cost effective. The second question is how sensitive the cost is to the genetic model and allele frequency. In this paper, we compare the cost under different sampling strategies, different genetic models, and different phenotyping:genotyping cost ratios. Because our knowledge of the underlying genetic model for a trait is limited, the discordant-sib-pair design proves to be the most robust. When the cost for screening probands is not included, the design that genotypes sibs with one sib in the top 10% and the other sib in the bottom 30% of the population with respect to the trait of interest is, across most models studied, the optimum among the designs considered in this paper. The cost under this design, across different genetic models, appears to be relatively robust to allele frequency and model type, whether additive or dominant. If probands initially must be screened as well, then 25% appears to be the optimal portions of the upper and lower distributions to be studied.     

A simulation study of the effects of assignment of prior identity-by-descent probabilities to unselected sib pairs, in covariance-structure modeling of a quantitative-trait locus.

Sib pair-selection strategies, designed to identify the most informative sib pairs in order to detect a quantitative-trait locus (QTL), give rise to a missing-data problem in genetic covariance-structure modeling of QTL effects. After selection, phenotypic data are available for all sibs, but marker data-and, consequently, the identity-by-descent (IBD) probabilities-are available only in selected sib pairs. One possible solution to this missing-data problem is to assign prior IBD probabilities (i.e., expected values) to the unselected sib pairs. The effect of this assignment in genetic covariance-structure modeling is investigated in the present paper. Two maximum-likelihood approaches to estimation are considered, the pi-hat approach and the IBD-mixture approach. In the simulations, sample size, selection criteria, QTL-increaser allele frequency, and gene action are manipulated. The results indicate that the assignment of prior IBD probabilities results in serious estimation bias in the pi-hat approach. Bias is also present in the IBD-mixture approach, although here the bias is generally much smaller. The null distribution of the log-likelihood ratio (i.e., in absence of any QTL effect) does not follow the expected null distribution in the pi-hat approach after selection. In the IBD-mixture approach, the null distribution does agree with expectation.     

A unified sampling approach for multipoint analysis of qualitative and quantitative traits in sib pairs

Recent advances in molecular biology have enhanced the opportunity to conduct multipoint mapping for complex diseases. Concurrently, one sees a growing interest in the use of quantitative traits in linkage studies. Here, we present a multipoint sib-pair approach to locate the map position (tau) of a trait locus that controls the observed phenotype (qualitative or quantitative), along with a measure of statistical uncertainty. This method builds on a parametric representation for the expected identical-by-descent statistic at an arbitrary locus, conditional on an event reflecting the sampling scheme, such as affected sib pairs, for qualitative traits, or extreme discordant (ED) sib pairs, for quantitative traits. Our results suggest that the variance about tau&d4;, the estimator of tau, can be reduced by as much as 60%-70% by reducing the length of intervals between markers by one half. For quantitative traits, we examine the precision gain (measured by the variance reduction in tau&d4;) by genotyping extremely concordant (EC) sib pairs and including them along with ED sib pairs in the statistical analysis. The precision gain depends heavily on the residual correlation of the quantitative trait for sib pairs but considerably less on the allele frequency and exact genetic mechanism. Since complex traits involve multiple loci and, hence, the residual correlation cannot be ignored, our finding strongly suggests that one should incorporate EC sib pairs along with ED sib pairs, in both design and analysis. Finally, we empirically establish a simple linear relationship between the magnitude of precision gain and the ratio of the number of ED pairs to the number of EC pairs. This relationship allows investigators to address issues of cost effectiveness that are due to the need for phenotyping and genotyping subjects.     

Mapping trait loci by use of inferred ancestral recombination graphs

Large-scale association studies are being undertaken with the hope of uncovering the genetic determinants of complex disease. We describe a computationally efficient method for inferring genealogies from population genotype data and show how these genealogies can be used to fine map disease loci and interpret association signals. These genealogies take the form of the ancestral recombination graph (ARG). The ARG defines a genealogical tree for each locus, and, as one moves along the chromosome, the topologies of consecutive trees shift according to the impact of historical recombination events. There are two stages to our analysis. First, we infer plausible ARGs, using a heuristic algorithm, which can handle unphased and missing data and is fast enough to be applied to large-scale studies. Second, we test the genealogical tree at each locus for a clustering of the disease cases beneath a branch, suggesting that a causative mutation occurred on that branch. Since the true ARG is unknown, we average this analysis over an ensemble of inferred ARGs. We have characterized the performance of our method across a wide range of simulated disease models. Compared with simpler tests, our method gives increased accuracy in positioning untyped causative loci and can also be used to estimate the frequencies of untyped causative alleles. We have applied our method to Ueda et al.'s association study of CTLA4 and Graves disease, showing how it can be used to dissect the association signal, giving potentially interesting results of allelic heterogeneity and interaction. Similar approaches analyzing an ensemble of ARGs inferred using our method may be applicable to many other problems of inference from population genotype data.     

Mapping quantitative trait loci in selected breeding populations: A segregation distortion approach

Quantitative trait locus (QTL) mapping is often conducted in line-crossing experiments where a sample of individuals is randomly selected from a pool of all potential progeny. QTLs detected from such an experiment are important for us to understand the genetic mechanisms governing a complex trait, but may not be directly relevant to plant breeding if they are not detected from the breeding population where selection is targeting for. QTLs segregating in one population may not necessarily segregate in another population. To facilitate marker-assisted selection, QTLs must be detected from the very population which the selection is targeting. However, selected breeding populations often have depleted genetic variation with small population sizes, resulting in low power in detecting useful QTLs. On the other hand, if selection is effective, loci controlling the selected trait will deviate from the expected Mendelian segregation ratio. In this study, we proposed to detect QTLs in selected breeding populations via the detection of marker segregation distortion in either a single population or multiple populations using the same selection scheme. Simulation studies showed that QTL can be detected in strong selected populations with selected population sizes as small as 25 plants. We applied the new method to detect QTLs in two breeding populations of rice selected for high grain yield. Seven QTLs were identified, four of which have been validated in advanced generations in a follow-up study. Cloned genes in the vicinity of the four QTLs were also reported in the literatures. This mapping-by-selection approach provides a new avenue for breeders to improve breeding progress. The new method can be applied to breeding programs not only in rice but also in other agricultural species including crops, trees and animals.     

The International Psoriasis Genetics Study: assessing linkage to 14 candidate susceptibility loci in a cohort of 942 affected sib pairs

In an effort to confirm previously reported linkages to psoriasis, we analyzed 942 affected sibling pairs (ASPs) from 710 pedigrees for 53 polymorphic microsatellites spanning 14 psoriasis candidate regions at an intermarker spacing of ~5 cM. Maximum LOD score (MLS) analysis of ASPs yielded allele sharing of 60% for markers within the major histocompatibility complex (MHC) (P=2×10^-14), which yielded a gene-specific λ_s of 1.6. Across the remainder of the genome, the strongest evidence of allele sharing was obtained on chromosomes 16q (D16S3032; MLS=1.3; P=.007) and 10q22–q23 (D10S2327; MLS=1.1; P=.012). None of the remaining loci exceeded MLS=0.9, the value expected to occur by chance once in this study. In agreement with previous studies, strong linkage disequilibrium was also observed between psoriasis and the MHC (pedigree disequilibrium test P=3.9×10^-8 for D6S1014). Two psoriasis-associated MHC haplotypes were identified with the haplotype-based transmission/disequilibrium test. Analysis of only those families carrying either of these haplotypes significantly increased the chromosome 16q LOD score from 1.3 to 2.4 (P=.045). These results underscore the importance of the MHC in psoriasis and provide a rationale for more-detailed examination of candidate regions on chromosomes 16q and 10q.     

Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny

In plants and laboratory animals, QTL mapping is commonly performed using F(2) or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F(2) individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F(3) progeny derived from selfing F(2) plants in place of the F(2) phenotype itself. All F(3) progeny derived from the same F(2) plant belong to the same F(2:3) family, denoted by F(2:3). If the size of each F(2:3) family (the number of F(3) progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F(2) plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F(2) marker genotypes and F(3) average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F(2:3) strategy. We also propose to combine both the F(2) phenotypes and the F(2:3) average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F(2:3) families of heterozygous F(2) plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F(2) design, even if only a single F(3) progeny is collected from each F(2:3) family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.     

Linkage analysis of extremely discordant and concordant sibling pairs identifies quantitative trait loci influencing variation in human menopausal age

Age at natural menopause may be used as parameter for evaluating the rate of ovarian aging. Environmental factors determine only a small part of the large variation in menopausal age. Studies have shown that genetic factors are likely to be involved in variation in menopausal age. To identify quantitative-trait loci for this trait, we performed a genomewide linkage study with age at natural menopause as a continuous quantitative phenotype in Dutch sister pairs, through use of a selective sampling scheme. A total of 165 families were ascertained using extreme selected sampling and were genotyped for 417 markers. Data were analyzed by Haseman-Elston regression and by an adjusted variance-components analysis. Subgroup analyses for early and late menopausal age were conducted by Haseman-Elston regression. In the adjusted variance-components analysis, 12 chromosomes had a LOD score of > or =1.0. Two chromosomal regions showed suggestive linkage: 9q21.3 (LOD score 2.6) and Xp21.3 (LOD score 3.1). Haseman-Elston regression showed rather similar locations of the peaks but yielded lower LOD scores. A permutation test to obtain empirical P values resulted in a significant peak on the X chromosome. To our knowledge, this is the first study to attempt to identify loci responsible for variability in menopausal age and in which several chromosomal regions were identified with suggestive and significant linkage. Although the finding of the region on the X chromosome comes as no surprise, because of its widespread involvement in premature ovarian failure, the definition of which particular gene is involved is of great interest. The region on chromosome 9 deserves further consideration. Both findings require independent confirmation.     

Segregation and linkage analysis of serum angiotensin I-converting enzyme levels: evidence for two quantitative-trait loci.

Human serum angiotensin I-converting enzyme (ACE) levels vary substantially between individuals and are highly heritable. Segregation analysis in European families has shown that more than half of the total variability in ACE levels is influenced by quantitative-trait loci (QTL). One of these QTLs is located within or close to the ACE locus itself. Combined segregation/linkage analysis in a series of African Caribbean families from Jamaica shows that the ACE insertion-deletion polymorphism is in moderate linkage disequilibrium with an ACE-linked QTL. Linkage analysis with a highly informative polymorphism at the neighboring growth-hormone gene (GH) shows surprisingly little support for linkage (LOD score [Z] = 0.12). An extended analysis with a two-QTL model, where an ACE-linked QTL interacts additively with an unlinked QTL, significantly improves both the fit of the model (P = .002) and the support for linkage between the ACe-linked QTL interacts additively with an unlinked QTL, significantly improves both the fit of the model (P = .002) and the support for linkage between the ACe-linked QTL and GH polymorphism (Z = 5.0). We conclude that two QTLs jointly influence serum ACE levels in this population. One QTL is located within or close to the ACE locus and explains 27% of the total variability; the second QTL is unlinked to the ACE locus and explains 52% of the variability. The identification of the molecular mechanisms underlying both QTLs is necessary in order to interpret the role of ACE in cardiovascular disease.     

HLA-DR typing in identical twins with insulin-dependent diabetes: difference between concordant and discordant pairs.

A total of 106 pairs of identical twins, of whom 56 were concordant and 50 discordant for insulin-dependent diabetes, were typed for HLA-DR. In both the concordant and discordant groups there was a high prevalence of the antigens DR3 and DR4, a low prevalence of DR5 and DR7, and a virtual absence of DR2. The heterozygous phenotype DR3,DR4 was more prevalent in concordant than discordant pairs. This was therefore the first demonstration of a genetic difference between concordant and discordant identical twin pairs. These findings suggest that possession of both DR3 and DR4 antigens confers a greater genetic predisposition to insulin-dependent diabetes than does the possession of either antigen alone.     

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.