A power study of bivariate LOD score analysis of a complex trait and fear/discomfort with strangers

Complex diseases are often reported along with disease-related traits (DRT). Sometimes investigators consider both disease and DRT phenotypes separately and sometimes they consider individuals as affected if they have either the disease or the DRT, or both. We propose instead to consider the joint distribution of the disease and the DRT and do a linkage analysis assuming a pleiotropic model. We evaluated our results through analysis of the simulated datasets provided by Genetic Analysis Workshop 14. We first conducted univariate linkage analysis of the simulated disease, Kofendrerd Personality Disorder and one of its simulated associated traits, phenotype b (fear/discomfort with strangers). Subsequently, we considered the bivariate phenotype, which combined the information on Kofendrerd Personality Disorder and fear/discomfort with strangers. We developed a program to perform bivariate linkage analysis using an extension to the Elston-Stewart peeling method of likelihood calculation. Using this program we considered the microsatellites within 30 cM of the gene pleiotropic for this simulated disease and DRT. Based on 100 simulations of 300 families we observed excellent power to detect linkage within 10 cM of the disease locus using the DRT and the bivariate trait.     

Powerful allele sharing statistics for nonparametric linkage analysis

Nonparametric linkage analysis is widely used to map susceptibility genes for complex diseases. This paper introduces six nonparametric statistics for measuring marker allele sharing among the affected members of a pedigree. We compare the power of these new statistics and three previous statistics to detect linkage with Mendelian diseases having recessive, additive, and dominant modes of inheritance. The nine statistics represent all possible combinations of three different IBD scoring functions and three different schemes for sampling genes among affecteds. Our results strongly suggest that the statistic T(rec)(blocks) is best for recessive traits, while the two statistics T(kin)(pairs) and T(all)(kin) vie for best for an additive trait. The best statistic for a dominant trait is less clear. The statistics T(kin)(pairs) and T(all)(kin) are equally promising for small sibships, but in extended pedigrees the statistics T(dom)(blocks) and T(dom)(pairs) appear best. For a complex trait, we advocate computing several of these statistics.     

Power of maximum HLOD tests to detect linkage to obesity genes

Background

We investigate the power of heterogeneity LOD test to detect linkage when a trait is determined by several major genes using Genetic Analysis Workshop 13 simulated data. We consider three traits, two of which are disease-causing traits: 1) the rate of change in body mass index (BMI); and 2) the maximum BMI; and 3) the disease itself (hypertension). Of interest is the power of "HLOD2", the maximum heterogeneity LOD obtained upon maximizing over the two genetic models.

Results

Using a trait phenotype Obesity Slope, we observe that the power to detect the two markers closest to the two genes (S1, S2) at the 0.05 level using HLOD2 is 13% and 10%. The power of HLOD2 for Max BMI phenotype is 12% and 9%. The corresponding values for the Hypertension phenotype are 8% and 6%.

Conclusion

The power to detect linkage to the slope genes is quite low. But the power using disease-related traits as a phenotype is greater than the power using the disease (hypertension) phenotype.

     

Parametric and nonparametric multipoint linkage analysis with imprinting and two-locus-trait models: application to mite sensitization

We present two extensions to linkage analysis for genetically complex traits. The first extension allows investigators to perform parametric (LOD-score) analysis of traits caused by imprinted genes-that is, of traits showing a parent-of-origin effect. By specification of two heterozygote penetrance parameters, paternal and maternal origin of the mutation can be treated differently in terms of probability of expression of the trait. Therefore, a single-disease-locus-imprinting model includes four penetrances instead of only three. In the second extension, parametric and nonparametric linkage analysis with two trait loci is formulated for a multimarker setting, optionally taking imprinting into account. We have implemented both methods into the program GENEHUNTER. The new tools, GENEHUNTER-IMPRINTING and GENEHUNTER-TWOLOCUS, were applied to human family data for sensitization to mite allergens. The data set comprises pedigrees from England, Germany, Italy, and Portugal. With single-disease-locus-imprinting MOD-score analysis, we find several regions that show at least suggestive evidence for linkage. Most prominently, a maximum LOD score of 4.76 is obtained near D8S511, for the English population, when a model that implies complete maternal imprinting is used. Parametric two-trait-locus analysis yields a maximum LOD score of 6.09 for the German population, occurring exactly at D4S430 and D18S452. The heterogeneity model specified for analysis alludes to complete maternal imprinting at both disease loci. Altogether, our results suggest that the two novel formulations of linkage analysis provide valuable tools for genetic mapping of multifactorial traits.     

Linkage analysis: principles and methods for the analysis of human quantitative traits.

Currently, mapping genes for complex human traits relies on two complementary approaches, linkage and association analyses. Both suffer from several methodological and theoretical limitations, which can considerably increase the type-1 error rate and reduce the power to map human quantitative trait loci (QTL). This review focuses on linkage methods for QTL mapping. It summarizes the most common linkage statistics used, namely Haseman-Elston-based methods, variance components, and statistics that condition on trait values. Methods developed more recently that accommodate the X-chromosome, parental imprinting and allelic association in linkage analysis are also summarized. The type-I error rate and power of these methods are discussed. Finally, rough guidelines are provided to help guide the choice of linkage statistics.     

Multivariate variance-components analysis of longitudinal blood pressure measurements from the Framingham Heart Study

Multivariate variance-components analysis provides several advantages over univariate analysis when studying correlated traits. It can test for pleiotropy or (in the longitudinal context) gene x age interaction. It can also have more power than univariate analyses to detect a quantitative trait locus influencing several traits. We apply multivariate variance components to longitudinal systolic blood pressure data from the Framingham Heart Study. We find evidence for a polygenic influence on blood pressure (heritabilities at different ages range from 27% to 38%). Tests based on a factor-analytic parameterization of the polygenic variance find significant (p < 2 x 10(-3)) evidence that different genes affect blood pressure at different ages. Still, estimates for the proportion of polygenic variance due to shared genes ran as high as 85% for some trait pairs. Univariate and multivariate linkage analyses replicate previous linkage results on chromosome 17 (maximum LOD scores of 2.2 and 2.4, respectively). In this study, multivariate analysis provides no increase in power; this is likely due to the strong positive correlation in systolic blood pressure measured at different ages.     

Some capabilities for model-based and model-free linkage analysis using the program package S.A.G.E. (Statistical Analysis for Genetic Epidemiology)

For both model-free and model-based linkage analysis the S.A.G.E. (Statistical Analysis for Genetic Epidemiology) program package has some unique capabilities in analyzing both continuous traits and binary traits with variable age of onset. Here we highlight model-based linkage analysis of a quantitative trait (plasma dopamine β hydroxylase) that is known to be largely determined by monogenic inheritance, using a prior segregation analysis to produce the best fitting model for the trait. For a binary trait with variable age of onset (schizophrenia), we illustrate how using age of onset information to obtain a quantitative susceptibility trait leads to more statistically significant linkage signals, suggesting better power.     

Collection of pedigree data for genetic analysis in isolate populations

Pedigree data are useful for a wealth of research purposes in human population biology and genetics. The collection of extended pedigrees represents the most powerful sampling design for quantitative genetic and linkage studies of both normal and disease-related quantitative traits. In this paper we outline an approach for collecting pedigree data in stable isolate populations. As an example, the pedigree for the Jirel population, which was obtained using the methods presented, is described. The Jirel pedigree contains 2,000 study participants and more than 62,000 pairwise relationships that are informative for genetic analysis. Once such pedigrees are genetically characterized by a genome scan for a given trait, they become an invaluable resource for future genetic studies of any quantitative trait.     

Improved statistics for genome-wide interaction analysis

Recently, Wu and colleagues [1] proposed two novel statistics for genome-wide interaction analysis using case/control or case-only data. In computer simulations, their proposed case/control statistic outperformed competing approaches, including the fast-epistasis option in PLINK and logistic regression analysis under the correct model; however, reasons for its superior performance were not fully explored. Here we investigate the theoretical properties and performance of Wu et al.'s proposed statistics and explain why, in some circumstances, they outperform competing approaches. Unfortunately, we find minor errors in the formulae for their statistics, resulting in tests that have higher than nominal type 1 error. We also find minor errors in PLINK's fast-epistasis and case-only statistics, although theory and simulations suggest that these errors have only negligible effect on type 1 error. We propose adjusted versions of all four statistics that, both theoretically and in computer simulations, maintain correct type 1 error rates under the null hypothesis. We also investigate statistics based on correlation coefficients that maintain similar control of type 1 error. Although designed to test specifically for interaction, we show that some of these previously-proposed statistics can, in fact, be sensitive to main effects at one or both loci, particularly in the presence of linkage disequilibrium. We propose two new "joint effects" statistics that, provided the disease is rare, are sensitive only to genuine interaction effects. In computer simulations we find, in most situations considered, that highest power is achieved by analysis under the correct genetic model. Such an analysis is unachievable in practice, as we do not know this model. However, generally high power over a wide range of scenarios is exhibited by our joint effects and adjusted Wu statistics. We recommend use of these alternative or adjusted statistics and urge caution when using Wu et al.'s originally-proposed statistics, on account of the inflated error rate that can result.     

Direct power comparisons between simple LOD scores and NPL scores for linkage analysis in complex diseases.

Several methods have been proposed for linkage analysis of complex traits with unknown mode of inheritance. These methods include the LOD score maximized over disease models (MMLS) and the "nonparametric" linkage (NPL) statistic. In previous work, we evaluated the increase of type I error when maximizing over two or more genetic models, and we compared the power of MMLS to detect linkage, in a number of complex modes of inheritance, with analysis assuming the true model. In the present study, we compare MMLS and NPL directly. We simulated 100 data sets with 20 families each, using 26 generating models: (1) 4 intermediate models (penetrance of heterozygote between that of the two homozygotes); (2) 6 two-locus additive models; and (3) 16 two-locus heterogeneity models (admixture alpha = 1.0,.7,.5, and.3; alpha = 1.0 replicates simple Mendelian models). For LOD scores, we assumed dominant and recessive inheritance with 50% penetrance. We took the higher of the two maximum LOD scores and subtracted 0.3 to correct for multiple tests (MMLS-C). We compared expected maximum LOD scores and power, using MMLS-C and NPL as well as the true model. Since NPL uses only the affected family members, we also performed an affecteds-only analysis using MMLS-C. The MMLS-C was both uniformly more powerful than NPL for most cases we examined, except when linkage information was low, and close to the results for the true model under locus heterogeneity. We still found better power for the MMLS-C compared with NPL in affecteds-only analysis. The results show that use of two simple modes of inheritance at a fixed penetrance can have more power than NPL when the trait mode of inheritance is complex and when there is heterogeneity in the data set.     

Regression-based sib pair linkage analysis for binary traits

The Haseman-Elston (HE) regression method offers a mathematically and computationally simpler alternative to variance-components (VC) models for the linkage analysis of quantitative traits. However, current versions of HE regression and VC models are not optimised for binary traits. Here, we present a modified HE regression and a liability-threshold VC model for binary-traits. The new HE method is based on the regression of a linear combination of the trait squares and the trait cross-product on the proportion of alleles identical by descent (IBD) at the putative locus, for sibling pairs. We have implemented both the new HE regression-based method and have performed analytic and simulation studies to assess its type 1 error rate and power under a range of conditions. These studies showed that the new HE method is well-behaved under the null hypothesis in large samples, is more powerful than both the original and the revisited HE methods, and is approximately equivalent in power to the liability-threshold VC model.     

Linkage analysis in the next-generation sequencing era

Linkage analysis was developed to detect excess co-segregation of the putative alleles underlying a phenotype with the alleles at a marker locus in family data. Many different variations of this analysis and corresponding study design have been developed to detect this co-segregation. Linkage studies have been shown to have high power to detect loci that have alleles (or variants) with a large effect size, i.e. alleles that make large contributions to the risk of a disease or to the variation of a quantitative trait. However, alleles with a large effect size tend to be rare in the population. In contrast, association studies are designed to have high power to detect common alleles which tend to have a small effect size for most diseases or traits. Although genome-wide association studies have been successful in detecting many new loci with common alleles of small effect for many complex traits, these common variants often do not explain a large proportion of disease risk or variation of the trait. In the past, linkage studies were successful in detecting regions of the genome that were likely to harbor rare variants with large effect for many simple Mendelian diseases and for many complex traits. However, identifying the actual sequence variant(s) responsible for these linkage signals was challenging because of difficulties in sequencing the large regions implicated by each linkage peak. Current 'next-generation' DNA sequencing techniques have made it economically feasible to sequence all exons or the whole genomes of a reasonably large number of individuals. Studies have shown that rare variants are quite common in the general population, and it is now possible to combine these new DNA sequencing methods with linkage studies to identify rare causal variants with a large effect size. A brief review of linkage methods is presented here with examples of their relevance and usefulness for the interpretation of whole-exome and whole-genome sequence data.     

Multivariate segregation analysis for quantitative traits in line crosses

Segregation analysis is a method of detecting major genes for quantitative traits without using marker information. It serves as an important tool in helping investigators to plan further studies such as quantitative trait loci mapping or more sophisticated genomic analyses. However, current methods of segregation analysis for a single trait typically have low statistical power. We propose a multivariate segregation analysis (MSA) that takes advantage of the correlation structure of multiple quantitative traits to detect major genes. This method not only increases the statistical power, but allows dissection of the genetic architecture underlying the trait complex. In MSA the observed phenotypes of multiple correlated traits are fitted to a multivariate Gaussian mixture model. Model parameters are estimated under the maximum likelihood framework via the expectation-maximization algorithm. The presence of major genes is tested using likelihood ratio test statistics. Pleiotropy is distinguished from close linkage by comparing three possible models using the Bayesian information criterion. Two simulation experiments were performed based on the F(2) mating design. In the first, the statistical properties of MSA under varying heritabilities and sample sizes were investigated and the results compared with those obtained from single-trait analysis. In the second simulation the efficacy of MSA in separating pleiotropy from close linkage was demonstrated. Finally, the new method was applied to real data and detected a major gene responsible for both plant height and tiller number in rice.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

Models and tests of linkage and association studies of quantitative trait locus for multi-allele marker Loci

In this paper, we explore models and tests for association and linkage studies of a quantitative trait locus (QTL) linked to a multi-allele marker locus. Based on the difference between an offspring's conditional trait means of receiving and not receiving an allele from a parent at marker locus, we propose three statistics T(m), T(m,row) and T(m,col) to test association or linkage disequilibrium between the marker locus and the QTL. These tests are composite tests, and use the offspring marginal sample means including offspring data of both homozygous and heterozygous parents. For the linkage study, we calculate the offspring's conditional trait mean given the allele transmission status of a heterozygous parent at the marker locus. Based on the difference between the conditional means of a transmitted and a nontransmitted allele from a heterozygous parent, we propose statistics T(parsi), T(satur), T(gen) and T(m,het) to perform composite tests of linkage between the marker locus and the quantitative trait locus in the presence of association. These tests only use the offspring data that are related to the heterozygous parents at the marker locus. T(parsi) is a parsimonious or allele-wise statistic, T(satur) and T(gen )are satured or genotype-wise statistics, and T(m,het) compares the row and column sample means for offspring data of heterozygous parents. After comparing the powers and the sample sizes, we conclude that T(parsi) has higher power than those of the bi-allele tests, T(satur), T(gen), and T(m,het). If there is tight linkage between the marker and the trait locus, T(parsi) is powerful in detecting linkage between the marker and the trait locus in the presence of association. By investigating the goodness-of-fit of T(parsi), we find that T(satur) does not gain much power compared to that of T(parsi). Moreover, T(parsi) takes into account the pattern of the data that is consistent with linkage and linkage disequilibrium. As the number of alleles at the marker locus increases, T(parsi) is very conservative, and can be useful even for sparse data. To illustrate the usefulness and the power of the methods proposed in this paper, we analyze the chromosome 6 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

A score test for the linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs

We propose a general likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from sib-pairs. We consider the likelihood of IBD data conditional on phenotypes and test the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction theta between the two loci. This method unifies the linkage analysis of qualitative and quantitative traits into a single inferential framework, yielding a simple and intuitive test statistic. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows sib-pairs from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. In particular, it allows the selection of sib-pairs based on their trait values and the analysis of only those pairs having the most informative phenotypes. The score test is based on the full likelihood, i.e. the likelihood based on all phenotype data rather than just differences of sib-pair phenotypes. Considering only phenotype differences, as in Haseman and Elston (1972) and Kruglyak and Lander (1995), may result in important losses in power. The linkage score test is derived under general genetic models for the trait, which may include multiple unlinked genes. Population genetic assumptions, such as random mating or linkage equilibrium at the trait loci, are not required. This score test is thus particularly promising for the analysis of complex human traits. The score statistic readily extends to accommodate incomplete IBD data at the test locus, by using the hidden Markov model implemented in the programs MAPMAKER/SIBS and GENEHUNTER (Kruglyak and Lander, 1995; Kruglyak et al., 1996). Preliminary simulation studies indicate that the linkage score test generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes.     

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation*

“Magic traits,” in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these “pseudomagic traits” can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.     

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

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

Multilocus linkage analysis of affected sib pairs

OBJECTIVE: The conventional affected sib pair methods evaluate the linkage information at a locus by considering only marginal information. We describe a multilocus linkage method that uses both the marginal information and information derived from the possible interactions among several disease loci, thereby increasing the significance of loci with modest effects. METHODS: Our method is based on a statistic that quantifies the linkage information contained in a set of markers. By a marker selection-reduction process, we screen a set of polymorphisms and select a few that seem linked to disease. RESULTS: We test our approach on genome scan data for inflammatory bowel disease (InfBD) and on simulated data. On real data we detect 6 of the 8 known InfBD loci; on simulated data we obtain improvements in power of up to 40% compared to a conventional single-locus method. CONCLUSION: Our extensive simulations and the results on real data show that our method is in general more powerful than single-locus methods in detecting disease loci responsible for complex traits. A further advantage of our approach is that it can be extended to make use of both the linkage and the linkage disequilibrium between disease loci and nearby markers.     

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.