Recent advances in human quantitative-trait-locus mapping: comparison of methods for selected sibling pairs

Computationally efficient multipoint linkage analysis on extended pedigrees for trait models with two contributing major Loci

We have developed a computationally efficient method for multipoint linkage analysis on extended pedigrees for trait models having a two-locus quantitative trait loci (QTL) effect. The method has been implemented in the program, hg_lod, which uses the Markov chain Monte Carlo (MCMC) method to sample realizations of descent patterns conditional on marker data, then calculates the trait likelihood for each realization by efficient exact computation. Given its computational efficiency, hg_lod can handle data on large pedigrees with a lot of unobserved individuals, and can compute accurate estimates of logarithm of odds (lod) scores at a much larger number of hypothesized locations than can any existing method. We have compared hg_lod to lm_twoqtl, the first publically available linkage program for trait models with two major loci, using simulated data. Results show that our method is orders of magnitude faster while the accuracy of QTL localization is retained. The efficiency of our method also facilitates analyses with multiple trait models, for example, sensitivity analysis. Additionally, since the MCMC sampling conditions only on the marker data, there is no need to resample the descent patterns to compute likelihoods under alternative trait models. This achieves additional computational efficiency.

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

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

Family-based analysis of a myocardial infarction endophenotype: comparison of sampling designs

The power of linkage analysis of a quantitative disease endophenotype was compared for the following family selection designs: 1) Random samples: randomly chosen nuclear families, 2) "coronary artery calcification (CAC)" samples: selection of each nuclear family through a proband with abnormally high levels of the simulated quantitative endophenotype, CAC, and (3) "MI" samples: selection of each nuclear family through a disease affected proband, in this case a proband who had been simulated to have a myocardial infarction (MI) event.

We assessed the power to detect linkage to five loci (two pairs of epistatic loci and one locus with an over-dominant allele) that were modeled as determinants of the simulated CAC levels. We did this using a Haseman-Elston regression-based linkage analysis of the adjusted CAC levels that considered each locus separately and then used a multiple regression extension of the Haseman-Elston method in which we considered the allele sharing at two true epistatic loci simultaneously and their interaction as possible factors related to the squared sibpair differences in adjusted CAC.

Based on comparison of the mean square root of the LOD scores, there was no one sampling design that resulted in consistently greater power for these five loci. That is, we observed significant locus-by-sampling-design interaction (p < 0.0001). We noted however, that the largest average score was observed for the epistasis between τ₃ and τ₄ (mean > 1.8, SE = 0.06) in the MI-selected samples and the CAC-selected samples.

Influence of genotyping error in linkage mapping for complex traits--an analytic study

Background

Despite the current trend towards large epidemiological studies of unrelated individuals, linkage studies in families are still thoroughly being utilized as tools for disease gene mapping. The use of the single-nucleotide-polymorphisms (SNP) array technology in genotyping of family data has the potential to provide more informative linkage data. Nevertheless, SNP array data are not immune to genotyping error which, as has been suggested in the past, could dramatically affect the evidence for linkage especially in selective designs such as affected sib pair (ASP) designs. The influence of genotyping error on selective designs for continuous traits has not been assessed yet.

Results

We use the identity-by-descent (IBD) regression-based paradigm for linkage testing to analytically quantify the effect of simple genotyping error models under specific selection schemes for sibling pairs. We show, for example, that in extremely concordant (EC) designs, genotyping error leads to decreased power whereas it leads to increased type I error in extremely discordant (ED) designs. Perhaps surprisingly, the effect of genotyping error on inference is most severe in designs where selection is least extreme. We suggest a genomic control for genotyping errors via a simple modification of the intercept in the regression for linkage.

Conclusion

This study extends earlier findings: genotyping error can substantially affect type I error and power in selective designs for continuous traits. Designs involving both EC and ED sib pairs are fairly immune to genotyping error. When those designs are not feasible the simple genomic control strategy that we suggest offers the potential to deliver more robust inference, especially if genotyping is carried out by SNP array technology.

Robust score statistics for QTL linkage analysis

The traditional variance components approach for quantitative trait locus (QTL) linkage analysis is sensitive to violations of normality and fails for selected sampling schemes. Recently, a number of new methods have been developed for QTL mapping in humans. Most of the new methods are based on score statistics or regression-based statistics and are expected to be relatively robust to non-normality of the trait distribution and also to selected sampling, at least in terms of type I error. Whereas the theoretical development of these statistics is more or less complete, some practical issues concerning their implementation still need to be addressed. Here we study some of these issues such as the choice of denominator variance estimates, weighting of pedigrees, effect of parameter misspecification, effect of non-normality of the trait distribution, and effect of incorporating dominance. We present a comprehensive discussion of the theoretical properties of various denominator variance estimates and of the weighting issue and then perform simulation studies for nuclear families to compare the methods in terms of power and robustness. Based on our analytical and simulation results, we provide general guidelines regarding the choice of appropriate QTL mapping statistics in practical situations.

QTL mapping under ascertainment

Mapping quantitative trait loci (QTL) using ascertained sibships is discussed. It is shown that under the standard normality assumption of variance components analysis the efficient scores are unchanged by ascertainment, and two different schemes of ascertainment correction suggested in the literature are asymptotically equivalent. The use of conditional maximum likelihood estimators derived under the normality assumption to estimate nuisance parameters is shown to result in only a small loss of power compared to the case of known parameters, even when the distribution of phenotypes is non-normal and/or the ascertainment criterion is ill defined.

Genome-wide scan for loci influencing quantitative immune response traits in the Belém family study: comparison of methods and summary of results

Here we report the results from a genome-wide linkage scan to identify genes and chromosomal regions that influence quantitative immune response traits, using multi-case leprosy and tuberculosis families from north-eastern Brazil. Total plasma IgE, antigen-specific IgG to Mycobacterium leprae soluble antigen (MLSA), M. tuberculosis soluble antigen (MTSA) and M. tuberculosis purified protein derivative (PPD), and antigen-specific lymphocyte proliferation (stimulation index or SI) and interferon-gamma (IFN-gamma) release to MLSA and PPD, were measured in 16 tuberculosis (184 individuals) and 21 leprosy (177 individuals) families. The individuals were genotyped at 382 autosomal microsatellite markers across the genome. The adjusted immune-response phenotypes were analysed using a variety of variance components and regression-based methods. These analyses highlighted a number of practical issues and problems with regard to implementation of the methods and, interestingly, differences were observed between several standard statistical and genetic analysis packages used. From this we determined that, for this set of traits in these pedigrees, significant p values for linkage using variance components analysis, supported by significance using the Visscher-Hopper modification of the Haseman-Elston method, provided the most compelling evidence for linkage. Using these criteria, linkage (5.8 x 10(-5) < p < 0.008) was seen for: total plasma IgE on chromosome 2; IgG to MLSA on chromosomes 8, 17 and 21; IgG to PPD on chromosome 12; SI to PPD on chromosome 1; IFN-gamma to MLSA on chromosomes 6, 7, 10, 12 and 14; and IFN-gamma to PPD on chromosomes 1, 16 and 19.

Genome scans with gene-covariate interaction

Genetic models for gene-covariate interactions are described. Methods of linkage analysis that utilize special features of these models and the corresponding score statistics are derived. Their power is compared with that of simple genome scans that ignore these special features, and substantial gains in power are observed when the gene-covariate interaction is strong. Quantitative trait mapping in randomly ascertained sibships and affected sibpair mapping are discussed. For the latter case, a simpler statistic is proposed that has similar performance to the score statistic, but does not require the estimation of nuisance parameters. Since the nuisance parameters are not estimable solely from affected sib-pair data, this statistic would be much easier to apply in practice. Similarities with linkage analysis of models for longitudinal data and multivariate phenotypes are also briefly discussed. Approximations for the P-value and power are derived under the framework of local alternatives.

QTL mapping with discordant and concordant sibling pairs: new statistics and new design strategies

The term "extreme discordant and concordant" (EDAC) sampling has been used to describe a variety of strategies for quantitative trait locus mapping using sibling pairs sampled from the corners of the bivariate trait distribution. The principle of the design is to gain efficiency by genotyping only the most informative of the available sibling pairs. EDAC-type designs have been studied in a number of papers, and have been applied in a few others. This literature is somewhat out of date, however, because there are many new statistics that are appropriate for EDAC data. With newer statistics, the power of EDAC designs can be improved. Moreover, the relative power of different designs must be re-evaluated, because the newer statistics improve the power of some designs more than others. That is, there is a circular relationship between design and statistic choices. In this report, we review a number of available design and statistic choices for EDAC studies, and use simulation to show what statistics are most powerful for each design. We then use those more powerful statistics to suggest strategies for making design choices among various EDAC and non-EDAC designs that use sibling pairs. We find that when genotyping must be minimized, an EDAC design with predominantly discordant pairs is the best choice, and when a balance of genotyping and phenotyping effort must be achieved, single proband ascertainment can do better. We also show that moderately selected samples (as opposed to very extreme samples) can be an efficient choice for many studies.

Selection of eating-disorder phenotypes for linkage analysis

Vulnerability to anorexia nervosa (AN) and bulimia nervosa (BN) arise from the interplay of genetic and environmental factors. To explore the genetic contribution, we measured over 100 psychiatric, personality, and temperament phenotypes of individuals with eating disorders from 154 multiplex families accessed through an AN proband (AN cohort) and 244 multiplex families accessed through a BN proband (BN cohort). To select a parsimonious subset of these attributes for linkage analysis, we subjected the variables to a multilayer decision process based on expert evaluation and statistical analysis. Criteria for trait choice included relevance to eating disorders pathology, published evidence for heritability, and results from our data. Based on these criteria, we chose six traits to analyze for linkage. Obsessionality, Age-at-Menarche, and a composite Anxiety measure displayed features of heritable quantitative traits, such as normal distribution and familial correlation, and thus appeared ideal for quantitative trait locus (QTL) linkage analysis. By contrast, some families showed highly concordant and extreme values for three variables-lifetime minimum Body Mass Index (lowest BMI attained during the course of illness), concern over mistakes, and food-related obsessions-whereas others did not. These distributions are consistent with a mixture of populations, and thus the variables were matched with covariate linkage analysis. Linkage results appear in a subsequent report. Our report lays out a systematic roadmap for utilizing a rich set of phenotypes for genetic analyses, including the selection of linkage methods paired to those phenotypes.

Multipoint linkage mapping using sibpairs: non-parametric estimation of trait effects with quantitative covariates

Multipoint linkage analysis using sibpair designs remains a common approach to help investigators to narrow chromosomal regions for traits (either qualitative or quantitative) of interest. Despite its popularity, the success of this approach depends heavily on how issues such as genetic heterogeneity, gene-gene, and gene-environment interactions are properly handled. If addressed properly, the likelihood of detecting genetic linkage and of efficiently estimating the location of the trait locus would be enhanced, sometimes drastically. Previously, we have proposed an approach to deal with these issues by modeling the genetic effect of the target trait locus as a function of covariates pertained to the sibpairs. Here the genetic effect is simply the probability that a sibpair shares the same allele at the trait locus from their parents. Such modeling helps to divide the sibpairs into more homogeneous subgroups, which in turn helps to enhance the chance to detect linkage. One limitation of this approach is the need to categorize the covariates so that a small and fixed number of genetic effect parameters are introduced. In this report, we take advantage of the fact that nowadays multiple markers are readily available for genotyping simultaneously. This suggests that one could estimate the dependence of the generic effect on the covariates nonparametrically. We present an iterative procedure to estimate (1) the genetic effect nonparametrically and (2) the location of the trait locus through estimating functions developed by Liang et al. ([2001a] Hum Hered 51:67-76). We apply this new method to the linkage study of schizophrenia to illustrate how the onset ages of each sibpair may help to address the issue of genetic heterogeneity. This analysis sheds new light on the dependence of the trait effect on onset ages from affected sibpairs, an observation not revealed previously. In addition, we have carried out some simulation work, which suggests that this method provides accurate inference for estimating the location of quantitative trait loci.

Robust estimation of critical values for genome scans to detect linkage

Estimation of study specific critical values for linkage scans (suggestive and significant thresholds) is important to identify promising regions. In this report, I propose a fast and concrete recipe for finding study specific critical values. Previously, critical values were derived theoretically or empirically. Theoretically-derived values are often conservative due to their assumption of fully informative transmissions. Empirically-derived critical values are computer and skill intensive and may not even be computationally feasible for large pedigrees. In this report, I propose a method to estimate critical values for multipoint linkage analysis using standard, widely used statistical software. The proposed method estimates study-specific critical values by using Autoregressive (AR) models to estimate the correlation between standard normal statistics at adjacent map points and then use this correlation to estimate study-specific critical values. The AR-based method is evaluated using different family structures and density of markers, under both the null hypothesis of no linkage and the alternative hypothesis of linkage between marker and disease locus. Simulations results show the AR-based method accurately predicts critical values for a wide range of study designs.

Power and robustness of linkage tests for quantitative traits in general pedigrees

There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this report, we use computer simulations to investigate the power and robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method.

Theoretical and empirical power of regression and maximum-likelihood methods to map quantitative trait loci in general pedigrees

Both theoretical calculations and simulation studies have been used to compare and contrast the statistical power of methods for mapping quantitative trait loci (QTLs) in simple and complex pedigrees. A widely used approach in such studies is to derive or simulate the expected mean test statistic under the alternative hypothesis of a segregating QTL and to equate a larger mean test statistic with larger power. In the present study, we show that, even when the test statistic under the null hypothesis of no linkage follows a known asymptotic distribution (the standard being chi(2)), it cannot be assumed that the distribution under the alternative hypothesis is noncentral chi(2). Hence, mean test statistics cannot be used to indicate power differences, and a comparison between methods that are based on simulated average test statistics may lead to the wrong conclusion. We illustrate this important finding, through simulations and analytical derivations, for a recently proposed new regression method for the analysis of general pedigrees to map quantitative trait loci. We show that this regression method is not necessarily more powerful nor computationally more efficient than a maximum-likelihood variance-component approach. We advocate the use of empirical power to compare trait-mapping methods.

Mapping quantitative traits with random and with ascertained sibships

Use of a robust score statistic based on a variance components model to map quantitative trait loci in randomly sampled pedigrees is reviewed. Sibships ascertained through a single proband are discussed. Under a standard assumption of multivariate normality, two suggested methods of ascertainment correction are shown to be asymptotically equivalent when the number of sibships is large.

Score test for detecting linkage to complex traits in selected samples

We present a unified approach to selection and linkage analysis of selected samples, for both quantitative and dichotomous complex traits. It is based on the score test for the variance attributable to the trait locus and applies to general pedigrees. The method is equivalent to regressing excess IBD sharing on a function of the traits. It is shown that when population parameters for the trait are known, such inversion does not entail any loss of information. For dichotomous traits, pairs of pedigree members of different phenotypic nature (e.g., affected sib pairs and discordant sib pairs) can easily be combined as well as populations with different trait prevalences.

Recent advances in human quantitative-trait-locus mapping: comparison of methods for discordant sibling pairs

Extreme discordant sibling pairs (EDSPs) are theoretically powerful for the mapping of quantitative-trait loci (QTLs) in humans. EDSPs have not been used much in practice, however, because of the need to screen very large populations to find enough pairs that are extreme and discordant. Given appropriate statistical methods, another alternative is to use moderately discordant sibling pairs (MDSPs)--pairs that are discordant but not at the far extremes of the distribution. Such pairs can be powerful yet far easier to collect than extreme discordant pairs. Recent work on statistical methods for QTL mapping in humans has included a number of methods that, though not developed specifically for discordant pairs, may well be powerful for MDSPs and possibly even EDSPs. In the present article, we survey the new statistics and discuss their applicability to discordant pairs. We then use simulation to study the type I error and the power of various statistics for EDSPs and for MDSPs. We conclude that the best statistic(s) for discordant pairs (moderate or extreme) is (are) to be found among the new statistics. We suggest that the new statistics are appropriate for many other designs as well-and that, in fact, they open the way for the exploration of entirely novel designs.