Methods for linkage analysis of quantitative trait loci in humans

Approaches to genetic linkage analysis

Genetic linkage analysis concerns the estimation of genetic distance between two or more genetic loci. In genetic epidemiology, it is predominantly used to identify, or map, a genetic locus that is associated with quantitative trait variation or, in the case of binary or discrete traits, modification of the risk of being affected with a disease or phenotype. Linkage analysis uses a panel of reference genetic markers to track the segregation of genomic segments within families or sets of relatives. Individuals within the families must be measured for the trait, and often the families have been selected because they segregate the phenotype of interest.

Susceptibility genes in common complex kidney disease

PURPOSE OF REVIEW

This paper reviews recent efforts to identify genetic variants conferring risk for chronic kidney disease. A brief overview of methods for identifying gene variants is provided, along with genetic associations and new avenues under exploration.

RECENT FINDINGS

The role of renal failure susceptibility genes, including MYH9, ELMO1, UMOD and ACTN4, has become clearer over the past 18 months. The spectrum of MYH9-associated kidney disease, including focal segmental glomerulosclerosis, global glomerulosclerosis and collapsing glomerulopathy, related entities contributing to approximately 43% of end-stage renal disease in African-Americans, has come to light.

SUMMARY

MYH9 will re-categorize focal segmental glomerulosclerosis and related disorders, and has clarified the relationship between hypertension and kidney disease. MYH9 polymorphisms account for much of the excess risk of HIV-associated nephropathy and nondiabetic kidney disease in African-Americans. Kidney disease associations with ELMO1 and UMOD have been replicated and applications of genome-wide association studies based on expression data are providing novel insights on renal protein expression. These breakthroughs will alter our approach to kidney disease surveillance and lead to new therapeutic options.

The power of linkage analysis of a disease-related endophenotype using asymmetrically ascertained sib pairs

A linkage study of a qualitative disease endophenotype in a sample of sib pairs, consisting of one disease affected proband and one sibling is considered. The linkage statistic compares marker allele sharing with the proband in siblings with an abnormal endophenotype to siblings with the normal endophenotype. Expressions for the distribution of this linkage statistic, in terms of the recombination fraction are derived and (1) the genetic parameter values (allele frequency and endophenotype and disease penetrance) and (2) the abnormal endophenotype rates in the population and in classes of relatives of disease affected probands. It is then shown that when either the disease or the abnormal endophenotype has additive penetrance, the expressions simplify to a monotonic function of the difference between abnormal endophenotype rates in siblings and in the population. Thought disorder is considered as a putative schizophrenia endophenotype. Forty sets of genetic parameter values that correspond to the known prevalence values for thought disorder in schizophrenic patients, siblings of schizophrenics and the general population are evaluated. For these genetic parameter values, numerical results show that the test statistic has>70% power (α = 0.0001) in general with a sample of 200 or more proband-sibling pairs to detect the linkage between a marker (θ = 0.01), and a locus pleiotropic for schizophrenia and thought disorder.

Identifying modifier genes of monogenic disease: strategies and difficulties

Substantial clinical variability is observed in many Mendelian diseases, so that patients with the same mutation may develop a very severe form of disease, a mild form or show no symptoms at all. Among the factors that may explain these differences in disease expression are modifier genes. In this paper, we review the different strategies that can be used to identify modifier genes and explain their advantages and limitations. We focus mainly on the statistical aspects but illustrate our points with a variety of examples from the literature.

Multiple quantitative trait loci Haseman-Elston regression using all markers on the entire genome

The Haseman-Elston (HE) regression, developed in the 1970s, remains in common use to detect genetic linkage between a quantitative trait and a genetic marker. Although the technique has been improved in a number of ways, it predicts a high rate of false positive quantitative trait locus (QTL) because it is based on a single-QTL model. We have extended the origin HE regression to multi-QTL HE (MQHE) regression, so that all markers across the entire genome can be exploited simultaneously. The parameters have been estimated by the penalized maximum likelihood method, and several response variables for phenotypic difference have been compared in order to optimize the procedure. The method has been tested by simulation in a pedigree population of maize inbred lines of known ancestry. These simulations show that the trait product is the optimal response variable for phenotypic difference. The false positive rate produced by the MQHE regression is substantially lower than that generated by either variance component analysis or the origin HE regression. The MQHE regression, with the trait product as the response variable, represents a significant improvement on existing methods for QTL mapping in a set of inbred lines (or cultivars) of known ancestry.

Exact trait-model-free tests for linkage detection in pedigrees

A number of trait-model-free tests have been proposed for linkage detection between a genomic region and a trait. These tests involve testing the dependence in segregation between a trait and marker alleles by assigning a score to every possible identity-by-descent configuration of the pedigree members without modeling the trait, and then averaging the scores over all such configurations compatible with the observed marker genotypes and genealogical relationship of the pedigree members. In this paper we propose a permutation test as an alternative to the existing exact trait-model-free tests for linkage detection. The proposed test is computationally efficient and is applicable on complex multigeneration pedigree structures. In this paper, we have compared the performance of the permutation test with two other exact trait-model-free tests for linkage detection on simulated datasets. We have demonstrated that the proposed permutation test is fully robust against mispecification of marker allele frequencies and has very good power for linkage detection. The permutation test is implemented in the program lm_ibdtests within the framework of MORGAN 2.8 (http://www.stat.washington.edu/thompson/Genepi/MORGAN/Morgan.shtml).

Separation of base allele and sampling term effects gives new insights in variance component QTL analysis

Background

Variance component (VC) models are commonly used for Quantitative Trait Loci (QTL) mapping in outbred populations. Here, the QTL effect is given as a random effect and a critical part of the model is the relationship between the phenotypic values and the random effect. In the traditional VC model, each individual has a unique QTL effect and the relationship between these random effects is given as a covariance structure (known as the identity-by-descent (IBD) matrix).

Results

We present an alternative notation of the variance component model, where the elements of the random effect are independent base generation allele effects and sampling term effects. The relationship between the phenotypic vales and the random effect is given by an incidence matrix, which results in a novel, but statistically equivalent, version of the traditional VC model. A general algorithm to estimate this incidence matrix is presented. Since the model is given in terms of base generation allele effects and sampling term effects, these effects can be estimated separately using best linear unbiased prediction (BLUP). From simulated data, we showed that biallelic QTL effects could be accurately clustered using the BLUP obtained from our model notation when markers are fully informative, and that the accuracy increased with the size of the QTL effect. We also developed a measure indicating whether a base generation marker homozygote is a QTL heterozygote or not, by comparing the variances of the sampling term BLUP and the base generation allele BLUP. A ratio greater than one gives strong support for a QTL heterozygote.

Conclusion

We developed a simple presentation of the VC QTL model for identification of base generation allele effects in QTL linkage analysis. The base generation allele effects and sampling term effects were separated in our model notation. This clarifies the assumptions of the model and should also enhance the development of genome scan methods.

Extension of the Haseman-Elston regression model to longitudinal data

We propose an extension to longitudinal data of the Haseman and Elston regression method for linkage analysis. The proposed model is a mixed model having several random effects. As response variable, we investigate the sibship sample mean corrected cross-product (smHE) and the BLUP-mean corrected cross product (pmHE), comparing them with the original squared difference (oHE), the overall mean corrected cross-product (rHE), and the weighted average of the squared difference and the squared mean-corrected sum (wHE). The proposed model allows for the correlation structure of longitudinal data. Also, the model can test for gene x time interaction to discover genetic variation over time. The model was applied in an analysis of the Genetic Analysis Workshop 13 (GAW13) simulated dataset for a quantitative trait simulating systolic blood pressure. Independence models did not preserve the test sizes, while the mixed models with both family and sibpair random effects tended to preserve size well.

On normality, ethnicity, and missing values in quantitative trait locus mapping

Background

This paper deals with the detection of significant linkage for quantitative traits using a variance components approach. Microsatellite markers were obtained for the Genetic Analysis Workshop 14 Collaborative Study on the Genetics of Alcoholism data. Ethnic heterogeneity, highly skewed quantitative measures, and a high rate of missing values are all present in this dataset and well known to impact upon linkage analysis. This makes it a good candidate for investigation.

Results

As expected, we observed a number of changes in LOD scores, especially for chromosomes 1, 7, and 18, along with the three factors studied. A dramatic example of such changes can be found in chromosome 7. Highly significant linkage to one of the quantitative traits became insignificant when a proper normalizing transformation of the trait was used and when analysis was carried out on an ethnically homogeneous subset of the original pedigrees.

Conclusion

In agreement with existing literature, transforming a trait to ensure normality using a Box-Cox transformation is highly recommended in order to avoid false-positive linkages. Furthermore, pedigrees should be sorted by ethnic groups and analyses should be carried out separately. Finally, one should be aware that the inclusion of covariates with a high rate of missing values reduces considerably the number of subjects included in the model. In such a case, the loss in power may be large. Imputation methods are then recommended.

The bias introduced by population stratification in IBD based linkage analysis

The lack of replication of model-free linkage analyses performed on complex diseases raises questions about the robustness of these methods to various biases. The confounding effect of population stratification on a genetic association study has long been recognized in the genetic epidemiology community. Because the estimation of the number of alleles shared identical by descent (IBD) does not depend on the marker allele frequency when founders of families are observed, model-free linkage analysis is usually thought to be robust to population stratification. However, for common complex diseases, the genotypes of founders are often unobserved and therefore population stratification has the potential to impair model-free linkage analysis. Here, we demonstrate that, when some or all of the founder genotypes are missing, population stratification can introduce deleterious effects on various model-free linkage methods or designs. For an affected sib pair design, it can cause excess false-positive discoveries even when the trait distribution is homogeneous among subpopulations. After incorporating a control group of discordant sib pairs or for a quantitative trait, two circumstances must be met for population stratification to be a confounder: the distributions for both the marker and the trait must be heterogeneous among subpopulations. When this occurs, the bias can result in either a liberal, and hence invalid, test or a conservative test. Bias can be eliminated or alleviated by inclusion of founders' or other family members' genotype data. When this is not possible, new methods need to be developed to be robust to population stratification.

Linkage of speech sound disorder to reading disability loci

BACKGROUND

Speech sound disorder (SSD) is a common childhood disorder characterized by developmentally inappropriate errors in speech production that greatly reduce intelligibility. SSD has been found to be associated with later reading disability (RD), and there is also evidence for both a cognitive and etiological overlap between the two disorders. The present study tested whether SSD is linked to replicated risk loci for RD.

METHOD

One hundred and eleven probands with SSD and their 76 siblings were tested with measures of speech, phonological memory (Nonword Repetition-NWR), and phonological awareness and genotyped for linkage markers on chromosomes 1p36, 6p22, and 15q21. Both single point and multipoint linkage were tested with multiple methods.

RESULTS

The speech and NWR phenotypes were linked to the RD loci on chromosomes 6 and 15, with suggestive results for the RD locus on chromosome 1.

CONCLUSIONS

It now appears that several RD loci are pleiotropic for SSD, extending the findings of Stein et al. (2004) for the RD locus on Chromosome 3.

A powerful and robust method for mapping quantitative trait loci in general pedigrees

The variance-components model is the method of choice for mapping quantitative trait loci in general human pedigrees. This model assumes normally distributed trait values and includes a major gene effect, random polygenic and environmental effects, and covariate effects. Violation of the normality assumption has detrimental effects on the type I error and power. One possible way of achieving normality is to transform trait values. The true transformation is unknown in practice, and different transformations may yield conflicting results. In addition, the commonly used transformations are ineffective in dealing with outlying trait values. We propose a novel extension of the variance-components model that allows the true transformation function to be completely unspecified. We present efficient likelihood-based procedures to estimate variance components and to test for genetic linkage. Simulation studies demonstrated that the new method is as powerful as the existing variance-components methods when the normality assumption holds; when the normality assumption fails, the new method still provides accurate control of type I error and is substantially more powerful than the existing methods. We performed a genomewide scan of monoamine oxidase B for the Collaborative Study on the Genetics of Alcoholism. In that study, the results that are based on the existing variance-components method changed dramatically when three outlying trait values were excluded from the analysis, whereas our method yielded essentially the same answers with or without those three outliers. The computer program that implements the new method is freely available.

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.

Quantitative trait linkage analysis by generalized estimating equations: unification of variance components and Haseman-Elston regression

Two of the major approaches for linkage analysis with quantitative traits in humans include variance components and Haseman-Elston regression. Previously, these were viewed as quite separate methods. We describe a general model, fit by use of generalized estimating equations (GEE), for which the variance components and Haseman-Elston methods (including many of the extensions to the original Haseman-Elston method) are special cases, corresponding to different choices for a working covariance matrix. We also show that the regression-based test of Sham et al. ([2002] Am. J. Hum. Genet. 71:238-253) is equivalent to a robust score statistic derived from our GEE approach. These results have several important implications. First, this work provides new insight regarding the connection between these methods. Second, asymptotic approximations for power and sample size allow clear comparisons regarding the relative efficiency of the different methods. Third, our general framework suggests important extensions to the Haseman-Elston approach which make more complete use of the data in extended pedigrees and allow a natural incorporation of environmental and other covariates.

Efficiency robust tests for mapping quantitative trait loci using extremely discordant sib pairs

In 1972, Haseman and Elston proposed a pioneering regression method for mapping quantitative trait loci using randomly selected sib pairs. Recently, the statistical power of their method was shown to be increased when extremely discordant sib pairs are ascertained. While the precise genetic model may not be known, prior information that constrains IBD probabilities is often available. We investigate properties of tests that are robust against model uncertainty and show that the power gain from further constraining IBD probabilities is marginal. The additional linkage information contained in the trait values can be incorporated by combining the Haseman-Elston regression method and a robust allele sharing test.

Regression models for linkage: issues of traits, covariates, heterogeneity, and interaction

Regression methods offer a common framework to analyze linkage for quantitative trait loci as well as linkage for affection status using affected sib-pairs. Although numerous papers on regression methods for linkage have been published, some common themes and important caveats tend to be scattered across the literature. For example, the typical approach is to regress a function of traits on identical-by-descent (IBD) information, but the reversal (regression of IBD on a function of traits) offers important insights. A second example is the use of regression equations to assess linkage heterogeneity or gene-environment interaction, and why these two different etiologies are difficult to distinguish with affected sib-pair data. A third example has to do with the differences, and similarities, between linear regression and non-linear regression methods for affected sib-pair data. The purposes of this paper are to review some recent developments in the linkage regression framework, to emphasize strengths and weaknesses of various proposed methods, and to highlight some important assumptions and caveats.

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

During the past few years, there has been a great deal of new work on methods for mapping quantitative-trait loci by use of sibling pairs and sibships. There are several new methods based on linear regression, as well as several more that are based on score statistics. In theory, most of the new methods should be relatively robust to violations of distributional assumptions and to selected sampling, but, in practice, there has been little evaluation of how the methods perform on selected samples. We survey most of the new regression-based statistics and score statistics and propose a few minor variations on the score statistics. We use simulation to evaluate the type I error and the power of all of the statistics, considering (a) population samples of sibling pairs and (b) sibling pairs ascertained on the basis of at least one sibling with a trait value in the top 10% of the distribution. Most of the statistics have correct type I error for selected samples. The statistics proposed by Xu et al. and by Sham and Purcell are generally the most powerful, along with one of our score statistic variants. Even among the methods that are most powerful for "nice" data, some are more robust than others to non-Gaussian trait models and/or misspecified trait parameters.

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.

Powerful regression-based quantitative-trait linkage analysis of general pedigrees

We present a new method of quantitative-trait linkage analysis that combines the simplicity and robustness of regression-based methods and the generality and greater power of variance-components models. The new method is based on a regression of estimated identity-by-descent (IBD) sharing between relative pairs on the squared sums and squared differences of trait values of the relative pairs. The method is applicable to pedigrees of arbitrary structure and to pedigrees selected on the basis of trait value, provided that population parameters of the trait distribution can be correctly specified. Ambiguous IBD sharing (due to incomplete marker information) can be accommodated in the method by appropriate specification of the variance-covariance matrix of IBD sharing between relative pairs. We have implemented this regression-based method and have performed simulation studies to assess, under a range of conditions, estimation accuracy, type I error rate, and power. For normally distributed traits and in large samples, the method is found to give the correct type I error rate and an unbiased estimate of the proportion of trait variance accounted for by the additive effects of the locus-although, in cases where asymptotic theory is doubtful, significance levels should be checked by simulations. In large sibships, the new method is slightly more powerful than variance-components models. The proposed method provides a practical and powerful tool for the linkage analysis of quantitative traits.