Power and robustness of a score test for linkage analysis of quantitative traits using identity by descent data on sib pairs

Identification of genes involved in complex traits by traditional (lod score) linkage analysis is difficult due to many complicating factors. An unfortunate drawback of non-parametric procedures in general, though, is their low power to detect genetic effects. Recently, Dudoit and Speed [2000] proposed using a (likelihood-based) score test for detecting linkage with IBD data on sib pairs. This method uses the likelihood for theta, the recombination fraction between a trait locus and a marker locus, conditional on the phenotypes of the two sibs to test the null hypothesis of no linkage (theta = (1/2)). Although a genetic model must be specified, the approach offers several advantages. This paper presents results of simulation studies characterizing the power and robustness properties of this score test for linkage, and compares the power of the test to the Haseman-Elston and modified Haseman-Elston tests. The score test is seen to have impressively high power across a broad range of true and assumed models, particularly under multiple ascertainment. Assuming an additive model with a moderate allele frequency, in the range of p = 0.2 to 0.5, along with heritability H = 0.3 and a moderate residual correlation rho = 0.2 resulted in a very good overall performance across a wide range of trait-generating models. Generally, our results indicate that this score test for linkage offers a high degree of protection against wrong assumptions due to its strong robustness when used with the recommended additive model.     

Bivariate quantitative trait linkage analysis: Pleiotropy versus co-incident linkages

Power to detect linkage and localization of a major gene were compared in univariate and bivariate variance components linkage analysis of three related quantitative traits in general pedigrees. Although both methods demonstrated adequate power to detect loci of moderate effect, bivariate analysis improved both power and localization for correlated quantitative traits mapping to the same chromosomal region, regardless of whether co-localization was the result of pleiotropy. Additionally, a test of pleiotropy versus co-incident linkage was shown to have adequate power and a low error rate. © 1997 Wiley-Liss, Inc.     

Unified sampling approach for multipoint linkage disequilibrium mapping of qualitative and quantitative traits

Rapid development in biotechnology has enhanced the opportunity to deal with multipoint gene mapping for complex diseases, and association studies using quantitative traits have recently generated much attention. Unlike the conventional hypothesis-testing approach for fine mapping, we propose a unified multipoint method to localize a gene controlling a quantitative trait. We first calculate the sample size needed to detect linkage and linkage disequilibrium (LD) for a quantitative trait, categorized by decile, under three different modes of inheritance. Our results show that sampling trios of offspring and their parents from either extremely low (EL) or extremely high (EH) probands provides greater statistical power than sampling in the intermediate range. We next propose a unified sampling approach for multipoint LD mapping, where the goal is to estimate the map position (tau) of a trait locus and to calculate a confidence interval along with its sampling uncertainty. Our method builds upon a model for an expected preferential transmission statistic at an arbitrary locus conditional on the sampling scheme, such as sampling from EL and EH probands. This approach is valid regardless of the underlying genetic model. The one major assumption for this model is that no more than one quantitative trait locus (QTL) is linked to the region being mapped. Finally we illustrate the proposed method using family data on total serum IgE levels collected in multiplex asthmatic families from Barbados. An unobserved QTL appears to be located at tau; = 41.93 cM with 95% confidence interval of (40.84, 43.02) through the 20-cM region framed by markers D12S1052 and D12S1064 on chromosome 12. The test statistic shows strong evidence of linkage and LD (chi-square statistic = 18.39 with 2 df, P-value = 0.0001).     

Leveraging population information in family‐based rare variant association analyses of quantitative traits

Confounding due to population substructure is always a concern in genetic association studies. Although methods have been proposed to adjust for population stratification in the context of common variation, it is unclear how well these approaches will work when interrogating rare variation. Family‐based association tests can be constructed that are robust to population stratification. For example, when considering a quantitative trait, a linear model can be used that decomposes genetic effects into between‐ and within‐family components and a test of the within‐family component is robust to population stratification. However, this within‐family test ignores between‐family information potentially leading to a loss of power. Here, we propose a family‐based two‐stage rare‐variant test for quantitative traits. We first construct a weight for each variant within a gene, or other genetic unit, based on score tests of between‐family effect parameters. These weights are then used to combine variants using score tests of within‐family effect parameters. Because the between‐family and within‐family tests are orthogonal under the null hypothesis, this two‐stage approach can increase power while still maintaining validity. Using simulation, we show that this two‐stage test can significantly improve power while correctly maintaining type I error. We further show that the two‐stage approach maintains the robustness to population stratification of the within‐family test and we illustrate this using simulations reflecting samples composed of continental and closely related subpopulations.     

Removing phenotypic distribution assumptions from tests of linkage disequilibrium for quantitative traits

The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.     

A brute force dichotomization approach to quantitative trait linkage analysis

The effect of dichotomizing a continuous phenotype in linkage analysis of a simulated oligogenic trait is explored. We conclude that dichotomization does not in itself preclude the detection of loci which account for as little as 16% of the genetic variance of the disease. The effects of inclusion of known covariates and quantitative trait linkage analysis are also discussed. © 1995 Wiley-Liss, Inc.     

Ordered subset analysis in genetic linkage mapping of complex traits

Etiologic heterogeneity is a fundamental feature of complex disease etiology; genetic linkage analysis methods to map genes for complex traits that acknowledge the presence of genetic heterogeneity are likely to have greater power to identify subtle changes in complex biologic systems. We investigate the use of trait-related covariates to examine evidence for linkage in the presence of heterogeneity. Ordered-subset analysis (OSA) identifies subsets of families defined by the level of a trait-related covariate that provide maximal evidence for linkage, without requiring a priori specification of the subset. We propose that examining evidence for linkage in the subset directly may result in a more etiologically homogeneous sample. In turn, the reduced impact of heterogeneity will result in increased overall evidence for linkage to a specific region and a more distinct lod score peak. In addition, identification of a subset defined by a specific trait-related covariate showing increased evidence for linkage may help refine the list of candidate genes in a given region and suggest a useful sample in which to begin searching for trait-associated polymorphisms. This method provides a means to begin to bridge the gap between initial identification of linkage and identification of the disease predisposing variant(s) within a region when mapping genes for complex diseases. We illustrate this method by analyzing data on breast cancer age of onset and chromosome 17q [Hall et al., 1990, Science 250:1684-1689]. We evaluate OSA using simulation studies under a variety of genetic models.     

Multilocus quantitative trait analysis using the multipoint identity-by-descent method

The multipoint identity-by-descent method (MIM) was extended to test for evidence of quantitative trait loci in two independent genetic regions. This method is a fast and feasible implementation of a multiple-marker, two-region linkage analysis for quantitative traits. It tests for significant evidence of quantitative trait loci (QTL) in neither, one or both genetic regions tested, and could be extended to an arbitrary number of independent genetic regions. A two-stage analysis was used for the nuclear family data from GAW10. Initially, an analysis of the genomic search was carried out using single-region MIM, with sets of six adjacent markers. Chromosomal regions that showed some evidence of linkage were identified and used in a two-region MIM analysis. © 1997 Wiley-Liss, Inc.     

Testing causal hypotheses in multivariate linkage analysis of quantitative traits: General formulation and application to sibpair data

We provide a general framework for the development of model-free methods for the linkage analysis of multivariate phenotypic data. It is possible within this framework to test both for linkage of a set of phenotypes to one or more markers and for the presence of structural relations among the phenotypes themselves. This report presents the general model, paying special attention to the assumptions that enter its formulation, and outlines the estimation procedures that may be used. Genet. Epidemiol. 15:263–278, 1998. © 1998 Wiley-Liss, Inc.     

On the use of phylogeny‐based tests to detect association between quantitative traits and haplotypes

With the increasing availability of genetic data, several SNPs in a candidate gene can be combined into haplotypes to test for association with a quantitative trait. When the number of SNPs increases, the number of haplotypes can become very large and there is a need to group them together. The use of the phylogenetic relationships between haplotypes provides a natural and efficient way of grouping. Moreover, it allows us to identify disease or quantitative trait‐related loci. In this article, we describe ALTree‐q , a phylogeny‐based approach to test for association between quantitative traits and haplotypes and to identify putative quantitative trait nucleotides (QTN). This study focuses on ALTree‐q association test which is based on one‐way analyses of variance (ANOVA) performed at the different levels of the tree. The statistical properties (type‐one error and power rates) were estimated through simulations under different genetic models and were compared to another phylogeny‐based test, TreeScan, (Templeton, 2005) and to a haplotypic omnibus test consisting in a one‐way ANOVA between all haplotypes. For dominant and additive models ALTree‐q is usually the most powerful test whereas TreeScan performs better under a recessive model. However, power depends strongly on the recurrence rate of the QTN, on the QTN allele frequency, and on the linkage disequilibrium between the QTN and other markers. An application of the method on Thrombin Activatable Fibronolysis Inhibitor Antigen levels in European and African samples confirms a possible association with polymorphisms of the CPB2 gene and identifies several QTNs. Genet. Epidemiol. 33:729–739, 2009. © 2009 Wiley‐Liss, Inc.     

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. Genet. Epidemiol. 35:46–56, 2011. © 2010 Wiley‐Liss, Inc.     

Accumulating quantitative trait linkage evidence across multiple datasets using the posterior probability of linkage

Genome scans for complex disorders are frequently inconclusive, prompting researchers to increase sample size in an effort to obtain stronger evidence. However, increasing sample size in the presence of locus heterogeneity may actually, on average, decrease the linkage signal at a true susceptibility gene. The posterior probability of linkage, or PPL, was specifically designed to address this issue in the context of categorical trait analysis, by appropriately accumulating evidence either for or against linkage as new data are added. We now formulate a quantitative trait (QT) analog, the QT-PPL, which directly measures the evidence that a QT is linked to a genetic marker or location. The new QT-PPL is based on a classical single-locus QT likelihood with the trait parameters (allele frequency, genotypic means and variances) integrated out. We show using simulations that the QT-PPL is robust to two key modeling violations (multiple trait loci and non-normality in the form of excess kurtosis), as well as being inherently ascertainment corrected, and illustrate the advantages of the QT-PPL for accumulating linkage evidence across multiple sets of data compared to other QT linkage methods.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.     

Trade-off between false positives and false negatives in the linkage analysis of complex traits

This study examines the issue of false positives in genomic scans for detecting complex trait loci using sibpair linkage methods and investigates the trade-off between the rate of false positives and the rate of false negatives. It highlights the tremendous cost in terms of power brought about by an excessive control of type I error and, at the same time, confirms that a larger number of false positives can occur otherwise in the course of a genomic scan. Finally, it compares the power and rate of false positives obtained in preplanned replicated studies conducted using a liberal significance level to those for single-step studies that use the same total sample size but stricter levels of significance. For the models considered here, replicate studies were found more attractive as long as one is willing to accept a trade-off, exchanging a much lower rate of false negatives for a slight increase in the rate of false positives. Genet. Epidemiol. 14:453–464,1997. © 1997 Wiley-Liss, Inc.     

Mapping quantitative traits in unselected families: algorithms and examples

Linkage analysis has been widely used to identify from family data genetic variants influencing quantitative traits. Common approaches have both strengths and limitations. Likelihood ratio tests typically computed in variance component analysis can accommodate large families but are highly sensitive to departure from normality assumptions. Regression‐based approaches are more robust but their use has primarily been restricted to nuclear families. In this paper, we develop methods for mapping quantitative traits in moderately large pedigrees. Our methods are based on the score statistic, which in contrast to the likelihood ratio statistic can use nonparametric estimators of variability to achieve robustness of the false‐positive rate against departures from the hypothesized phenotypic model. Because the score statistic is easier to calculate than the likelihood ratio statistic, our basic mapping methods utilize relatively simple computer code that performs statistical analysis on output from any program that computes estimates of identity by descent. This simplicity also permits development and evaluation of methods to deal with multivariate and ordinal phenotypes, and with gene‐gene and gene‐environment interaction. We demonstrate our methods on simulated data and on fasting insulin, a quantitative trait measured in the Framingham Heart Study. Genet. Epidemiol. 33:617–627, 2009. © 2009 Wiley‐Liss, Inc.     

Improving the power of association tests for quantitative traits in family studies

Association mapping based on family studies can identify genes that influence complex human traits while providing protection against population stratification. Because no gene is likely to have a very large effect on a complex trait, most family studies have limited power. Among the commonly used family-based tests of association for quantitative traits, the quantitative transmission-disequilibrium tests (QTDT) based on the variance-components model is the most flexible and most powerful. This method assumes that the trait values are normally distributed. Departures from normality can inflate the type I error and reduce the power. Although the family-based association tests (FBAT) and pedigree disequilibrium tests (PDT) do not require normal traits, nonnormality can also result in loss of power. In many cases, approximate normality can be achieved by transforming the trait values. However, the true transformation is unknown, and incorrect transformations may compromise the type I error and power. We propose a novel class of association tests for arbitrarily distributed quantitative traits by allowing the true transformation function to be completely unspecified and empirically estimated from the data. Extensive simulation studies showed that the new methods provide accurate control of the type I error and can be substantially more powerful than the existing methods. We applied the new methods to the Collaborative Study on the Genetics of Alcoholism and discovered significant association of single nucleotide polymorphisms (SNP) tsc0022400 on chromosome 7 with the quantitative electrophysiological phenotype TTTH1, which was not detected by any existing methods. We have implemented the new methods in a freely available computer program.     

Increase in power of transmission-disequilibrium tests for quantitative traits

Allison ([1997] Am. J. Hum. Genet. 60:676-690) proposed four versions of the transmission-disequilibrium test (TDT) for quantitative traits when there is extreme-threshold sampling, i.e., the trios having an offspring trait value between a priori defined thresholds are excluded from the analysis. Keeping intact the ideology and construction of these tests, we propose here an extreme-offspring design for the trios: for each parent pair of which at least one is heterozygous at a marker locus, the offspring having the most extreme trait value is selected for the trio. Our simulation studies show that the effect of the extreme-offspring design can be quite substantial (up to 30% increase in test power), and that the increase is greater for smaller values of the association parameter and for traits with smaller heritability: just those cases where the increase in power is especially desirable.     

Use of the regressive models in linkage analysis of quantitative traits

Use of the regressive models to account for residual familial correlations in linkage analysis of complex quantitative traits can increase the power to detect linkage. This is especially observed when the effect of the gene to be mapped is small or when the residual correlations are substantial. © 1993 Wiley-Liss, Inc.     

A more powerful robust sib-pair test of linkage for quantitative traits

A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3-19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linakge that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that uses information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.