A Flexible Approach for the Analysis of Rare Variants Allowing for a Mixture of Effects on Binary or Quantitative Traits
Multiple rare variants either within or across genes have been hypothesised to collectively influence complex human traits. The increasing availability of high throughput sequencing technologies offers the opportunity to study the effect of rare variants on these traits. However, appropriate and computationally efficient analytical methods are required to account for collections of rare variants that display a combination of protective, deleterious and null effects on the trait. We have developed a novel method for the analysis of rare genetic variation in a gene, region or pathway that, by simply aggregating summary statistics at each variant, can: (i) test for the presence of a mixture of effects on a trait; (ii) be applied to both binary and quantitative traits in populationbased and familybased data; (iii) adjust for covariates to allow for nongenetic risk factors and; (iv) incorporate imputed genetic variation. In addition, for preliminary identification of promising genes, the method can be applied to association summary statistics, available from metaanalysis of published data, for example, without the need for individual level genotype data. Through simulation, we show that our method is immune to the presence of bidirectional effects, with no apparent loss in power across a range of different mixtures, and can achieve greater power than existing approaches as long as summary statistics at each variant are robust. We apply our method to investigate association of type1 diabetes with imputed rare variants within genes in the major histocompatibility complex using genotype data from the Wellcome Trust Case Control Consortium.
Published in the journal:
. PLoS Genet 9(8): e32767. doi:10.1371/journal.pgen.1003694
Category:
Research Article
doi: 10.1371/journal.pgen.1003694
Summary
Multiple rare variants either within or across genes have been hypothesised to collectively influence complex human traits. The increasing availability of high throughput sequencing technologies offers the opportunity to study the effect of rare variants on these traits. However, appropriate and computationally efficient analytical methods are required to account for collections of rare variants that display a combination of protective, deleterious and null effects on the trait. We have developed a novel method for the analysis of rare genetic variation in a gene, region or pathway that, by simply aggregating summary statistics at each variant, can: (i) test for the presence of a mixture of effects on a trait; (ii) be applied to both binary and quantitative traits in populationbased and familybased data; (iii) adjust for covariates to allow for nongenetic risk factors and; (iv) incorporate imputed genetic variation. In addition, for preliminary identification of promising genes, the method can be applied to association summary statistics, available from metaanalysis of published data, for example, without the need for individual level genotype data. Through simulation, we show that our method is immune to the presence of bidirectional effects, with no apparent loss in power across a range of different mixtures, and can achieve greater power than existing approaches as long as summary statistics at each variant are robust. We apply our method to investigate association of type1 diabetes with imputed rare variants within genes in the major histocompatibility complex using genotype data from the Wellcome Trust Case Control Consortium.
Introduction
Despite the recent successes of genomewide association studies (GWAS), which can be well powered under the common disease, common variant hypothesis, the majority of the genetic component of many complex traits remains unexplained. For example, hundreds of common genetic variants, in at least 180 loci, have been associated with height in studies of up to more than 180,000 individuals. However, the individual effects of these variants are modest and their cumulative effect explains just over 10% of the phenotypic variation in height [1], [2], [3], [4]. Rare variants may play an important role in explaining the “missing heritability” of complex traits. Due to recent advances in highthroughput resequencing technology, it is becoming financially feasible to assay rare genetic variation in thousands of individuals on the scale of the wholeexome, or even the whole genome. Furthermore, with the availability of wholegenome resequencing reference panels, such as those made available through the 1000 Genomes Project [5], imputation allows the possibility to predict genotypes at rare variants not present on, or captured by, GWAS genotyping arrays. Therefore, we now have an exciting opportunity to explore a range of models that may help to explain the missing heritability of complex traits using rare genetic variation. One such model is that where a gene or region affects a complex trait as a consequence of the combined effects of its constituent rare variants. The effects at each rare variant can be either modest or highly penetrant, and can act to either increase or decrease the trait or disease risk.
Recently published methods for the analysis of multiple rare variants illustrate that power can be greatly increased by combining information in a joint analysis in comparison to studying individual variants one at a time [6], [7], [8], [9], [10], [11]. These so called “burden tests” are optimal when all variants have the same direction of effect. However, these variants may act individually to either increase or decrease trait values, or they may be neutral (i.e. no effect on the trait). Ideally, we wish to test for the presence of a mixture of increaser, decreaser and neutral effects at multiple rare variants on a complex binary or quantitative trait. Zelterman and Chen [12] describe tests of homogeneity against such central mixture alternatives for general sampling distributions that are based on the score function. These so called “Calpha” tests are powerful for detecting the presence of central mixtures [13]. Neale et al. [14] proposed a Calpha test for the analysis of sequence level data for association with binary (disease) traits based on binomially distributed measures of effect at each site. Their approach has the advantage of allowing for a mixture of risk, protective and neutral effects, but cannot explicitly be applied to quantitative traits, account for nongenetic risk factors as covariates, or allow for imputed variation. More recently, scorebased variance component tests SKAT (sequence kernel association test) [15] and an optimized version (SKATO) [16] have been proposed for the detection of a mixture of effects which can be applied to both binary and quantitative traits and which can adjust for covariates. These tests have been shown to outperform burden tests and the Binomial Calpha test in a wide range of scenarios.
Here, we introduce a Calpha test for the analysis of rare genetic variation for association with both binary and quantitative traits based on normally distributed measures of effect at each site. Measures of effect at each site can be calculated from resequencing, array genotyping or imputed data or taken directly from summary measures of effect available, for example, from metaanalysis or published data. Our test assesses the evidence for a mixture of increaser, decreaser and neutral effects in a gene, region or pathway and can be applied to both population and familybased association studies and can adjust for covariates to allow for nongenetic risk factors, such as indicators of population stratification. We refer to our test as the Generalised Calpha test. We report the results of simulations to investigate the power of our test to detect rare variant association with a quantitative trait, and compare performance with existing approaches.
The HLA class II genes in the major histocompatibility locus (MHC) play a major role in susceptibility to type1 diabetes (T1D) [17], but common variants mapping to other genes in this region have also been implicated in the disease. Imputation into existing GWAS genotype data up to publicly available reference panels of sequence data can be used to identify novel and refined signals of association with common SNPs (MAF>1%) [18] and is feasible for the evaluation of rare variants [19]. We have used our Generalised Calpha test to evaluate the evidence for rare variant association with T1D within genes in the MHC using GWAS genotype data from the Wellcome Trust Control Consortium (WTCCC) [20] imputed up to reference panels made available through the 1000 Genomes Project [5].
Materials and Methods
Generalised Calpha Test
Consider a gene, region or pathway containing K variants, each with a minor allele frequency (MAF) less than a predefined threshold and assayed in a sample of individuals measured for a binary or a quantitative trait. Suppose that at each variant a normally distributed estimate of the effect of the minor allele on the trait of interest can be obtained. For example, in a casecontrol association study such an estimate may be the log allelic odds ratio obtained as a coefficient in a logistic regression; or in a quantitative trait association study, the estimate may be the perallele increase in phenotypic value obtained as a coefficient in a linear regression. For each variant alone, there is unlikely to be enough information to make inference about association, unless the sample size is unfeasibly large. However, if the gene is not associated with the trait, then the distribution of estimates across all variants will be Gaussian with mean zero. Conversely, if variants in the gene are associated with the trait, there will be a mixture of Gaussian distributions with different means, manifested as “overdispersion”, which can be detected by a Calpha test.
More formally, let denote the effect estimate, and it's corresponding estimate of standard deviation, at variant k, k = 1,…,K. We assume that are independent Gaussian distributed random variables with mean and standard deviation . As described, such estimates will typically have been obtained from a logistic (binary trait) or linear (quantitative trait) regression of trait value on genotype. The Calpha test of homogeneity can be derived for a given sampling model. Here the effects are treated as sampling units from a Gaussian sampling model. Under the null hypothesis of no association with the trait, we assume that all are equal to some fixed, unknown value, denoted . Under the alternative hypothesis, we assume that the take on a mixture of values, centred at . The Calpha test statistic for a test of homogeneity of against a central mixture of alternative Gaussian hypotheses is
where is an estimate of under the null hypothesis. In practice, we estimate by the observed standard deviation . Notice that S is simply the sum of the differences between the variance of the observed measures of association and the expected variance under the null hypothesis. To standardise S, we require the estimated normalizing variance
The standardised Calpha test statistic is then
which is asymptotically standard Gaussian distributed. The null hypothesis of no association is rejected for values of Z_{NORM} significantly larger than that expected using a onetailed test of size α. The quantities S and c are easily derived using methods detailed in Zelterman and Chen [12] for sampling units from a distribution belonging to the exponential family: in this case, the Gaussian distribution, where is treated as a nuisance parameter. Note that a natural adjustment for the effect of nongenetic risk factors can be achieved by including covariates in the regression model used to estimate . Furthermore, we can consider imputed variation by replacing direct genotypes with dosages under an additive model, or by maximisation of the missing data likelihood of the distribution of genotypes.
For genetic association studies, the expected effect of a minor allele is zero, so that , and the Calpha statistic reduces to:
The assumption that the distribution of Z_{NORM} is Gaussian depends on: (i) the degree of sparseness in the data, as summarised by the relationship between sample size and MAF at each variant; (ii) the number of variants that are considered and (iii) the independence of variants. When the data are too sparse, because the sample size is too small and/or the MAF too low, the maximum likelihood estimates of effect size computed at each site are typically unstable. Furthermore, the discrepancy between the empirical variance of the estimates, and their variance under the reference asymptotic distribution can be large, resulting in inaccurate type I error [21]. It is reasonable to assume that large numbers of individuals will be genotyped because in a practical study design, tests require large numbers of individuals for adequate power, however the minimum MAF must be constrained to ensure stability of estimates in the presence of, for example, private mutations. The second and third requirements ensure convergence of the null distribution of the Z_{NORM} to Gaussian by the central limit theorem. To estimate significance accurately for low MAF, where small numbers of variants are considered or where variants are correlated, standard permutation testing is required. See Text S1 for details of the standard permutation approach utilised here.
Simulation Study
We conduct simulations to investigate the performance of the Generalised Calpha test for the identification of rare variants associated with a binary or quantitative trait. We compare the performance of the Generalised Calpha test to three existing approaches: (i) the optimized scorebased variance component test (SKATO, by Lee et al. [15] (ii) the Binomial Calpha rare variant test by Neale et al. [14], and (iii) GRANVIL, a burden test of association of binary or quantitative traits with accumulations of minor alleles at rare variants in a generalised linear modelling framework by Morris and Zeggini [10]. A short summary of these tests is given here.

SKATO performs a test of association between genetic variants in a region and binary or continuous traits using kernel machine methods. SKATO aggregates individual score test statistics obtained at each variant to compute an overall pvalue for the region. SKATO can be applied to imputed data and can allow adjustment for covariates.

The Binomial Calpha test is a rare variant test developed for binary (disease) traits. The test models the number of minor alleles, y_{k}, at variant k out of a total of n_{k} observations by a binomial (n_{k}, p_{k}) distribution, where k = 1,…,K. Under the null hypothesis, p_{k} = p_{0}, the proportion of cases present in the sample. Under the alternative hypothesis, p_{k} can take on a mixture of values across the K variants, with some variants deleterious (i.e. with greater frequency in the cases than controls, p_{k}>p_{0}), some protective (i.e. with greater frequency in the controls than the cases p_{k}<p_{0}), and some neutral (i.e. with equal frequency in cases and controls p_{k} = p_{0}). It can then be shown that the Binomial Calpha test statistic is simply:

GRANVIL models the trait value of an individual as a function of the proportion of rare variants at which they carry at least one minor allele in a generalised linear regression framework. GRANVIL can thus be applied to binary and quantitative traits, can incorporate imputed genotypes, and can allow adjustment for covariates. However, GRANVIL is a burden test, and thus assumes the direction of effect of all rare variants is the same, within the same gene or pathway.
Our simulations make use of a simple model of population genetics to generate highdensity haplotype data in 30–200 kb genomic regions, designed to represent a gene. Haplotypes are then randomly paired together to form individuals for analysis, and quantitative trait values are generated according to their genotypes at rare causal variants, selected at random according to the underlying trait association model. In the trait association model that we consider here, we assume that the expected phenotypic value of an individual is determined by the net effect of a combination of increaser causal variants, which serve to elevate the mean trait value in the population, and decreaser causal variants, which serve to reduce it. The trait association model is parameterised in terms of: (i) the maximum MAF of each individual causal variant; (ii) the total MAF of all causal variants in the gene; (iii) the relative proportion of increaser and decreaser causal variants; and (iv) the joint contribution of the causal variants in the gene to the trait variance. Full details of the simulation process are described in Text S1.
The Generalised Calpha test, SKATO and GRANVIL are applied directly to the simulated quantitative trait. However, to apply tests designed for binary traits, we dichotomise the quantitative distribution by assigning individuals as “cases” if they belong to the upper 50% of the trait distribution, or “controls” otherwise. The Generalised Calpha test, as well as the Binomial Calpha test, is then applied to the dichotomised trait. The significance of the Generalised Calpha and Binomial Calpha test statistics are evaluated empirically by standard permutation testing (see Text S1 for details), whilst GRANVIL relies on the asymptotic properties of a linear regression model and SKATO uses Davies method [22] for approximating the distribution of the test statistic. For each simulation, we permute 1,000 or 100,000 times to ensure accurate assessment at 0.05 and 1×10^{−5} significance levels, respectively. Simulations are repeated 10,000 times for each set of parameter values.
Rare Variant Analysis of Imputed Data with T1D
We evaluated the evidence for rare variant (MAF<1%) signals of association with T1D in genes on chromosome 6 using the Generalised Calpha test applied to rare variants using genotype data from the WTCCC [18]. All WTCCC samples are ascertained from the UK. We applied the same quality control (QC) filters employed and described by the WTCCC to exclude samples and SNPs from the analysis. These highquality samples were imputed up to the Phase 1 1000 Genomes Project reference panel (June 2011 interim release) [5] comprising 1,094 phased individuals from multiple ancestry groups. Adjustment for finescale population structure is critical in rare variant analysis because recent founder effects can exert greater impact on association analyses with rare variants than with common variants [23]. To control for population structure we constructed principal components to represent axes of genetic variation within the UK and included these as covariates in association analyses to obtain estimates of effect at each SNP that are adjusted for ancestry. These procedures for imputation and control of finescale population structure are the same as those utilised by Magi et al. [24], full details of which are presented in their paper.
For each gene, the Generalised Calpha test was applied to SNPs in two MAF ranges: 0.1%<MAF<0.5% (very rare) and 0.5%<MAF<1% (rare). Measures of effect at each SNP used in the Generalised Calpha test were the log odds ratios estimated from single SNP additive tests of association using simple logistic regression. The Generalised Calpha test was applied to the original data and then, in order to determine a permuted pvalue, to repeated permutations of the case/control status and covariate data (see Text S1 for details of the standard permutation approach). We performed two separate analyses with and without adjustment for the lead MHC SNP for T1D, rs9268645. Assuming there are approximately 30,000 genes in the human genome [25], a pvalue of less than 0.05/30,000 = 1.7×10^{−6} is required to ensure genomewide significance. Hence for each analysis, we performed 600,000 permutations and declared genomewide significance for a given gene if less than 1 of 600,000 (<1.7×10^{−6}) permutations resulted in a Calpha test statistic larger than the original.
Results
Simulation Study
The assumption that the Calpha statistic is normally distributed under the null hypothesis depends on the quantity and independence of the variants considered as well as the accuracy of the individual estimates at each variant, which in turn depends on the sample size and the MAF. By considering regions of a fixed size and varying the minimum MAF of alleles considered and the sample size, we were able to effectively vary the number of variants and the allele frequency distribution in order to explore type I error and power.
Type I error
We began by considering evaluation of the type 1 error rate of the Generalised Calpha test by performing simulations of 2,000 samples in a 50 kb region under a null model where there are no causal variants. Table 1 presents estimated type I errors of the Generalised Calpha test applied to a quantitative trait and a binary trait (where the binary trait is a dichotomised version of the quantitative trait). Over all simulations, the mean number of rare variants with at least 4 copies of the minor allele (0.2%<MAF<1%) was 34; and with at least 10 copies (0.5%<MAF<1%) was 15. Results indicate that the type I error of the Generalised Calpha tests applied to both the quantitative and the binary trait is well calibrated.
Power comparison
Next, we considered evaluation of the power of the Generalised Calpha test by performing simulations of 5,000 and 10,000 samples in a 100 kb region under a range of trait association models. In all simulations, we assume that the maximum MAF of any causal variant is 1%, and the total MAF of causal variants within the gene is 5%, which together account for 0.6% of the trait variance. Simulation results evaluating power are shown in Figure 1 for 10,000 samples and in Figure S1 for 5,000 samples. The Generalised CAlpha tests, the Binomial Calpha and SKATO are robust to the presence of a mixture of risk and protective variants.
For quantitative traits and sufficiently large minimum MAF (see asymptotic properties), the Generalised Calpha performed better than all the other tests compared. In the examples we selected, it performed equally as well or better than SKATO for variants with more than ∼15–25 copies of the minor allele (MAF>∼0.3% for 5,000 samples or MAF>∼0.25% for 10,000 samples) for any combination of risk or protective variants (only shown for 50% risk causal variants). However, the SKATO was optimal for variants with fewer copies of the minor allele. In our qualitative analyses of a binary trait, the Binomial Calpha test and the Generalised Calpha test were comparable for variants with MAF>∼0.5% but the power of the Generalised Calpha test declined for variants with fewer than ∼15–20 copies of the minor allele (MAF<∼0.3% for 5,000 samples and MAF<∼0.2% for 10,000 samples).
Asymptotic properties
The power of the Generalised Calpha test applied to the quantitative and the dichotomised traits decreases rapidly as the number of copies of the minor allele for included rare variants falls below ∼10 in the models we have considered (MAF<∼0.2% for 5,000 samples or MAF<∼0.1% for 10,000 samples). Rapid decreases in power with decreasing MAF are likely to be a consequence of increasing sparseness leading to violation of the assumptions of asymptotic normality in the Generalised Calpha test. Of course, in a given region, the total number of variants considered increases as the minimum MAF decreases – in simulations for 10,000 individuals, the number of variants in our simulated 100 kb region when minimum MAF is 0.5% is 28 increasing to 94 for a minimum MAF of 0.1%  and losses in power are also a consequence of an increased number of noncausal variants being included in this total, but this factor affects the power of all the tests similarly (Figure S2).
Computation time
Computation time for the Generalised Calpha depends on the sample size, the number of markers and the method used to estimate the normally distributed measures of effect at each variant. To analyse all ∼160 markers sequenced on 5,000 or 10,000 individuals in a 100 kb region and obtain permuted pvalues with 1,000 permutations in a Generalised Calpha test of association required ∼5.0 s and ∼10 s, respectively, for a quantitative trait (using estimates of effect derived from linear regression) and ∼20% longer for a binary trait (using estimates of effect derived from logistic regression). Increasing the number of permutations to 100,000 increased the run times ∼20fold. Halving the number of markers analysed only marginally reduced run times. These estimates were based on simple code programmed in R and run on a Unix operating system. Coding in a language that allows faster numerical computation times is expected to reduce run times.
Rare Variant Analysis of Imputed Data with T1D
After QC and imputation, the WTCCC data comprised 2,938 T1D cases and 1,963 controls with directly or imputed genotypes available at 490,888 SNPs with 0<MAF<1%, located in 1,611 distinct genes on chromosome 6; gene boundaries were identified from the UCSC human genome database (build 37). Table 2 shows the genes demonstrating genomewide significant evidence of rare variant association with type1 diabetes on chromosome 6. Genomewide significant (Bonferroni correction for 30,000 genes at a 5% significance level: p<1.7×10^{−6}) evidence of association with T1D were observed with rare variants in 17 genes throughout the 7.5 Mb extended Major Histocompatibility Complex (MHC) region (ranging from the GNL1 gene to the COL11A2 gene). The strongest signal of association was observed at C6orf10 (Z_{NORM} = 89.1, p<1.7×10^{−6}), which contains rare variants previously implicated in susceptibility to T1D [26].
Common SNPs in the MHC have been previously associated with T1D [17], [20]. Exactly which and how many loci in the MHC determine susceptibility remains unclear as a consequence of the high gene density and the strong association between alleles in the region. To take account of established associations in the MHC, we repeated our analyses on the genes with rare variants showing genomewide significance evidence of association with T1D with adjustment for the lead MHC SNP (rs9268645) [17]. The common SNP explained the rare variant association in 11 of the MHC genes; 6 MHC genes achieved genomewide significant evidence of rare variant association with T1D after adjustment for the lead MHC SNP.
Discussion
We have developed the Generalised Calpha test for the analysis of multiple rare variants that display a mixture of increaser and decreaser effects on a binary or quantitative trait. The Generalised Calpha test is a score test combining routinely calculated Gaussian distributed measures of effect at multiple variants in order to increase the power to detect an effect at the gene, region or pathway level. The Binomial Calpha test for binary traits, [14] and, more recently, SKATO [15], have been shown to have several advantages over previously proposed tests by Li and Leal [8], Madsen and Browning [9] and Price et al. [11]: most notably increased power in the presence of a mixture of increaser and decreaser effects. Our results confirm that the Generalised Calpha test is also robust to the presence of bidirectional effects, with no apparent loss in power across a range of different mixtures.
The Generalised Calpha test performs better than SKATO when the data is not too sparse: in our examples we showed the Generalised Calpha was optimal as long as there were at least 15–25 copies of a minor allele at each rare variant. When data is sparse, so that either the sample size is too small and/or the MAF is too low, estimates of allelic effects at each SNP are not robust, and the asymptotic assumptions on which the Generalised Calpha test are based are inappropriate. Similarly, for testing rare variant association with a binary trait, we have shown that the Generalised Calpha test has lower power that the Binomial Calpha test in the presence of variants with very low minor allele counts: a minimum MAF>∼0.5% is recommended in order to achieve comparable power in these tests.
In any application, the Generalised Calpha test works on the assumptions that there are (i) a sufficiently large set of variants; (ii) that estimates of effect based on these variants are robust and independent and; (iii) normally distributed. These assumptions are often unrealistic: they are violated for example, in the presence of linkage disequilibrium, small sample size, low MAF or few variants. Hence, it is imperative that permutation testing is employed for accurate estimation of significance. For analysis of the whole genome, 1,000 permutations, for which a simply coded version of the test can be run in a matter of seconds, is recommended as a first approach; regions where the test is significant with a pvalue<0.001 can then be rerun with 100,000 or more permutations for an accurate estimate of genomewide significance.
Unlike the Binomial Calpha test, the Generalised Calpha test can naturally adjust for additional covariates and can easily incorporate imputed variation. Unlike SKATO, the Generalised Calpha test can be applied to summary statistics, without requirement of the individual level genotype data. For example, the Generalised Calpha test can be quickly and easily applied to published data. However, this is recommended only for discovery as permutation testing cannot be implemented in this case and test statistics are likely to be inflated leading to increased type I errors: In this case, any regions identified would require further investigation for any confirmation of association.
Evaluation of rare variants extracted from existing GWAS data via imputation up to resequencing reference panels, such as those made available by the 1000 Genomes Project, has been demonstrated to be feasible [18]. We applied the Generalised Calpha test to rare variants imputed into the WTCCC T1D GWAS across the MHC where genes have been shown to play the single most important role in susceptibility to T1D in both common variant and haplotype analyses. Genomewide significant association with T1D, independent of the lead common variant GWAS signal in the region, was observed at multiple genes. These included HLA class II genes, DR and DQ, where coding polymorphisms have been shown to account for most of the association with T1D observed at the HLA locus [27], [28], [29]. The identification of rare diseaseassociated variants within genes in this region highlights the complex genetic architecture of T1D in the MHC, and requires further investigation to disentangle the effects of common and rare variation on immune disease susceptibility.
In summary, the Generalised Calpha test is a novel, flexible and powerful method for the analysis of rare genetic variation. There is no single alternative test, amongst those we have considered, that is uniformly most powerful over all models and genetic architectures. Our test, however, has the unique advantage that it can be applied to summary statistics from published literature, without the need for individual level genetic data. The fact that the Generalised Calpha test simply aggregates data from summary statistics allows for great flexibility in general allowing direct application to both binary and quantitative traits, to population (using summary statistics from generalized linear models, as illustrated here) and family based data (using summary statistics from the transmission disequilibrium test, for example), and to imputed genotype data whilst simultaneously allowing for the adjustment of additional covariates. We are already using the method in our analyses and it is currently implemented using the RPLINK/SEQ library available from: http://atgu.mgh.harvard.edu/plinkseq/. R package is available from http://www.well.ox.ac.uk/~rivas/calphanorm.tar.gz.
Supporting Information
Zdroje
1. GudbjartssonDF, WaltersGB, ThorleifssonG, StefanssonH, HalldorssonBV, et al. (2008) Many sequence variants affecting diversity of adult human height. Nat Genet 40: 609–615.
2. LettreG, JacksonAU, GiegerC, SchumacherFR, BerndtSI, et al. (2008) Identification of ten loci associated with height highlights new biological pathways in human growth. Nat Genet 40: 584–591.
3. WeedonMN, LangoH, LindgrenCM, WallaceC, EvansDM, et al. (2008) Genomewide association analysis identifies 20 loci that influence adult height. Nature genetics 40: 575–583.
4. Lango AllenH, EstradaK, LettreG, BerndtSI, WeedonMN, et al. (2010) Hundreds of variants clustered in genomic loci and biological pathways affect human height. Nature 467: 832–838.
5. A map of human genome variation from populationscale sequencing. Nature 467: 1061–1073.
6. CohenJC, KissRS, PertsemlidisA, MarcelYL, McPhersonR, et al. (2004) Multiple rare alleles contribute to low plasma levels of HDL cholesterol. Science 305: 869–872.
7. MorgenthalerS, ThillyWG (2007) A strategy to discover genes that carry multiallelic or monoallelic risk for common diseases: a cohort allelic sums test (CAST). Mutation research 615: 28–56.
8. LiB, LealSM (2008) Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. American journal of human genetics 83: 311–321.
9. MadsenBE, BrowningSR (2009) A groupwise association test for rare mutations using a weighted sum statistic. PLoS genetics 5: e1000384.
10. MorrisAP, ZegginiE (2010) An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genet Epidemiol 34: 188–193.
11. PriceAL, KryukovGV, de BakkerPI, PurcellSM, StaplesJ, et al. (2010) Pooled association tests for rare variants in exonresequencing studies. American journal of human genetics 86: 832–838.
12. ZeltermanD, ChenCF (1988) Homogeneity Tests against CentralMixture Alternatives. Journal of the American Statistical Association 83: 179–182.
13. NeymanJ, ScottE (1966) On the use of c(α) optimal tests of composite hypotheses. Bulletin of the International Statistical Institute 41: 477–497.
14. NealeBM, RivasMA (2011) Testing for an unusual distribution of rare variants. PLoS Genet 7.
15. WuMC, LeeS, CaiT, LiY, BoehnkeM, et al. (2011) Rarevariant association testing for sequencing data with the sequence kernel association test. American journal of human genetics 89: 82–93.
16. LeeS, WuMC, LinX (2012) Optimal tests for rare variant effects in sequencing association studies. Biostatistics 13: 762–775.
17. BarrettJC, ClaytonDG, ConcannonP, AkolkarB, CooperJD, et al. (2009) Genomewide association study and metaanalysis find that over 40 loci affect risk of type 1 diabetes. Nature genetics 41: 703–707.
18. HuangJ, EllinghausD, FrankeA, HowieB, LiY (2012) 1000 Genomesbased imputation identifies novel and refined associations for the Wellcome Trust Case Control Consortium phase 1 Data. European Journal of Human Genetics 2012;20: 801–805 doi: 10.1038/ejhg.2012.3
19. LiY, ByrnesAE, LiM (2010) To identify associations with rare variants, just WHaIT: Weighted haplotype and imputationbased tests. American journal of human genetics 87: 728–735.
20. Genomewide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447: 661–678.
21. CochranWG (1952) The Chi2 Test of Goodness of Fit. Annals of Mathematical Statistics 23: 315–345.
22. DaviesR (1980) The distribution of a linear combination of chisquare random variables. J R Stat Soc Ser C Appl Stat 29: 323–333.
23. BodmerW, BonillaC (2008) Common and rare variants in multifactorial susceptibility to common diseases. Nature genetics 40: 695–701.
24. MagiR, AsimitJL, DayWilliamsAG, ZegginiE, MorrisAP (2012) GenomeWide Association Analysis of Imputed Rare Variants: Application to Seven Common Complex Diseases. Genet Epidemiol 2012 Sep 5. doi: 10.1002/gepi.21675
25. Finishing the euchromatic sequence of the human genome. Nature 431: 931–945.
26. FengT, ZhuX (2010) Genomewide searching of rare genetic variants in WTCCC data. Human genetics 128: 269–280.
27. NobleJA, ValdesAM, CookM, KlitzW, ThomsonG, et al. (1996) The role of HLA class II genes in insulindependent diabetes mellitus: molecular analysis of 180 Caucasian, multiplex families. American journal of human genetics 59: 1134–1148.
28. SheJX (1996) Susceptibility to type I diabetes: HLADQ and DR revisited. Immunology today 17: 323–329.
29. ToddJA (1995) Genetic analysis of type 1 diabetes using whole genome approaches. Proceedings of the National Academy of Sciences of the United States of America 92: 8560–8565.
Štítky
Genetika Reprodukční medicínaČlánek vyšel v časopise
PLOS Genetics
2013 Číslo 8
Nejčtenější v tomto čísle
 Chromosomal Copy Number Variation, Selection and Uneven Rates of Recombination Reveal Cryptic Genome Diversity Linked to Pathogenicity
 GenomeWide DNA Methylation Analysis of Systemic Lupus Erythematosus Reveals Persistent Hypomethylation of Interferon Genes and Compositional Changes to CD4+ Tcell Populations
 Transposon Domestication versus Mutualism in Ciliate Genome Rearrangements
 Associations of Mitochondrial Haplogroups B4 and E with Biliary Atresia and Differential Susceptibility to Hydrophobic Bile Acid