Background An allele score is a single variable summarizing multiple genetic variants associated with a risk factor. It is calculated as the total number of risk factor-increasing alleles for an individual (unweighted score), or the sum of weights for each allele corresponding to estimated genetic effect sizes (weighted score). An allele score can be used in a Mendelian randomization analysis to estimate the causal effect of the risk factor on an outcome.Methods Data were simulated to investigate the use of allele scores in Mendelian randomization where conventional instrumental variable techniques using multiple genetic variants demonstrate ‘weak instrument’ bias. The robustness of estimates using the allele score to misspecification  and to violations of the instrumental variable assumptions was assessed.Results Causal estimates using a correctly specified allele score were unbiased with appropriate coverage levels. The estimates were generally robust to misspecification of the allele score, but not to instrumental variable violations, even if the majority of variants in the allele score were valid instruments. Using a weighted rather than an unweighted allele score increased power, but the increase was small when genetic variants had similar effect sizes. Naive use of the data under analysis to choose which variants to include in an allele score, or for deriving weights, resulted in substantial biases.Conclusions Allele scores enable valid causal estimates with large numbers of genetic variants. The stringency of criteria for genetic variants in Mendelian randomization should be maintained for all variants in an allele score. Allele scores  are a convenient way of summarizing a large number of genetic variants associated with a risk factor. An unweighted allele score is constructed as the total number of risk factor-increasing alleles present in the genotype of an individual. A weighted allele score can also be considered, where each allele contributes a weight reflecting an estimate of the effect of the corresponding genetic variant on the risk factor. These weights can be internally derived from the data under analysis, or externally derived from prior knowledge or an independent data source. In this way, multidimensional genetic data on variants associated with a risk factor can be collapsed into a single variable. Allele scores have been constructed for many traits, including fasting,Allele scores are important for the modelling of multifactorial polygenic traits, particularly when the allele score consists either of many common variants with small effects, or of rare variants. When several such variants are combined into an allele score, the score may explain a considerable proportion of variation in the risk factor, even if none of the variants individually does.,In this paper, we consider the use of allele scores in Mendelian randomization: that is the application of instrumental variable methods with genetic instruments to estimate the causal effect of a risk factor on an outcome from observational data.,In this paper, we assume the context of a continuous risk factor and a continuous outcome. In order to consistently estimate a causal effect, further structural assumptions are necessary, such as linearity in the association between the risk factor and the outcome. These assumptions have been discussed at length elsewhere,,CRP gene for the causal effect of C-reactive protein,IL6R gene for the causal effect of interleukin-6 receptor.Violation of the instrumental variable assumptions can occur for a number of biologically plausible reasons, including pleiotropic association of the genetic variant with a confounding variable or with the outcome directly, linkage disequilibrium with another functional variant associated with a confounding variable or the outcome, and population stratification where genetic associations reflect latent strata in the population.Allele scores are used in Mendelian randomization for reasons of simplicity, increased poweret al.et al.et al.et al. chose five variants from genetic regions which showed significant P-values in the dataset, although the precise choice of variants was from a separate meta-analysis . In Ehret et al., several of the 29 variants used in the allele score were novel, and were chosen on the basis of P-values in the dataset. Voight et al.P-values in the dataset.To motivate the methodological issues considered in this paper, we here provide some examples of how allele scores have been used in practice. Lin In order to evaluate the performance of various methods for causal estimation with multiple genetic variants and allele scores, we undertake a simulation study. The study is presented as a ‘theme and variations’, with an initial analysis performed where each of the genetic variants is a valid instrumental variable for the risk factor and has the same magnitude of effect on the risk factor, and with further analyses varying the data-generating mechanism and comparing methods used for constructing the allele score and for instrumental variable analysis.X) which is a linear sum of a confounder (U), assumed unmeasured, a set of J independently distributed genetic variants  representing the number of minor alleles for each variant and a normally distributed error term. The outcome (Y) is a continuous variable calculated as the linear sum of the risk factor, the confounder and an independent error term. The initial data-generating model for individual i is:We generate simulated data for a risk factor . Parameters are chosen to take plausible values with reference to real examples, for example scenario 2, which is motivated by the example of type 1 diabetes, and principles, for example that main effects are generally larger than interaction terms.In further simulations, scenarios 1 to 7 below, we consider various departures from the data-generating model (1) which reflect practical issues relating to constructing and using allele scores. We examine how estimates from instrumental variable methods using an allele score are affected by these changes. Unless otherwise stated, all parameters take the same values as in the initial simulation. In the main paper, we describe situations with 25 variants; results from models with 9 and 100 variants obtained by scaling the genetic parameters accordingly are given in the j from independent normal distributions with mean 0.06 and standard deviation 0.018; so nearly all of the genetic effects sizes are between 0.02 and 0.12. In addition to an unweighted standard allele score where each risk-increasing allele contributed the same value to the allele score, we construct weighted allele scores , and vice versa . In this way the correlation between the weights and the data under analysis is removed. In the third case, a 10-fold cross-validation approach is used, so that 10 estimated sets of weights are calculated, each using 90% of the available data, rather than 50%. In the fourth and fifth cases, weights are generated by sampling from a normal distribution around the true weight with a standard deviation of 0.04 and of 0.01. This represents uncertainty in the estimation of weights taken from the regression of the risk factor on the variants in an external data source of approximately the same size as the original dataset  and of 16 times the size of the original dataset . In the final case, the coefficients from the generating model are the true weights.In the first case, taking the weights from the data under analysis , the estimate from a weighted allele score method is the same as that obtained from a 2SLS method with a separate coefficient for each variant, as the weights are the same as the coefficients from the first-stage regression in the 2SLS analysis. In the second case, using 2-fold cross-validation, the sample is divided randomly into two equal halves. Two sets of weights are estimated in the separate halves of the data  and other secondary variants may have smaller effects, a model called a ‘major-gene/polygene model’ by Pierce P-value . Estimates were obtained using an unweighted allele including only the selected variants.In practice, it may be that the investigator is uncertain if each of the alleles is truly associated with the risk factor in the population of interest and decides to include in an allele score only the variants which show the strongest association with the risk factor. To illustrate this approach, variants were ranked according to their strength of association with the risk factor and selected using two criteria: a fixed number of variants , and a threshold In practice, it may be that some genetic variants do not have linear  effects on the risk factor. We modify the data-generating model (1) by replacing the first line with:In practice, it may be that there are statistical interactions between the genetic variants. These are often called gene–gene interactions, though are more properly thought of as variant–variant interactions.We modify the data-generating model (1) by replacing the first line with:We set In practice, it may be that there are statistical interactions between a genetic variant and a covariate which is not a confounder. These are often called gene–environment interactions, though are more properly thought of as examples of effect modification.V is introduced as a covariate affecting the risk factor but not the outcome, so that V is not a confounder but an effect-modifier. To ensure that the model is similar to those considered previously in terms of instrument strength, we let We modify the data-generating model (1) by replacing it with:In each of scenarios 4, 5 and 6, an unweighted allele score  by replacing the first line with:j is directly associated with the risk factor X  and zero if the variant is associated with the confounder U . The strength of association between the variant and either X or U is constrained to be the same. We draw the We here consider pleiotropic associations of variants with the unmeasured confounder We initially present the results from the initial analysis to demonstrate the performance of the methods in an idealized setting, before giving those from the various additional situations considered.ivreg2 command in Stata, and so the correction has not been implemented here as it is likely that practitioners would use the default option. The median estimates using the allele score are unbiased with correct coverage levels throughout. The precision of the allele score method is greater (i.e. has a lower IQR) than LIML, but the power is similar (where the coverage of each method is close to the correct 95%). This is expected for variants with equal-sized effects as, in this case with a correctly specified allele score, no information is lost by converting the multivariate data on genetic variants to a univariate unweighted allele score.We see that the estimates using 2SLS are biased throughout and coverage is less than the nominal 95% level. Bias acts in the direction of confounding, and is especially serious with large numbers of genetic variants of smaller effect size. Although the power reaches 100% in some cases, this is meaningless when the coverage is below the nominal level and is due to the large bias. The LIML estimates show good performance with bias compatible with zero, but coverage levels decrease as the number of variants increases. This is a known problem, and coverage can be improved by using a correction to the method due to Bekker.In summary, when correctly specified, allele scores allow valid estimation of causal effects using large numbers of genetic variants where conventional methods  suffer from problems of bias and/or reduced coverage . The LIML approach is a reasonable alternative (with less than 10 variants) or a sensitivity analysis (with large numbers of variants) as it is approximately unbiased even with large numbers of instruments.Supplementary data available at IJE online). In each case, we present the median estimates across simulations, and the coverage; the IQR of estimates for a null effect and power for a non-null effect are also shown.We see as follows:For variants with different sizes of effect, the use of true weights rather than an unweighted allele score gave some improvement in power. When the alleles had similar sizes of effect (scenario 1), the gain in power was generally only 3–4%, whereas when the alleles had considerably different sizes of effect (scenario 2), the gain was 12–15%. Results using an unweighted allele score were unbiased even though the model was misspecified. Naive use of weights derived from the same data under analysis resulted in severe bias. Use of precisely estimated externally derived weights was as efficient as use of the true weights, although power was reduced when the weights were less precisely estimated even, in some cases, to below that of the unweighted score. Estimates using weights from a cross-validation approach were unbiased, with power in the 10-fold cross-validation analysis slightly below that with the imprecisely measured external weights, and in the 2-fold cross-validation analysis lower still due to the weights being estimated in a smaller sample. In scenario 2, the composite method results using three instrumental variables indicate a small amount of bias consistent with weak instrument bias. Although nominal coverage levels appear to be maintained, the apparent power is slightly greater than when the true weights are used, possibly due to the slight upward bias in estimates. Composite approaches should only be used therefore when there are variants with substantially different magnitudes of association, and where the composite instrument is reasonably strong.The use of variants chosen according to their strength of association with the risk factor in the data under analysis gave seriously biased estimates, with bias in the direction of the confounded association. The bias is a result of the so-called ‘winner's curse’, whereby the estimate of the lead variant's association with the risk factor is likely to be overestimated because of chance correlation with confounders, leading to bias in the estimate of the causal effect.None of the ways of misspecifying the analysis model considered  affected the bias, coverage or power of estimates using the unweighted allele score.The use of invalid genetic variants in an allele score severely biased estimates of causal effects, even when 90% of the variants in the score were valid instruments.To summarize, the use of an allele score did not seem to be sensitive to implicit parametric assumptions made by the procedure, such as the linearity of the genetic associations. However, estimates are sensitive to how the score is constructed, both how the variants included in the score are chosen and how the weights in a weighted score are determined.The overall conclusion from this simulation study is that unweighted allele scores can be used as instruments in Mendelian randomization if each of the variants used in constructing the allele score satisfies the assumptions of an instrumental variable. We consider an estimator to be valid if it is consistent for the parameter of interest, the finite-sample bias is not large and the nominal coverage of confidence intervals is maintained. The validity of the unweighted allele score did not appear to be adversely affected by misspecifications of the genetic model, at least in the range of simulation examples considered, such as the assumption of equal effect sizes for variants, non-linear genetic effects, or effect modification by variant–variant or variant–environment interactions. This is important because, in practice, the true genetic model is unknown.N-fold cross-validation, where N is the sample size) approach may give even greater precision.When an allele score is proposed for use in a Mendelian randomization analysis, researchers should make clear precisely how the decisions leading to the construction of the score were made. If variants have different sizes of effect on the risk factor, then precision can be gained by using a weighted allele score, although the use of an unweighted score gave reasonable estimates in the examples considered. If variants have considerably different sizes of effect, then a weighted allele score would be thought to be advisable, although the weights should not be generated naively from the data under analysis.The use of an allele score enables reliable instrumental variable analysis with much larger numbers of genetic variants than conventional methods  can handle. Although LIML performed reasonably well in terms of bias, the coverage of the LIML estimate was below nominal levels with large numbers of variants. For variants with different sizes of effect on the risk factor, LIML gave improved power over an unweighted score method, but did not dominate a weighted allele score method in terms of precision. Estimates from the 2SLS method showed bias and poor coverage throughout, a manifestation of the problems of weak instrument bias.In order to make comparisons across simulations with different numbers of variants, we have assumed that the effect size is smaller when there are more variants in the allele score. In practice, there is no trade-off that the effect size decreases as the number of instruments increases. The choice as to how many (and which) variants to include in an allele score should be a question addressed using scientific knowledge rather than statistical testing. Unless variants are very highly correlated, all variants which can be reasonably assumed to be valid instruments should be included in a Mendelian randomization analysis to improve the precision of the causal estimate.The use of large numbers of genetic variants associated with a risk factor has been proposed in Mendelian randomization, on the premise that pleiotropic effects may be expected to ‘balance out’.,Previous work on the use of multiple genetic variants in the context of Mendelian randomization has demonstrated that using an allele score results in increases in power compared with using single genetic variants, with slight reductions in power compared with using multiple variants, but better bias properties.Table A3, available as Supplementary Data at IJE online). Further departures from the analysis model in the data-generating model could be considered. For example, we have here considered genetic interactions on a linear scale; interactions could be considered on a multiplicative scale. We have limited this paper to the case of a continuous outcome. Although the outcome in Mendelian randomization is often binary, binary outcomes result in other difficulties in effect estimation.,Although the simulations have covered a range of different scenarios, the conclusions are limited by the reliance on simulated rather than theoretical results. Different simulation parameters could be investigated in further investigations. In response to concerns from a reviewer, simulations were repeated with a 10-fold larger sample size; overall findings were unchanged  or a cross-validation approach (if the sample size is large or the effect sizes are diverse) would be preferred. In choosing between approaches, there is a tradeoff between an unweighted score , a cross-validation approach , and an external source .One assumption which we have not varied is the independence of genetic variants. If several variants are included in an allele score which are in high linkage disequilibrium (highly correlated), then it would be unnecessary to include all the variants in an allele score, especially if they all happened to be correlated with the same functional variant. This would also lead to difficulties in estimating and interpreting weights in a weighted allele score.A disadvantage of using multiple genetic variants, and allele scores in particular, is sporadic missing data leading to reduced sample sizes for analysis.Supplementary data are available at IJE online.Wellcome Trust (grant number 100114).Stephen Burgess is supported by the


Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects.The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods.The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies. Single Nucleotide Polymorphism (SNP) information has enabled the use of linkage disequilibrium to detect and localize loci affecting phenotypes. The first methods developed searched for disequilibrium between one or a few marker loci and loci responsible for disease susceptibility. Case–control designs were used . TypicalDetection of spurious associations is a major issue that has been investigated by many authors. Such errors occur when population classification based on marker information is confounded with another source of heterogeneity that affects the trait being analyzed. The problem of genetic heterogeneity has been the most widely studied. Two non-exclusive situations can occur: (i) the population consists of genetically different subpopulations and (ii) the population consists of related individuals, which may be recorded through pedigree or not. Several studies have clearly shown that neither relative risk nor simple regression is robust to genetic stratification of the population resulting from the mixture of different groups  or families -9.ad hoc families have to be recruited. They are based on the association, within heterozygous parents family, of segregation distortion at a marker locus and progeny phenotypes. This idea was first implemented in the transmission disequilibrium test (tdt) designed by Spielman et al. )Although limiting spurious associations by using within-family analyses was very successful, case–control association studies in populations consisting of individuals assumed to be unrelated were nevertheless frequently performed, in particular because the recruitment of the corresponding samples is much easier . A numbeConcerning quantitative traits, known or hidden population structures can be modeled in mixed models where the phenotype expectation is modeled as the sum of fixed effects, including the effect of the genetic marker being tested, and a random individual polygenic effect. Covariances between the individual polygenic effects are proportional to the polygenic variance and coancestry coefficients, which can be estimated from pedigree or marker information -36. ThisIn these mixed models, polygenic and residual variances have to be estimated separately for each marker fitted before its significance is tested. This estimation phase, to be repeated for each marker tested, can be a limiting factor in large designs and simpler approaches have been proposed. The GRAMMAR method was developed by Aulchenko et al. ,42 and bOther approaches have been proposed, with the aim of accelerating computations  QTL, and random noise e (y = 1μ + xβ + u + e). Hereafter, this model is designated as the “true model”. The approximate methods, mentioned in the introduction, estimate β using simplified models. Generally, for each of these simplified models (i), the regression coefficient of the SNP effect  is estimated by the general least squares estimator (i). The t-tests can then be formulated as:The statistics compared in this paper are testing whether, or not, the variability of a quantitative trait, χ2 distribution, these tests are assumed to follow non-central t-distributions with non-centrality parameter y does not follow the simplified model (i); only if the tests are computed with expectations and variance of y, do the tests follow a t-distribution. Let y follows the true model. Then, the valid Student’s tests are:As the ratio of a normal distribution with unit variance and an independent square root τi)( that is used instead of ti)( can be expressed as τi). These normal distributions have mean riance 1 . The tesand variance:y, i.e. the matrix of relationships among individuals and the polygenic variance. The true type 1 error rate and power of the tests of model (i) were analytically determined. Under the null hypothesis , the tests τi), where Φ is the standardized cumulative normal distribution. With the same threshold, knowledge of the true variance and expectation of the tests τi) is the expectation of the test statistic and Vβ = 0(τi) the variance of the test statistic under the null hypothesis. Under the alternative hypothesis , the statistical power was computed as b. The bias of the estimator of the regression coefficient of the SNP effect was computed as The aim of the present study was to express these moments as a function of the parameters of the true model for (i) used for analysis are defined. The expectation and variance of the test τi), μ is the vector of the overall mean, β the regression coefficient of the fixed SNP effect, u the vector of random additive genetic effects of the animals and e the vector of random residuals. Let E(u) = 0, V(u) = Aσu2 with A being the relationship matrix and σu2 the additive polygenic variance, and V(e) = Iσe2 with σe2 the residual variance. Heritability was defined as the ratio between the polygenic genetic variance and the sum of polygenic variance and residual variance: σy2 = σu2 + σe2. The vector x is the incidence vector of the SNP effect, defined as w is p being the frequency of allele 2 and q the frequency of allele 1, so that E(w) = 0 and V(w) = 1. Based on the definition of x, the relationship between the regression coefficient of the true model and the allele substitution effect (the difference between genotype 11 and 12 or 12 and 22) is:where  example ), where So, the same statistical power was obtained for different allele substitution effects, depending on the allele frequencies. For the sake of simplicity, no other fixed effect was added to the model.(i), i = 1,…,4 was added to identify the effects specific to each of the four models.We analyzed four simpler models that were used to estimate the SNP effect instead of the true model. The first three models were association analyses and the fourth was a linkage and association analysis. The superscript 1) The first model was a simple regression model with no polygenic effect:2) The second model was the GRAMMAR method developed by  and 43]43]. GRAMthen the estimates of residuals are used to estimate the SNP effect:3) The third model was derived from the FASTA approach from . To homoy = 1μa)(2 + ua)(2 + ea)(2), i.e. with but with variance components estimated from the same random model like in the first step of GRAMMAR  The fourth model was the linkage analysis and association method, QTDT, developed by . Let z=xβb(4) is the regression coefficient between families and βw(4) the regression coefficient within families.where Details on the algebra used to obtain the results are provided in Additional file ignoring the variance of the estimator of the SNP effect caused by estimation of the variance component instead of using true variance ,replacing quadratic forms by their expectations in products and ratios.Therefore, simulations were first performed to validate the formulae for each method. Validation was restricted to the family structures and heritability values used in the “Comparison of methods” section of the paper. The population used for the simulations therefore consisted of 600 genotyped individuals, offspring of 120, 20 and 10 sires that produced 5, 30 and 60 offspring, respectively. To do this, the genotypes for a SNP were simulated for sires and dams with allele frequencies of 0.5, and the genotypes of the offspring were extrapolated from their parents’ genotypes. Next, the polygenic values of the sires and offspring and the phenotypes of the offspring were computed with and without the effect of a corresponding QTL with an allele substitution effect of 0.20 . The robustness and power of each method were then evaluated using these two phenotypes (with or without a QTL) with a significance threshold of 5% (which is different from the 1% threshold used in the application section). The simulations were performed with heritabilities ranging from 0 to 1 by 0.1 steps. 10 000 replicates were simulated for each scenario. In total, 1 320 000 simulations were performed. For the GRAMMAR and FASTA methods, the ASREML software  was usedAn R program , the SNP effect was estimated by:y followed model (1), y follows the true model, the true expressions are as follows.If the vector The expectation of this estimator is:The variance of the estimator is:So the variance of the estimator of the SNP effect was a function of heritability and of the relationship matrix, in addition to the usual factor involving residual variance. The residual variance was estimated using the sum of squares of residuals. The expectation is:n is the number of animals analyzed.where Finally, the mean and variance of the test statistic that was actually used are:Assuming model (2b), the SNP effect was estimated by:y followed model (2b), Assuming wherey followed the true model:Then, assuming that The estimates of the polygenic effects were biased, and:Thus, when computing the expectation of estimator of the SNP effect:the estimator of the SNP effect was biased,and the residual variance was estimated using the sum of squares of residuals:Hence,The only difference between this model and the true model was the variance components used, which were the same as in the GRAMMAR model. The mixed model equation for model (3) is:If:the estimator of the SNP effect is:y follows model (3), y, areAssuming Hence,Assuming model (4), two regression coefficients had to be estimated:,If assuming model (4), the variance and expectation of the estimators are: and assuming the true model, the expectation and variance of estimates of the regression coefficients are in fact:and the sum of the squares of residuals:Thus, the expectation and variance of the test on M]3,3 denotes the coefficient of line 3 and column 3 that of matrix M.where [With the true model, the classical formulae are:w, the marker genotypes  and the known variance component of the polygenic effects. These formulae can be applied to any kind of data.The above formulae give the conditional expectation of the estimators of the SNP effects and the conditional expectation and variance of test statistics based on specific data, i.e., given x and z and the variance components of the random model (2) were replaced by their expectation. If Ex denotes these expectations and aij is the relationship coefficient between animals i and j, then the relationship coefficient for the Mendelian sampling variance dii can be defined as:The aim of this section is to derive the marginal expectation and variance of the test statistics, by integrating over the distribution of genotypes and the variance components of the random polygenetic effects, given the relationship matrix and variance components of the true model. For this purpose, the quadratic forms involving si is the sire of animal i and di the dam. where D is the diagonal matrix with elements dii. Assuming Hardy Weinberg equilibrium, we know that [Ex(wiwj) = aij, Ex(wiwi) = aii, Ex(wizi) = Ex(zizi) = aii − dii, and Ex(zizj) = aij,when the genotype, w, is expressed in a standardized form, as shown in the introduction. Thus:now that :Ex(wiwj)and for the sums involved in the QTDT (as in ):These expectations replace their corresponding terms in the preceding formulae in order to express all expectations and variances of the tests used for detection of the SNP effect as a function of heritability and the relationship matrix. To this end, the following approximations were made: expectations of ratios and products were replaced by ratios and products of expectations. For the expectation of variance components given the relationships, the following expectations were used:As pointed out in the Methods section, simulations were performed in order to validate the previous analytical results. Table nd = 5, 30 and 60 half-sibs, which is typical for animal breeding data. The power was calculated for a SNP with a regression coefficient of 0.14 in phenotypic standard deviations  of 50% or an effect of 0.33 for a MAF of 10%. The effect of changes in the total number of animals, and estimates of variance components used in GRAMMAR and FASTA was also analyzed.The above formulae can be applied to any data without simulation when the relationship matrix is known. The results presented here are an illustration based on 600 recorded and genotyped progenies belonging to 120, 20 and 10 families of respectively Cuu(2), Cuu(2) between half-sibs, Cuu(2) between animals from different families. Diagonal coefficients of the relationship matrix A were 1 and off-diagonal coefficients were Â¼ between half-sibs and 0 elsewhere. Matrix D was diagonal with coefficients ½. It should be noted that with families of equal sizes:For families of half-sibs, the preceding formulae concerning expectation and variance of the tests throughout the Results section were calculated using:h2 = 0.50 and families of 60 half-sibs. With the GRAMMAR model, the type 1 error rate decreased with heritability and family size. FASTA and QTDT models were practically not affected by polygenic variance and relationships.For an assumed type 1 error rate of 1%, the expected true type 1 error rate is plotted in Figures Figures 2 = 0.10 and a family size of 60 half-sibs, the power of the FASTA model and the true mixed model were 73.2% and 73.3%, respectively).The power was also calculated for the same true type 1 error rate Figure . In thath2 = 0.50 and families of 60 half-sibs).Only the GRAMMAR model resulted in biased estimators of the SNP effect and this is plotted in Figure h2 = 0.50, families of 60 half-sibs and an assumed type 1 error rate of 1%, true type 1 error rate was 11.9% with a total sample of 600 animals and 12.6% with 6000 animals. With the same data structure and the GRAMMAR method, type 1 error rate was 0.38% with 600 animals and 0.35% with 6000 animals.Robustness did not deviate greatly with total sample size. For example, with the regression method and for For both the GRAMMAR and FASTA methods, the final models use variance components that are estimated with the same simple random model. Results presented in the previous section were marginal expectations using the distribution of the estimator of the variance components. However, one question is: what happens if the variance components are not estimated using the same sample as that used to estimate the SNP effect? Heritability can be introduced in the model if the user considers that a better estimate of heritability was obtained using other data. Figure Our algebraic results can be used as a tool to design populations or estimate the success of a given design before starting the genotyping process. FASTA statistics, which are not subject to type 1 error rate due to population stratification, should be used for this purpose.As shown in Figure The genomic control (GC) inflation factor developped by Delvin and Roeder  is a verThe formulae presented in the Methods section of this paper are not easy to interpret. In the following, we explain the behavior of each method in common terms.β = b), the variance of the test was still higher than 1 and increased with heritability, while the expectation of the test did not vary greatly with heritability. So when the threshold chosen for type 1 error rate (tα/2) was lower than the expectation of the test (power greater than 50%), a smaller proportion of the normal distribution is expected to be greater than tα/2 as heritability increases. This explains why the power for the regression method decreased with heritability and the variance of relationships.The high type 1 error rate with high heritability for this method was caused by the probability of two half-sibs sharing the same SNP because of their relationship, rather than the effect of a common QTL genotype. If a polygenic effect is present, this local similarity in SNP is confounded with the similarity of relatives in phenotype due to the polygenic effect. The expectation of polygenic effect is null. Thus, the expectation of the estimate of SNP effect is not affected by this confusion between SNP and polygenes: the test is unbiased. However, the variance of the test increases according to the variability of the relationship level in the data. If all animals in the sample share the same level of relationship , they would all have a similar phenotype and the same probability of sharing the same SNP. Therefore, the increase in type 1 error rate was not caused by close relationships between genotyped animals but by the presence of a mixture of close and more distant relationships. This occurs when independent large families  are present in the data. The effect of this family structure on the variance of the test was proportional to the ratio of the polygenic variance and residual variance and hence increased exponentially with heritability. However, the increase in type 1 error rate with heritability and family size did not systematically result in an increase in power. Under the alternate hypothesis , used to test the SNP effect was approximately equal to the residual variance of the true model minus the genetic variance times (1 minus the reliability of estimates of polygenic effects). Reliability is defined as the square correlation between estimate of polygenic effect and true effect. However, due to the covariance between estimates of the polygenic effect of relatives, which are also likely to share the same SNP genotype, the variance of , which depends on the reliability of the estimates of polygenic effects, due to the mixed model  was higher with the regression method than with the FASTA method for low (large families) to moderate  heritability values. Power was always lower with the GRAMMAR method than with the fasta METHOD. However, for the same true type 1 error rate (i.e. with the threshold chosen to reach the same true type 1 error rate), power was always lower with the regression method than with the FASTA method and decreased very rapidly with heritability and family size. In this situation, powers of the GRAMMAR and FASTA methods were identical. Thus, using the true type 1 error rate, these two methods have the same power. The power of the two methods was also almost identical to that of the true mixed model, except for very low heritabilities, for which a very slight difference was observed between the FASTA and true mixed models.These results are in general agreement with the few papers on the subject that are present in the literature. Using a simple example with three pedigrees,  demonstrTherefore, as a general result, we do not recommend the regression and GRAMMAR models but do recommend the FASTA method. The FASTA method is very close to the full mixed model but is expected to be computationally faster. However, situations do exist for which the first two methods are preferred and using the FASTA method could be dangerous. The advantage of the regression model is that no heritability is required, so it could be useful when heritability is unknown or when the number of animals is too low to estimate heritability based on the data. The regression method may also be useful in situations in which having a large type 1 error rate is not a problem, for example if the objective is to first select markers before performing another type of analysis, since here the aim is to select only good markers, regardless of the number of bad ones. The advantage of the GRAMMAR method is that it has the same power as the FASTA method when corrected for underestimation of the type 1 error rate and that it allows derivation of empirical p-values, as residuals can be permuted. Correcting for underestimation of the type 1 error rate can be performed easily using analytical formulae or by analyzing the QQ plot , which wIt should be noted that this discussion concerned only the first and second moments of the test statistics and did not compare higher moments such as skewness and kurtosis, which could also be of interest.Analytical formulae of the first and second moments of the distribution of the test statistics used to detect the SNP effect in four of the most common models are given in the case of structured populations due to relationships between individuals. These formulae were used to compute the type 1 error rate and power of these methods for any type of genetic relationships between phenotyped and genotyped individuals in any situation of heritability for a polygenic effect. The objective was to determine if these formulae can be easily used to obtain the correct type 1 error rate and to calculate the power in order to design data collection. An R program is provided in Additional file The authors declare that they have no competing interests.All authors were involved in the conception of the study. JME and AR wrote the manuscript. AR derived analytical results. ST performed simulations and wrote the R package. All authors read and approved the final manuscript.Details on the algebraic formulae used to obtain the results. Details of matrix algebra used to construct the formulae in the main text.Click here for fileSimulations. Details and standard errors of the simulations used to confirm the analytical results.Click here for fileRobPower. This is the directory including Rpackage and documentation. This package computes all type 1 errors and the power of any kind of design with: 1. The A matrix obtained either from the pedigree file or from a known matrix. 2. The D matrix obtained either from the pedigree file or from a known matrix. 3. A value of heritability . 4. A threshold . 5. The phenotypic variance explained by the QTL . 6. The methods to compute . Methods are “reg” for regression model, “GRAMMAR”, “QTDT” and “FASTA”. 7. Genomic control (GC). If GC = TRUE then the GC value is computed (available for “reg” and “GRAMMAR” only). 8. Linkage disequilibrium (r2) between the marker tested and the QTL.Click here for file


Correlations between Educational Attainment (EA) and measures of cognitive performance are as high as 0.8. This makes EA an attractive alternative phenotype for studies wishing to map genes affecting cognition due to the ease of collecting EA data compared to other cognitive phenotypes such as IQ.In an Australian family sample of 9538 individuals we performed a genome-wide association scan (GWAS) using the imputed genotypes of ∼2.4 million single nucleotide polymorphisms (SNP) for a 6-point scale measure of EA. Top hits were checked for replication in an independent sample of 968 individuals. A gene-based test of association was then applied to the GWAS results. Additionally we performed prediction analyses using the GWAS results from our discovery sample to assess the percentage of EA and full scale IQ variance explained by the predicted scores.−7). In our independent replication sample six SNPs among the top 50 hits pruned for linkage disequilibrium (r2<0.8) had a p-value<0.05 but only one of these SNPs survived correction for multiple testing - rs7106258 (p = 9.7*10−4) located in an intergenic region of chromosome 11q14.1. The gene based test results were non-significant and our prediction analyses show that the predicted scores explained little variance in EA in our replication sample.The best SNP fell short of having a genome-wide significant p-value (p = 9.77×10While we have identified a polymorphism chromosome 11q14.1 associated with EA, further replication is warranted. Overall, the absence of genome-wide significant p-values in our large discovery sample confirmed the high polygenic architecture of EA. Only the assembly of large samples or meta-analytic efforts will be able to assess the implication of common DNA polymorphisms in the etiology of EA. Access to education is considered to be a predictor for a wide range of later life outcomes such as employment Biological processes involved in scholastic achievement and cognitive performance are likely to be shared to some extent. Twin studies that take advantage of differences between genetically identical twins (monozygotic or MZ) and fraternal twins (dizygotic or DZ), have shown that EA and cognitive performance are influenced to a large extent by common genetic factors COMT) BDNF) DRD4) Molecular genetics studies of EA have been largely limited to a candidate gene approach including the Catechol-O-methyltransferase (The participants for our discovery sample were drawn from two cohorts of adult twin families (cohorts 1 and 2) that have taken part in a wide range of studies of health and well-being. Individuals from Cohort 1 were born before 1964 and individuals from cohort 2 were born between 1964 and 1981. Both these cohorts have participated in previous postal questionnaire and telephone interview studies, and recruitment was extended to their relatives . Our total discovery sample was composed of 9538 individuals for whom both EA and genome-wide SNP genotype data were available. Our replication sample (Cohort 3) consisted of 968 individuals who are the parents of adolescent twins participating in our melanoma risk factors and cognition studies (1996-ongoing) For the prediction analysis of cognitive ability based on the EA GWAS results obtained in the discovery sample, we used one of the twin children of cohort 3. Their full scale IQ (FSIQ) was collected as part of the cognition study and genotyping data were available for 1842 adolescent twins and their siblings ranging in age from 15 to 22 years (mean = 16.28 years ±0.45 SD).Ethical approval, for the studies from which the data drawn, was obtained from the Human Research Ethics Committee of the Queensland Institute of Medical Research. Informed written consent for all measures was obtained from each participant and their parents/guardian if participants were younger than 18 years of age.Self reported educational attainment (EA) was collected as part as of questionnaires and telephone interviews. In the adult cohorts (1 and 2) three similar education scales were used to collect EA depending on the study in which an individual participated . Each inCognitive abilities were measured by full scale IQ (FSIQ) that was assessed using the Multi-dimensional Aptitude Battery (MAB) The genotypic data used in the current study come from a large genotyping project involving nine waves of genotyping that used three different Illumina SNP chips  2, YOB2×sex, age2, Age×sex and Age2×Sex were used as covariates. Both YOB and age were used as covariates in this study: YOB in order to account for changes in terms of access to education that have occurred since the early 1900's and age in order to account for the fact that the older an individual is, the less likely he/she is to undertake further education. Visualisation and annotation of the GWAS results was conducted using WGAViewer 2<0.8) of the top 200 SNPs was performed in SNAP Genome wide association analysis using dosage scores was performed in MERLIN offline Additionally, The VEGAS gene-based test −8) was detected. Results indicated that our sample provides 100%, 80% (799 out of the 1000 simulations) and 13% (130 out of the 1000 simulations) power to detect SNPs that explain 1%, 0.5% and 0.2% of the variance in EA, respectively.It is expected that many genes of very small effect size contribute to the genetic variance of complex traits. We estimated the empirical power our discovery sample provides to detect genetic variants explaining 1%, 0.5% and 0.2% of the phenotypic variance by running association tests on simulated datasets in Merlin. The simulated datasets are similar to the original data in terms of marker informativeness, spacing, allele frequency, trait distribution, and missing data patterns, but they are simulated such that a selected SNP accounts for a specified proportion of the variance. The selected SNP had minor allele frequency 0.25. Association analysis was conducted on 1000 data sets generated by the simulation procedure. The empirical power is estimated as that proportion of the 1000 association analyses in which a genome-wide significant association (α = 5*10http://cran.r-project.org/) to evaluate to percentage of variance explained (R2) by the predicted score and its level of significance. Similarly, we fitted the FSIQ of one of the twin children as a function of their predicted scores in a linear model (FSIQ∼predicted scores).Prediction analyses were conducted in two stages. In stage 1, the effect sizes of the 2,480,163 SNPs from GWAS for EA, as well as 5 sub-panels of SNPs , were extracted from the MERLIN th century , with the best-associated SNP rs2680324 having a p-value of 9.77×10−7 , however, it does not reach the multiple-testing correction threshold (p = 0.05/17549 = 2.8*10−6).To completely utilise the GWAS results, we then performed a gene-based test that maps SNPs to their respective genes if they are located within 50 kb of a gene locus. The gene-based test produced an empirical p-value for 17549 autosomal genes. The top 50 most associated genes are reported in 2 ranging between 0.0011 to 0.0023 (non-significant: p≥0.14) between the predicted scores and EA in the independent sample of adults in all 6 analyses. Similarly, in the children of these individuals (n = 799) when we attempted to predict FSIQ as a function of the predicted scores across the different thresholds of GWAS significance the regression r2 were non-significant (p≥0.15) and varied between 9.0*10−5 to 0.0026.Our Prediction analyses of EA in our replication sample using predicted scores for different thresholds of GWAS significance (from p<0.1 to the whole genome) showed a regression rth century from a mean EA of 8–10 years of schooling to around 12 years of schooling followed by apprenticeship, teacher college or technical college. This trend was the same for males and females. However, it should be noted that only 2% of our sample was born before 1926 and 31% before 1951. Thus the data are too sparse to comment on the changes of mean EA in relation to time specific events such as World War II. The majority of our sample was born post World War II and the mean EA for these individuals confirms that pursuing a tertiary education was much more common for these generations than it was for the previous generations. The mean EA for individuals born in this period remained fairly constant and major events such as the Vietnam War  or free access to university education (1974–1988) do not appear to have affected the level of EA in our sample.In the current study we observed that Educational attainment (EA) has increased constantly during the 20−8. Therefore, we tested the robustness of the top 50 most associated SNPs pruned for LD (r2<0.8) in a replication sample. Five of these 50 SNPs reached a p-value smaller than p = 0.05 and an effect in the same direction. Among these SNPs only one had a p-value surviving multiple correction, rs7106258 (p = 0.00097) located in an intergenic region of chromosome 11q14.1 . This region deserves future attention as it has been suggested to be involved in other brain phenotypes. This region contains the GAB2 gene, a candidate gene for Alzheimer's disease Using SNP genotyping data for these individuals, we performed a large GWAS study for EA. The strength of our study was its large sample size that conferred 100% and 80% power to detect polymorphisms (MAF = 0.25) explaining 1% and 0.5% of the phenotypic variance respectively. However, despite a good power, no SNP had a p-value significant at the genome wide level of 5×10Overall our GWAS findings are comparable to the latest GWAS report for general cognitive abilities in that no SNPs survived multiple testing correction for genome wide significance Another noticeable feature of our GWAS results is that none of the top 50 SNPs fall into exons. This is not surprising as more than 80% of associated variants detected by GWAS were found in non-coding regions FLJ 41766 was the best hit, however, there is no evidence for this gene to suggest a role in neurobiology. A similar observation was found when looking at the genes among the top hits one at the time. Additionally, both the gene-based test and GWAS showed no evidence of association for BDNF (rank = 16132 out of 17549 genes tested by VEGAS), COMT (rank = 197), and DRD4 (rank = 17451), which have been previously associated with EA Moving from a traditional single marker analysis, we performed the VEGAS gene-based test One of the major goals of genetic epidemiologists is to identify genetic variants that can be used to predict complex traits and susceptibility risk to diseases. So far, this has been harder than originally thought due to the difficulty of mapping loci of small effect that reflect the highly polygenic architecture of common diseases and complex traits. One recent approach that has been used in this exercise is to generate a predicted score based on a genome wide profile of SNPs effects In the present study we performed one of the largest genome wide association scans to examine the molecular genetics of educational attainment. Despite our large discovery sample and good genome coverage of the genome, no SNP reached genome wide evidence of association. As for many other complex traits . The grey shade area represents the 95% confidence intervals.(TIFF)Click here for additional data file.Figure S2Manhattan plot of GWAS for educational attainment for 9538 individuals.X-axis represents the chromosomal location for each SNPs, and Y-axis the −log10 P-value for association with educational attainment.(TIF)Click here for additional data file.Table S1Descriptive statistics for the different cohorts from which the educational attainment data originated.(DOC)Click here for additional data file.


Genomic predictions can be applied early in life without impacting selection candidates. This is especially useful for meat quality traits in sheep. Carcass and novel meat quality traits were predicted in a multi-breed sheep population that included Merino, Border Leicester, Polled Dorset and White Suffolk sheep and their crosses.Prediction of breeding values by best linear unbiased prediction (BLUP) based on pedigree information was compared to prediction based on genomic BLUP (GBLUP) and a Bayesian prediction method (BayesR). Cross-validation of predictions across sire families was used to evaluate the accuracy of predictions based on the correlation of predicted and observed values and the regression of observed on predicted values was used to evaluate bias of methods. Accuracies and regression coefficients were calculated using either phenotypes or adjusted phenotypes as observed variables.Genomic methods increased the accuracy of predicted breeding values to on average 0.2 across traits (range 0.07 to 0.31), compared to an average accuracy of 0.09 for pedigree-based BLUP. However, for some traits with smaller reference population size, there was no increase in accuracy or it was small. No clear differences in accuracy were observed between GBLUP and BayesR. The regression of phenotypes on breeding values was close to 1 for all methods, indicating little bias, except for GBLUP and adjusted phenotypes (regression = 0.78). Accuracies calculated with adjusted (for fixed effects) phenotypes were less variable than accuracies based on unadjusted phenotypes, indicating that fixed effects influence the latter. Increasing the reference population size increased accuracy, indicating that adding more records will be beneficial. For the Merino, Polled Dorset and White Suffolk breeds, accuracies were greater than for the Border Leicester breed due to the smaller sample size and limited across-breed prediction. BayesR detected only a few large marker effects but one region on chromosome 6 was associated with large effects for several traits. Cross-validation produced very similar variability of accuracy and regression coefficients for BLUP, GBLUP and BayesR, showing that this variability is not a property of genomic methods alone. Our results show that genomic selection for novel difficult-to-measure traits is a feasible strategy to achieve increased genetic gain. Sheep meat production is increasing and replacing wool production as the primary product of the Australian sheep industry. ImproviEstimating GEBV for selection candidates requires a reference population with both marker genotypes and phenotypes. Because selection candidates often lack phenotypic records, the predictive performance of GEBV can be assessed either with a set of validation individuals that have highly accurate EBV, e.g. sires with many progeny,10, or bFor difficult-to-measure and novel traits, individuals with highly accurate EBV often do not exist. Thus, in such cases, cross-validation is applied. In the cross-validation approach, the reference population is divided into a number of subsets and each subset is predicted using a reference population that excludes this particular subset. The method used to divide the data has been shown to affect prediction accuracy, e.g.,17,18. CThe utility of applying genomic prediction must be evaluated against what would be achieved with non-genomic approaches, such as best linear unbiased prediction (BLUP) using pedigree. Cross-vThe aim of this study was to predict GEBV for several carcass and novel meat quality traits in a multi-breed sheep population. A previous study in the same population investigated how much of the accuracy of GEBV could be attributed to population structure. Here, aDatasets from the Cooperative Research Centre for Sheep Industry Innovation  and SheeThe following traits were analysed and phenotypic information for these traits is provided in TableP-value cut-off of 1×10–15), if the genome location was unknown or if the SNP showed complete linkage disequilibrium (r2 > 0.99) with another SNP on the chip. Data for a genotyped animal were removed if the genotype call rate was less than 0.9 for that animal or if the animal’s mean heterozygosity was higher than 0.5, indicating sample contamination. The genotype database was built over a number of years, missing genotypes were initially imputed using fastPHASE[All animals were genotyped using the Illumina 50K ovine SNP chip, containing 54 977 single nucleotide polymorphisms (SNP) . After applying the following quality control measures, 48 599 SNP were retained: SNP were removed if the call rate was less than 95%, if the Illumina Gentrain score was less than 0.6, if the minor allele frequency was less than 0.01, if the SNP was not in Hardy-Weinberg equilibrium , using the following single-trait model:y is a vector of phenotypic records, X, and Z1 are design matrices relating the fixed and random effects to the phenotype, Q is a matrix containing breed proportions for each animal, derived from pedigree information, μ is the mean, b is a vector of fixed effects, a is a vector of random additive polygenic effects, q is a vector of random breed effects, fitted as partial regressions, and e is the vector of residuals. The following distributions were assumed: a ~ N , q ~ N , and e ~ N , where A is the numerator relationship matrix, σa2 is the additive variance, σq2 is the variance of breed effects, and σe2 is the residual variance. The base model included the following fixed effects: sex, birth type, rearing type, contemporary group (birth year × site × slaughter group), and age at trait recording. Age of the dam was fitted only for CRC data. HCWT was included as a fixed covariate for all traits except for DRESS and LMY. The size of the relevant pedigree was 16 985 individuals. The phenotypes (y) were restricted to genotyped animals to make a fair comparison to the genomic prediction methods.where Genomic breeding values were calculated using GBLUP, for which variance components were also estimated with REML analysis, using tZ2 is a design matrix, g is a vector of random additive genomic effects distributed as N , σg2 is the genomic variance, G is the genomic relationship matrix[G to improve numerical stability. Phenotypes, rather than de-regressed estimated breeding values, were used to ensure independence of reference and validation sets. If all phenotypes were used to calculate breeding values, then the accuracy of predicting an animal without a phenotype would be overestimated, because phenotypes of validation animals contributed to the reference pedigree breeding values.where p matrix. SNP wity = 1μ + Xb + Z1Qq + e). The resulting adjusted phenotypes (y*) or residuals were then analysed using BayesR in model:A Bayesian genomic prediction method using a mixture of four normal distributions with increasing variance for marker effects (BayesR) was implW is a design matrix relating adjusted phenotypes to random marker effects (m). BayesR is described in more detail in[σ12= 0, σ22= 0.0001σg2, σ32= 0.001σg2, or σ42= 0.01σg2, and starting values for σg2 were from GBLUP analysis. The prior for the proportion of markers in each distribution was drawn from a Dirichlet distribution. Priors for other parameters were chosen as in Erbe et al.[where etail in. Brieflye et al.. Ten parhttp://www.livestockgenomics.csiro.au/cgi-bin/gbrowse/oarv2.0/ using a 1 Mb interval with 0.5 Mb on each side of the SNP. The probability of the effect of a SNP being in the largest distribution (σ42) was also investigated.Posterior means of marker effects of BayesR resulting from post burn-in chains were averaged across chains and replicates and then standardised by dividing them by the standard deviation of the adjusted phenotypes (SD). SNP with effects greater than 0.005 SD were (arbitrarily) chosen and potential candidate genes were searched for ony) or adjusted phenotypes (y*). Accuracies were divided byNe ~ 850), Border Leicester , Polled Dorset , and White Suffolk [Performance of genomic prediction was evaluated using cross-validation. It is unlikely that potential selection candidates in the Australian sheep population have full or half-sibs in the reference population. Thus, entire sire families in the CRC dataset were randomly chosen and combined into subsets of approximately 500 individuals (CRC subsets). Thus, genomic predictions were evaluated across sire families and larger reference populations had more subsets. The SG dataset was not divided into subsets but was added to each reference population. The performance of predictions was not evaluated for the SG data, because this population is not expected to be representative of the general sheep population. Genomic predictions were calculated for each CRC subset, with the reference set consisting of all other CRC subsets and the SG dataset. Accuracy was evaluated in each validation subset as the Pearson correlation of genomic predicted breeding values  and both GBLUP and BayesR led to more accurate GEBV than pedigree-based BLUP . The results show a clear trend of increased accuracy with increasing size of the reference population and suggest that further increases in accuracy should be possible if the reference population is increased further.FigureNe (about 800)[Ne ~ 300), which results in a larger number of independent chromosome segments to be predicted[The accuracy of GEBV was lower in Border Leicester sire breed groups than in the Merino, Polled Dorset and White Suffolk breeds Figure. This isout 800) than theredicted-33. Thusredicted, reporteThe slope of regression of either phenotypes or adjusted phenotypes on GEBV was close to 1 for all methods, except when using adjusted phenotypes and GBLUP, which resulted in a regression coefficient of 0.78  are not strictly equivalent to the accuracy which would be obtained with purebred animals. However, in the absence of purebred individuals with carcass data, this represents the best possible approximation. However, while the selection of breeding stock takes place among purebred individuals, commercial stock results from crosses between terminal and maternal sheep breeds.Another aim of this study was to compare the variability of cross-validated EBV accuracies across subsets from pedigree-based BLUP and genomic methods. No large differences were observed, aside from the increase in accuracy using genomic data. In addition, accuracies from pedigree-based BLUP and genomic methods had very similar standard errors, indicating that cross-validation accuracies are just as variable across subsets for pedigree-based BLUP.σ42). In addition, the largest effects were consistently assigned to the same SNP across the 10 parallel BayesR chains.While BayesR did not increase the accuracy of genomic prediction compared to GBLUP, it does explicitly estimate marker effects and the proportion of markers in each of the four distributions. BayesR estimates of marker effects greater than 0.05 adjusted phenotypic trait SD are presented in TableABCG2) and Polycystin-2 (PKD2), which have been reported as having been under selection in an analysis of a large number of sheep breeds[ABCG2, a gene involved in ATP binding, has been found to contain a causative mutation that affects milk yield and composition in dairy cattle[NCK2 protein. This gene is close to SNP OAR3_64213489 (DRESS 0.0052SD) and codes for an adaptor protein that associates with tyrosine-phosphorylated growth-factor receptors. ARF GTPase-activating protein (GIT1), which is close to SNP OAR11_21345650_X , codes for a GTPase-activating protein that is possibly involved in vesicle trafficking, adhesions and cytoskeletal organisation.Potential candidate genes within a 1 Mb interval with 0.5 Mb on each side of the SNP are also presented in Tablep breeds. ABCG2, y cattle and has y cattle. AnotherThe main benefit of genomic selection for carcass and novel meat quality traits is that it is not necessary to sacrifice valuable selection candidates for testing, and GEBV can be obtained early in life. Genomic predictions can be trained within a set of industry representative individuals and then applied in the general sheep population. In its current form, this process is implemented in a centralised approach in sheep, in which test animals are housed in information nucleus flocks. However, data for training could also be collected during slaughter of industry stock, which could substantially increase the number of records. One advantage of an information nucleus is that animals are well identified and similarly managed, and fixed effects are fully recorded. Including industry records would require further investment in recording and tracking of animal production and movement and the development of uniform standards for measurement, sampling and testing at slaughter facilities.in vitro fertilisation[One application of genomic selection is the prediction of accurate breeding values of juveniles without phenotypic records. This allows for significant shortening of generation intervals. In addition, some sheep breeders use juvenile in-vitro fertilised embryo transfer (JIVET), which consists of harvesting immature oocytes from 6 to 8 week old ewe lambs and implanting these into sexually mature individuals after lisation. The comlisation-40.Ne is greater for most sheep breeds than in dairy cattle[The accuracies of EBV obtained with genomic methods were not substantially higher than accuracies of EBV obtained with pedigree-based BLUP. Given the large reference population size, one could have expected a larger increase. However, in our case, many breeds contributed to the reference population and the limited increase in accuracy could be explained by small contributions obtained from across-breed prediction, which has been found to be very low in this population. Increasy cattle. In Holsy cattle. Using tGenomic predictions for meat quality traits in sheep are potentially valuable because they can be applied early in life and do not require potential selection candidates to be sacrificed. In a large multi-breed sheep dataset, genomic prediction resulted in greater accuracies of EBV than pedigree-based BLUP, but for some traits the increase in accuracy was small. Accuracy increased as reference population size increased and the accuracy was greater for the Merino, Polled Dorset and White Suffolk breeds than for the Border Leicester breed. The latter result is explained in part by the lower proportion of Border Leicester sheep in the reference population. It also suggests that across-breed prediction is limited with the 50k SNP chip. The methods GBLUP and BayesR produced very similar accuracies of GEBV, with a mean accuracy of approximately 0.2 across traits. Few markers with large effects were discovered but one region on chromosome 6 was associated with large effects for several traits. Validation correlations of GEBV with phenotypes adjusted for estimates of fixed effects were less variable than correlations with unadjusted phenotypes, and there was little evidence of bias in the GEBV. The general behaviour of cross-validation accuracies was very similar for pedigree-based BLUP, GBLUP and BayesR. In conclusion, genomic breeding values can provide a powerful tool to increase genetic progress in sheep, especially when combined with reproductive technologies.The authors declare that they have no competing interests.HDD, JHJvdV and BJH designed the study, HDD and AAS analysed the data and HDD wrote the manuscript. All authors have read and approved the manuscript.Table S1. Accuracies per trait and sire breed group of BLUP, GBLUP and BayesR, Accuracy calculated as r/h, where the observed variable was either a phenotype or adjusted phenotype. Table S2. Evaluation of bias per trait and sire breed group of BLUP, GBLUP and BayesR. Regression of observed variables on EBV, where the observed variable was either a phenotype or an adjusted phenotype. Table S3. Mean of top 10 genomic relationships of validation animals to reference population. Table S4. Number of validation animals (SE) per sire breed across subsets used for calculating accuracy, bias and relationships to reference. Table S5. Description of potential candidate genes within 0.5Mb of SNP with greater than 0.05 adjusted phenotypic SD effects. Figure S1. Plots of absolute marker effects in adjusted phenotypic SD for all traits.Click here for file


Genome wide association studies (GWAS) are becoming the approach of choice to identify genetic determinants of complex phenotypes and common diseases. The astonishing amount of generated data and the use of distinct genotyping platforms with variable genomic coverage are still analytical challenges. Imputation algorithms combine directly genotyped markers information with haplotypic structure for the population of interest for the inference of a badly genotyped or missing marker and are considered a near zero cost approach to allow the comparison and combination of data generated in different studies. Several reports stated that imputed markers have an overall acceptable accuracy but no published report has performed a pair wise comparison of imputed and empiric association statistics of a complete set of GWAS markers.P < 10 -5 for type 2 Diabetes Mellitus and compared them with results obtained based on empirical allelic frequencies. Interestingly, despite their overall high correlation, association statistics based on imputed frequencies were discordant in 35 of the 73 (47%) associated markers, considerably inflating the type I error rate of imputed markers. We comprehensively tested several quality thresholds, the haplotypic structure underlying imputed markers and the use of flanking markers as predictors of inaccurate association statistics derived from imputed markers.In this report we identified a total of 73 imputed markers that yielded a nominally statistically significant association at Our results suggest that association statistics from imputed markers showing specific MAF (Minor Allele Frequencies) range, located in weak linkage disequilibrium blocks or strongly deviating from local patterns of association are prone to have inflated false positive association signals. The present study highlights the potential of imputation procedures and proposes simple procedures for selecting the best imputed markers for follow-up genotyping studies. Genome-wide association studies (GWAS) are a promising tool for the identification of genetic markers underlying phenotypes of interest and recently allowed the identification of markers associated with several human complex phenotypes. These sTo overcome these issues, genotyping imputation algorithms were developed. These methods use information provided by high quality markers combined with genome structure information for the population of interest organized in the HapMap database. These procedures can potentially be a nearly zero-cost alternative to increase both power and coverage in individual GWA studies. The imputation procedures allow meta- and pooled analyses of GWAS data generated by distinct genotyping platforms, maximizing their overlap and, consequently, the number of typed individuals. Despite promising, the success of imputation algorithms are relative since they could also amplify non-detected technical errors in genotyped markers, the available HapMap information may not be well consolidated for the population of interest or the applied imputation algorithm may not be well suited for a specific dataset .Here, we present a comprehensive comparative analysis of the data generated by the multipoint imputation algorithm and the data obtained by direct genotyping in a type-II diabetes GWAS dataset. This imputation algorithm uses a Markov chain to infer the allelic frequencies of a marker by the information provided by a large set of flanking markers. The analyzed dataset was generated and organized by the Welcome Trust Case Control Consortium (WTCCC) and is a constituent of a large epidemiological study focused in the determination of genetic markers that could predispose an individual to seven different diseases of interest . In thisThe results discussed herein are based on data available for approximately 2000 individuals accessed by type-II diabetes and 3000 healthy individuals (controls). We limited our evaluation to 387,662 biallelic markers with full information on both observed (genotyped) and imputed genotype frequencies. This set of markers covers all chromosomes, but sex-linked markers, having no major over-representation in any specific chromosome. A detailed list of the examined markers and their respective imputed and empiric frequencies is available upon request. In this report, the term empiric denotes markers whose allelic frequencies were determined by direct genotyping.P-values  assuming a multiplicative (log-additive) model of inheritance applied to empiric and imputed frequencies of markers in the complete and filtered dataset. The analysis of Figure Association studies using empiric or imputed frequencies are very sensitive to low quality markers. Accuracy of the Impute algorithm is significantly reduced in alleles showing small MAFs or low calling posterior probabilities . Initialon a -log0 scale aon a -log0 scale arS = 0.80). However, it is important to note some points. Firstly, the wide dispersion of dots around the upper left side of Figure -5 we observed that inferences based on truly genotyped markers yielded evidence for 38 markers possibly associated with type-II diabetes, whereas this number would be 73 SNPs had the same inference been based on imputed markers solely. Approximately 47% of markers that would be considered associated by imputed allelic frequencies were discordant to the evidence derived from direct genotyping. Table Using the filtered dataset, the examined imputation algorithm, as previously described for allele and genotype imputation, also presents a high overall accuracy when comparing the association statistics generated using genotyped and imputed markers . Our empirical analysis demonstrated that the magnitude of the odds ratio of false-positive associations lies in the range of effects typically found in the GWA setting: median 1.26 ; odds ratios were coined to be ≥1 for consistency. However, false-signals from imputed genotypes suggest more commonly protective effects (n = 47) rather than susceptibility effects (n = 26) for the minor allele variant.Next, we sought to examine characteristics of false-positive associations that could be used as predictors of the quality of association signal derived from imputated markers. An analysis of the characteristics of false-positive signals is of paramount importance to guide investigators in appropriately evaluating P-values and the observed bias between associations statistics were plotted against their relative chromosomal positions  to diabetes in contrast to their empiric frequencies, inflating considerably the number of associated markers. The number of these "low imputation quality" markers is limited especially when compared to the immense number of markers analyzed that could, consequently, pass undetected by common diagnostic analysis.It is accepted that some chromosomal regions, due to a higher number of recombination events, have less consolidated frequency panels in markers underlying these regions in human populations . Allelics Figure   thresholds could predict the observed bias between empiric and imputed frequencies. This feature was explored by using more stringent cutoffs for calling rates, Hardy-Weinberg disequilibrium (HWD) and the use of SNPs showing a MAF ≥1%. The number of markers excluded by these quality filters was determined. The minus log transformed association statistics of the remaining imputed or genotyped markers were compared by analyzing their degree of correlation . Initially, we determined markers of our filtered dataset that were also evaluated in the HapMap database. This group is composed of 317,255 polymorphisms and it will be used in our further analysis. For each marker, a haplotypic block was determined using the complete set of markers showing a linkage disequilibrium measure to the specific marker (See methods for further details). Each haplotypic block is composed by a limited set of marker-to-marker r2 statistics. In each block, four different descriptive statistics were evaluated: mean, median, maximum value and variance of the values of the r2 statistic. We plotted separately the four statistics against the observed bias between association statistics of the complete set of markers  would also present a higher chance of also being associated. In this scenario, a considerable proportion of markers flanking an associated SNP should also present significant levels of association for the phenotype under investigation. Imputed SNPs located in the same chromosomal region are inferred with similar accuracy since the same haplotypic structure information was used by the imputation algorithm. In the same hand, it is expected that a totally isolated associated marker within a well-known LD block will likely represent a false positive association. To evaluate the validity of this hypothesis, we developed an algorithm implementing a sliding window procedure that determines and collects minus log corrected association statistics of consecutive imputed markers using three different window sizes  (see methods for further discussion). We determined different sliding windows size centered in the 73 imputed markers considered associated for diabetes II, these sliding windows were separated in two groups of sliding windows based if their central marker was concordant or discordant to empirically measured association statistics and three different summary statistics  were collected.Using box plot graphical representations we evaluated the discriminative values of the different summary statistics of flanking markers as a predictor of imputation accuracy for association statistics. Interestingly, the use of the total sum of association values was very robust to efficiently separate true-positive and false-positive association statistics of imputed markers, independent of the size of the sliding window Figure . Using tIn a complementary way, we used a graphical representation to highlight this feature plotting the corrected association of statistics of sliding windows centered in true-positive and false-positive imputed markers considered associated in human chromosome 10 Figure . In the Genome wide association studies are a promising tool for the determination of genetic signatures that could, when associated with environmental factors, predispose an individual to a phenotype of interest. Quality control of data in a GWAS study has been implicated as an important source of bias and loss of power in both linkage analyses and population-based association studies . ImputatP-values of empiric and imputed allelic frequencies under a log-additive model of inheritance. We used a combined quality criteria of markers showing MAF > 0.01 and calling probability higher than 0,95 and filtered markers showing a considerably higher accuracy between association statistics using imputed and empiric frequencies  would be considered associated based on their empiric (directly genotyped) association statistics . The same pattern was observed when different and more stringent significance thresholds were used (10 -6 and 10 -7).This result suggests that imputation methods are prone to inflate the number of markers considered associated in any of the evaluated thresholds in this report. These results are not a contradiction to the overall high accuracy for predicting genotype status previously described. These few highly deviated markers would be considered associated even when using highly stringent significance thresholds (< 10 -7 or lower) which could considerably jeopardize follow-up studies based only on association statistics of imputed markers. Since imputed markers are indispensable for merging the information generated by different platforms or studies , it's important to identify these badly imputed and hugely biased markers.The association of imputation procedures with low density chips can offer a convenient way to enhance the cost efficiency ratio and statistical power of a GWAS, since more individuals/markers can be typed by the same cost . SeveralIn this report, we comprehensively tested several genotyping and imputation quality criteria, haplotypic information and chromosomal location as predictors of the quality of association statistics derived from imputed markers. As demonstrated in other reports dealing with the accuracy of genotypic determination, when the MAF of imputed markers are close to 50%  imputatiA commonly accepted source of bias is the use of not well consolidated haplotypic information as an input for imputation algorithms. This could lead to imputed allelic frequencies not coherent to the population under study and, consequently strongly biased association tests. To explore this hypothesis we determined haplotypic blocks centered in each marker of the WTCCC dataset that were also present in the HapMap database. The comparison between the observed biases and four different summary statistics, representing haplotypic block consistency, showed a modest success when variance and maximum values were tested as predictors. Interestingly, the comparison between mean and median values of linkage disequilibrium as predictors showed that imputed markers located in regions showing weaker linkage disequilibrium structure are prone to higher bias. Their imputation and subsequent analysis under different genetic models of inheritance should be carefully done especially if the imputed marker is to be considered strongly associated to the phenotype under study. A similar result was suggested by Bakker P. I.W et al, when constructing a guide to the use of imputed information in meta-analysis of genome wide association studies.-5) in the WTCCC hypertension dataset with similar results  - ). All the analyses were conducted on the R statistical environment; the complete set of developed programs can be obtained upon request.Markers typed in a specific chromosome were selected and sorted by their chromosomal position. The association statistics of a marker under a log-additive model of inheritance were collected and using a minus-log transformation plotted (Y-axis) with their position in the sorted vector. Markers in different specific chromosomes were plotted in grey and black, respectively. The bias was determined as the algebraic difference between minus log transformed association statistics derived from direct genotyping and imputation . A haplotypic block was defined as the complete set of rP-values of imputed and directly genotyped markers under a log-addictive model of inheritance was collected and ordered based on chromosomal position. Imputed markers that were considered associated using a pre-defined threshold (10 -5) were determined and classified into concordant and discordant markers in terms of their agreement within the association statistics. A locally developed Perl algorithm constructed sliding windows of different sizes  centered in the imputed markers (concordant or not) and collected the set of minus-log transformed association statistics of the flanking markers. A set of summary statistics, such as mean, median and variance of each sliding window was collected and referenced to the central marker. The complete set of raw results, summary statistics and markers comprised in each window can be obtained upon request.The complete set of minus log transformed MAAA: Conducted the statistical analysis, the implementation of the computational routines and drafted the manuscript; PSOL: Supervised the implementation of computational routines; TVP: conducted data filtering analysis and statistical analysis JEK: helped the concept and design of the study. ACP: conceived the study and drafted the manuscript. All authors read and approved the final manuscript.QQ plots of entire and filtered datasets. A. QQ plot of the entire dataset; B. QQ plot of dataset after standard filtering criteria.Click here for fileComplete set of imputed associated markers. All markers that would be considered associated based on imputed allelic frequencies using a significance treshold of 10-5. A markers determined as concordant (STATUS column) could be considered associated by imputed and empiric allelic frequencies.Click here for fileComparison of the number of considered associated markers by empiric and imputes allelic frequencies in hypertension database. Determination of markers showing concordance and discordance of association statistics based on imputed and empiric allelic frequencies based on information provided by hypertension database of WTCCC.Click here for fileThe effects of the use of different minimum thresholds for calling probabilities. We serially tested a series of different minimum thresholds for empiric and imputed frequencies and analysed the effect of such filtering in the remaining dataset by determining the correlation of association statistics and the outlier percentageClick here for fileThe effects of the use of different minimum thresholds for MAF . We serially tested a series of different minimum thresholds for minor allele frequencies and analysed the effect of such filtering in the remaining dataset by determining the correlation of association statistics and the outlier percentage.Click here for fileDispersion plots and histogram of markers showing extreme MAF conditions. Dispersion plots and histogram of markers showing extreme MAF (Minor Allele Frequency) conditions MAF < = 0,01 or MAF > = 0,49Click here for fileComplete set of comparisons of different size sliding windows. Each box-plot represents the tendency observed in association statistics of markers within different size sliding windows.Click here for fileSliding window algorithm applied in hypertension dataset. Each box-plot represents the tendency observed in association statistics of markers within different size sliding windows applied in hypertension dataset.Click here for file