The genome-wide association study (GWAS) approach has discovered hundreds of genetic variants associated with diseases and quantitative traits. However, despite clinical overlap and statistical correlation between many phenotypes, GWAS are generally performed one-phenotype-at-a-time. Here we compare the performance of modelling multiple phenotypes jointly with that of the standard univariate approach. We introduce a new method and software, MultiPhen, that models multiple phenotypes simultaneously in a fast and interpretable way. By performing ordinal regression, MultiPhen tests the linear combination of phenotypes most associated with the genotypes at each SNP, and thus potentially captures effects hidden to single phenotype GWAS. We demonstrate via simulation that this approach provides a dramatic increase in power in many scenarios. There is a boost in power for variants that affect multiple phenotypes and for those that affect only one phenotype. While other multivariate methods have similar power gains, we describe several benefits of MultiPhen over these. In particular, we demonstrate that other multivariate methods that assume the genotypes are normally distributed, such as canonical correlation analysis (CCA) and MANOVA, can have highly inflated type-1 error rates when testing case-control or non-normal continuous phenotypes, while MultiPhen produces no such inflation. To test the performance of MultiPhen on real data we applied it to lipid traits in the Northern Finland Birth Cohort 1966 (NFBC1966). In these data MultiPhen discovers 21% more independent SNPs with known associations than the standard univariate GWAS approach, while applying MultiPhen in addition to the standard approach provides 37% increased discovery. The most associated linear combinations of the lipids estimated by MultiPhen at the leading SNPs accurately reflect the Friedewald Formula, suggesting that MultiPhen could be used to refine the definition of existing phenotypes or uncover novel heritable phenotypes. Genome-wide association studies aim to identify associations between genotype and phenotype. While genotypes are well-defined biological entities, phenotypes are defined more subjectively and can relate to numerous biological processes. There has been much effort to characterise well-defined phenotypes that may correspond more to specific biological function for use in genome-wide association studies, but the definition of some phenotypes remains somewhat ad-hoc. Type 2 diabetes, the subject of the first major genome-wide association study FTO was reported to be 11 orders of magnitude more significant for BMI than weight While most quantitative traits are less ambiguously defined, many are defined as mathematical functions of several measurements in an attempt to better capture the underlying biology than individual quantities. There have been many more genetic determinants of Body-mass-index (BMI), defined as the ratio of weight to height squared, discovered than those of weight a priori defining a phenotype as a fixed function of traits. Such an approach circumvents the problems of phenotype definition by enabling association of genotype with flexible linear combinations of robust measurements, and could potentially be exploited by biologists and clinicians to define phenotypes that better reflect underlying biological processes.A primary aim of this study is to fully assess the performance of a multivariate approach to genome-wide association studies in comparison to that of the usual single-phenotype strategy. Rather than exploiting an available multivariate method, we introduce a new fast and interpretable approach, which addresses some of the limitations of previously suggested methods. In particular, we propose that linear combinations  of directly measured phenotypes may often capture unmeasured aspects of complex biological networks, such as reaction rates, protein mediators or other uncharacterised or clinically-inferred phenotypes. Modelling the association between linear combinations of phenotypes and the genotypes at each SNP may uncover genetic association hidden to both single phenotype GWAS and those based on P value for evidence of association between the SNP and the phenotypes. The usual genome-wide significance level is applied. While several approaches to multivariate analysis of GWAS have been introduced in recent years, the univariate approach is still routinely favoured We introduce a new method, MultiPhen, that rapidly performs GWAS on multiple phenotypes by identifying the linear combination of the phenotypes most associated with genotype at each SNP. This is achieved by reversing the regression, such that genotype is regressed on phenotype, rather than phenotype-on-genotype as in the standard GWAS approach. By applying ordinal regression , which models the genotype data as ordinal, multiple phenotypes can then be jointly modelled as predictors of the SNP genotypes to test for multi-phenotype associations (see Methods). This model makes no assumption on the phenotype distribution and so can accommodate both binary and continuous measurements. Our test for association is a likelihood ratio test for model fit, which provides a z scores) from each study, MultiPhen can be easily applied to perform meta-analysis of measured or imputed SNP data across a large number of phenotypes and studies. The similarity of the approach to that of the usual linear and logistic regressions performed in GWAS, and the presentation of P values for association in the usual way, make the approach highly interpretable and a natural extension of current methods for GWAS.We show via simulation that MultiPhen has markedly higher power than the standard single-phenotype approach to detect SNP-phenotype associations in many scenarios, even for identifying variants that affect only one of the phenotypes, as a result of jointly modelling the phenotypes. In addition, there are several convenient aspects of adopting our approach. As the phenotypes are treated as predictors rather than outcomes, there is no need to ensure their normality via transformation. Our MultiPhen software (available as a CRAN package for R) appropriately handles imputed SNP data and CNVs, can optionally perform a score test, and can perform univariate linear (standard) and ordinal (reversed) regressions for comparison with multivariate results (see Methods). A further advantage of our approach is its computational speed; applying MultiPhen to 10 traits is around 1.3 times faster than the corresponding set of standard single-phenotype analyses. With a natural test for combining results across studies as the (weighted) sum of the likelihood ratios .To formally compare the statistical power of MultiPhen, CCA and separately performed single phenotype analyses, we conducted a simulation study. We first investigate the potential power gains of using a multivariate approach over the standard univariate approach, then subsequently assess differences in power between the multivariate methods. We simulated replicates of a causal variant under several scenarios of its effect on two (simulated) continuous phenotypes. We simulated 10000 replicates of a causal SNP in a sample of 5000 individuals, where the risk allele explains 0.5% of the variance in the first phenotype and, in turn, 0.5%, 0.1% and 0% of the variance in the second phenotype. We simulate the variant as having different effects on the two ‘measured’ phenotypes in order to model association of the SNP with different linear combinations of the phenotypes. These scenarios were simulated across the range of between-phenotype correlations, from r = –0.9 to r = 0.9 in increments of 0.1. We first tested for SNP-phenotype associations by performing single phenotype analyses, calculating the Nyholt-Šidák corrected minimum P = 5x10–8) under these scenarios. MultiPhen outperforms the single-phenotype approach in detecting direct effects for the majority of the scenarios considered, and in many cases the boost in power is dramatic. MultiPhen performs particularly well when the genetic effects are not in the same direction as the correlation between the two phenotypes. For instance, when a variant only affects one of two highly correlated phenotypes, or a variant affects negatively correlated phenotypes in the same direction or positively correlated phenotypes in opposite directions (rections . Exemplarections . If the 2/β1 = r (the correlation between the phenotypes), assuming P1 and P2 both have a variance of 1 (see Methods). This could occur if P2 is immediately downstream of P1 in a biological pathway with no other P2-regulators associated with G. Conversely MultiPhen is expected to perform better when β2/β1 is not equal to r, that is, when the genetic effects are not in the same direction as the correlation. While we would expect effects of variants that explain a large proportion of phenotypic variation to be consistent with the correlation of the phenotypes, this may not be the case for variants that explain only a small portion of phenotypic variation, such as those discovered in GWAS. Given the complexity of biological pathways, we suggest that in many cases genetic effects will not have the same correlation structure as the phenotypes themselves. In these circumstances, we would expect that MultiPhen has an advantage over traditional single-phenotype approaches.We note that, from a theoretical perspective, the power of MultiPhen using two phenotypes P1 and P2, is worst when the association of P2 with genotype G is entirely explained by P1, that is when P2 is conditionally independent of G given P1. We show that this corresponds to the situation in which the ratio of the effect sizes βTo investigate the generalisability of the results of Next, we investigate the performance of MultiPhen when applied to case-control data. Finally, we compared the statistical power of CCA  and MultiPhen. Since the type 1 error rate of CCA is inflated for non-normal phenotypes in the scenarios we considered (see above), it is difficult to make a meaningful assessment of power in these scenarios. Therefore we restricted our analysis to normally distributed phenotypes. Next we describe the application of MultiPhen to lipid traits  in the Northern Finland Birth Cohort 1966 (NFBC1966). P value from the analyses of each of the phenotypes for each SNP and adjusted it for multiple testing using a “Nyholt-Šidák correction” A study in 2010 P values in this case was almost uniformly in favour of MultiPhen, and for one SNP the P value was almost 15 orders of magnitude smaller, and approximately 5 orders of magnitude smaller for another 3 SNPs. Of the 95 known associated SNPs, 8 showed genome-wide significance using single phenotype analyses, while a total of 11 SNPs were genome-wide significant under either MultiPhen or the single phenotype analyses . FurtherP values 2–3 orders of magnitude smaller than MultiPhen, no univariate SNP-phenotype association P values are 4 orders of magnitude or more smaller than the corresponding MultiPhen result. In contrast, there are 10 MultiPhen P values smaller than the univariate P values by at least 4 orders. MultiPhen identifies 21% more SNP-phenotype associations than the univariate approach, with 75 compared to 62 significant associations, relating to 12 SNPs. By combining all significant univariate and MultiPhen SNPs there are a total of 85 SNP-phenotype associations with P<2.5x10–8 (conservative Bonferonni correction applied), compared to 62 using the univariate strategy only. Therefore, based on these empirical findings, MultiPhen provides a 21% increase in detection of susceptibility loci if used instead of the single phenotype approach, and a 37% increase in detection if used in addition to univariate analyses.We also assessed the performance of MultiPhen relative to the univariate approach over different subsets of our measured lipid phenotypes, each reflecting hypothetical studies with measurements available only on certain traits, in order to gain further insight into the relative performance of the two approaches. We analysed all 3-phenotype combinations of the lipids  and all 2-phenotype combinations  and compared the number of genome-wide significant SNPs between MultiPhen and the univariate analyses , S15. OfIn order to test for false-positive results and assess any inflation of the test statistic, we applied MultiPhen to the four lipids genome-wide. The only genome-wide significant findings were from loci harbouring one of the established 95 lipid SNPs, confirming no false-positive results in these analyses. The inflation factor of the test statistic calculated from the genome-wide MultiPhen results was 1.06, indicating no unusual inflation of the test statistic. While we did not detect novel susceptibility loci using MultiPhen in the NFBC1966, this was not unexpected given that the sample size of Teslovich et al. Since the emergence of GWAS in 2007 with two seminal publications We have introduced a new multivariate method, MultiPhen, which addresses limitations of alternative multivariate methods. Key advantages of our approach are its computational speed, the modelling and subsequent availability of the linear combination of phenotypes most associated with each genotype, and its application to both quantitative – regardless of phenotype distribution – and case-control data.We demonstrated that the MultiPhen model provides appropriate type 1 error rate when applied to both common and rare variants, non-normal continuous phenotypes and binary phenotypes. In contrast, CCA By considering all 2, 3, and 4 phenotype combinations of the 4 lipid traits we were able to test empirically the performance of MultiPhen applied to phenotypes with different correlation structures, in comparison with the univariate approach. These results indicate a 21% greater yield of SNP-phenotype associations when MultiPhen is applied instead of the univariate approach, and a 37% increased yield over the univariate analysis when significant univariate and MultiPhen results are combined. However, given that these analyses relate to a limited number of phenotypes and significant SNPs, these figures should not be considered accurate estimates of the general performance of MultiPhen over the univariate approach, which can only be obtained from extensive future use on a variety of phenotypes. Our findings on the lipid data are, however, supportive of the results from our simulation study in indicating that MultiPhen may lead to greater discovery when used instead of the univariate approach, and suggest that applying both approaches and combining results could lead to even greater discovery.We consider it likely that causal variants commonly influence many separately defined phenotypes An overlap in loci identified by GWAS on different phenotypes This study was approved by the Ethical Committee of the Northern Ostrobothnia Hospital District; written, informed consent was obtained from all participants.Y, on genotype, X. We let iY = {i1Y, …, iKY} denote the phenotype data corresponding to K phenotypes for an individual i and iX = {i1X, …, iGX} denote their genotype data at G SNPs, where ig εX {0,1,2}. The regression performed at a SNP, g, and a phenotype, k, to test for association between the SNP genotypes and the phenotype is thus:igkε is the residual error assumed to be normally distributed. The null hypothesis of no association between SNP and genotype can be tested by performing a t-test on the null hypothesis In the standard GWAS approach, when considering a quantitative phenotype, a linear regression is usually performed of phenotype, X, become the dependent variable, and the K phenotypes under study become the predictor variables. The genotype data is an allele count and is therefore modelled using ordinal regression; we use proportional odds logistic regression. This model defines the class probabilities as follows.In our MultiPhen approach we invert the regression so that the SNP genotypes, g = 1,…,G we use a likelihood ratio test to test the null hypothesis g1 = … = βgK = β0. This test does not assume Hardy-Weinberg Equilibrium.At each SNP P values obtained from each analysis at each SNP were subsequently corrected for multiple testing using a “Nyholt- Šidák correction” P value Complete genotype and lipid trait data were available on 4476 individuals  represents a common environmental effect affecting both phenotypes, and ε is a random effect distributed 2)N. That is to say, when the residuals of 2Y, regressing out the effect of 1Y, are independent of X. If 2Y regressed on 1Y for individuals i = 1, …, N, then:MultiPhen has its worst power when the association of 1Y and 2Y on X gives:Regressing iX when Substituting (4) and (5) into (3) gives:iX when For standardised phenotype data, t were assumed to be a case for that trait. Heritability on the observed scale is given by:Binary traits were simulated assuming a classical liability threshold model. We used the same simulation as for continuous traits assuming the continuous traits were liability phenotypes. In this model all individuals with liability phenotypes greater than a threshold q is the disease prevalence and z is the height of the normal pdf at the threshold value t. All correlations on Figures relating to simulations involving binary traits (Where y traits  and S12 http://cran.r-project.org/) or any CRAN mirror, with documentation available here:The MultiPhen software was written in the R statistical language. R users can download and install MultiPhen from CRAN  applied to data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), sample size N = 5000, with MAF of simulated SNPs of 30% and 2 normally distributed phenotypes (without outliers) and correlations between the phenotypes of 0, 0.5 and 0.9. The plots show that all three methods have an appropriate null distribution, even when the correlation between the phenotypes is high.(TIFF)Click here for additional data file.Figure S2Behaviour under the null: without outliers, MAF = 0.5%. QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), sample size N = 5000, with MAF of simulated SNPs of 0.5% and 2 normally distributed phenotypes (without outliers) and correlations between the phenotypes of 0, 0.5 and 0.9. The plots show that all three methods have an appropriate null distribution, even when the correlation between the phenotypes is high.(TIFF)Click here for additional data file.Figure S3Behaviour under the null: with outliers, MAF = 30%. QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), sample size N = 5000, with MAF of simulated SNPs of 30% and 2 phenotypes where one has an outlier distribution and correlations between the phenotypes of 0, 0.5 and 0.9. The plots show that all three methods have an appropriate null distribution, even when the correlation between the phenotypes is high.(TIFF)Click here for additional data file.Figure S4Behaviour under the null: with outliers, MAF = 0.5%. QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), sample size N = 5000, with MAF of simulated SNPs of 0.5% and 2 phenotypes where one has an outlier distribution and correlations between the phenotypes of 0, 0.5 and 0.9. The plots show that while MultiPhen has an appropriate null distribution, even when the correlation between the phenotypes is high, the other two approaches have a highly inflated null distribution, which would produce an extremely high type 1 error rate, irrespective of the correlation between the phenotypes.(TIFF)Click here for additional data file.Figure S5Behaviour under the null: with outliers, MAF = 5% (N = 200). QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), sample size N = 200, with MAF of simulated SNPs of 5% and 2 phenotypes where one has an outlier distribution and correlations between the phenotypes of 0, 0.5 and 0.9. The plots show that while MultiPhen has an appropriate null distribution, even when the correlation between the phenotypes is high, the other two approaches have an inflated null distribution. Thus CCA and the univariate approach can have a high type 1 error rate for common, as well as rare, variants.(TIFF)Click here for additional data file.Figure S6Behaviour under the null: binary phenotypes, MAF = 30%. QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to case-control study data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), with sample size N = 5000 such that the first phenotype has 50% cases and controls whereas the second phenotype has 10% cases and 90% controls . The MAF of the simulated SNPs is 30% and the correlations between the phenotypes  are 0, 0.5 and 0.9. The plots show that all three methods have an appropriate null distribution when there are no SNP-phenotype effects, even when correlation between the phenotypes is high.(TIFF)Click here for additional data file.Figure S7Behaviour under the null: binary phenotypes, MAF = 0.5%. QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to case-control study data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), with sample size N = 5000 such that the first phenotype has 50% cases and controls whereas the second phenotype has 10% cases and 90% controls . The MAF of the simulated SNPs is 0.5% and the correlations between the phenotypes  are 0, 0.5 and 0.9. The plots show that while MultiPhen has an appropriate null distribution, even when the correlation between the phenotypes is high, the other two approaches have an inflated null distribution.(TIFF)Click here for additional data file.Figure S8Behaviour under the null: binary phenotypes, MAF = 5% (N = 200). QQ-plots, corresponding to MultiPhen, CCA and the univariate approach (Nyolt-Šidák corrected) applied to case-control study data simulated under the null hypothesis of no SNP-phenotype effects (100000 replicates for each), with sample size N = 200 such that the first phenotype has 50% cases and controls whereas the second phenotype has 10% cases and 90% controls . The MAF of the simulated SNPs is 5% and the correlations between the phenotypes  are 0, 0.5 and 0.9. The plots show that while MultiPhen has an appropriate null distribution, even when the correlation between the phenotypes is high, the other two approaches have an inflated null distribution.(TIFF)Click here for additional data file.Figure S9The power of MultiPhen in scenarios where the effect on the phenotypes is in the opposite direction. Power results based on simulations described in the text for MultiPhen (red lines) and the standard single-phenotype approach (black lines). Left panel: causal variant explains 0.5% of phenotypic variance of both phenotypes but in opposite directions. Right panel: causal variant explains 0.5% of the phenotypic variance of the first phenotype and 0.1% of the variance in the second phenotype in the opposite direction of the effect on the first. The X-axis corresponds to the correlation  between the phenotypes.(TIFF)Click here for additional data file.Figure S10The power of MultiPhen applied to two, three, five and ten phenotypes. Power results based on simulations described in the text for MultiPhen (red lines) and the standard single-phenotype approach (black lines), for 2 (bold), 3 (dashed), 5 (dotted), and 10 (dashed/dotted) phenotypes. Left panel: causal variant explains 0.5% of phenotypic variance of each phenotype. Middle panel: causal variant explains 0.5% of the phenotypic variance of the first phenotype and 0.1% of the variance in each of the other phenotypes. Right panel: causal variant explains 0.5% of phenotypic variance of the first phenotype and 0% of each of the other phenotypes. The X-axis corresponds to the correlation  between all pairs of phenotypes . The results are truncated when the pairwise correlations are low for multiple phenotypes because the corresponding correlation matrices of the phenotypes are not positive definite and so the multivariate gaussian distributions cannot be sampled via the Cholesky decomposition that we perform.(TIFF)Click here for additional data file.Figure S11The power of MultiPhen applied to two case-control phenotypes. Power results based on simulations described in the text for MultiPhen (red lines) and the standard single-phenotype approach (black lines) applied to two independent case-control studies, each with 1000 cases and 1000 controls where case-control status is used as the predictor variables. Heritability on the liability scale is 0.1% for one phenotype and 0.1% (left panel), 0.05% (middle panel) and 0% (right panel) for the other phenotype. Solid and dashed are for disease prevalences of 1% and 0.5%, respectively, for both studies. Correlation on the X-axis is with respect to the liability scale.(TIFF)Click here for additional data file.Figure S12The power of MultiPhen applied to one case-control and one quantitative phenotype. The power of MultiPhen applied to a case-control study with 1000 cases and 1000 controls using case-control status and a single measured quantitative phenotype as predictor variables. Heritability of the continuous phenotype is 0.2%; heritability of the binary trait on the liability scale is: 0.5% (a), 0.1% (b) and 0% (c). Solid and dashed lines are for disease prevalence of 1% and 0.5% respectively. Correlation on the X-axis is with respect to the liability scale.(TIFF)Click here for additional data file.Figure S13The power of CCA, compared to MultiPhen and the univariate approach. Power results based on simulations described in the text for CCA (blue), MultiPhen (red) and the single-phenotype approach (black), when applied to two continuous normally distributed phenotypes where the causal variant explains 0.5% of the phenotypic variance of the first phenotype and 0.1% of the variance of the other phenotype, with the simulated SNPs having MAF = 30%. The X-axis corresponds to the correlation  between the phenotypes. The difference in statistical power between CCA and MultiPhen in this scenario is reflective of the difference in power when the effect of the causal variants on the phenotypes differs and for different allele frequencies of the causal variant (data not shown).(TIFF)Click here for additional data file.Table S1Behaviour under the null: r = 0. The table relates to the simulation study to test the behaviour of the different methods under the null hypothesis of no association, described in the text and presented in P values smaller than that of the corresponding column header (expected number given in the second row of the column header), with the simulation scenario given in the left-hand column. This table gives the results for all simulations where the two phenotypes have a correlation of r = 0.(PDF)Click here for additional data file.Table S2Behaviour under the null: r = 0.5. The table relates to the simulation study to test the behaviour of the different methods under the null hypothesis of no association, described in the text and presented in P values smaller than that of the corresponding column header (expected number given in the second row of the column header), with the simulation scenario given in the left-hand column. This table gives the results for all simulations where the two phenotypes have a correlation of r = 0.5.(PDF)Click here for additional data file.Table S3Behaviour under the null: r = 0.9. The table relates to the simulation study to test the behaviour of the different methods under the null hypothesis of no association, described in the text and presented in P values smaller than that of the corresponding column header (expected number given in the second row of the column header), with the simulation scenario given in the left-hand column. This table gives the results for all simulations where the two phenotypes have a correlation of r = 0.9.(PDF)Click here for additional data file.Table S4Correlation matrix for the 4 lipids  based on the NFBC1966 data. The upper triangular elements of the correlation matrix show the pairwise Pearson’s correlation coefficient (r) between each pair of the traits: total cholesterol (CHOL), triglycerides (TRIG), high-density lipoprotein (HDL) and low-density lipoprotein (LDL).(PDF)Click here for additional data file.Table S5Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-TRIG-HDL-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S6Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: TRIG-HDL-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S7Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-HDL-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S8Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-TRIG-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S9Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-TRIG-HDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S10Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-TRIG combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S11Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-HDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S12Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: CHOL-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S13Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: TRIG-HDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S14Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: TRIG-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.Table S15Results under standard GWAS and MultiPhen approaches for genome-wide significant SNPs: HDL-LDL combination. Results compare univariate and MultiPhen P values, presented on the -log10 scale for ease of comparison, for all SNPs with genome-wide significant P values  from either approach. Genome-wide significant results shown in bold . The difference in terms of orders of magnitude of the MultiPhen P value and the smallest univariate P value for each SNP is given in the final column.(PDF)Click here for additional data file.


P < 10−5) with high-density lipoprotein cholesterol and identified Apoa2 and Scarb1, both of which have been previously reported, as candidate genes for these associations. Additional suggestive associations (P < 10−3) identified in this study were also concordant with published quantitative trait loci, suggesting that we are sampling from a limited pool of genetic diversity that has already been well characterized. These findings dampen our enthusiasm for currently available commercial outbred stocks as genetic mapping resources and highlight the need for new outbred populations with greater genetic diversity. Despite the lack of novel associations in the NMRI population, our analysis strategy illustrates the utility of methods that could be applied to genome-wide association studies in humans.Recent developments in high-density genotyping and statistical analysis methods that have enabled genome-wide association studies in humans can also be applied to outbred mouse populations. Increased recombination in outbred populations is expected to provide greater mapping resolution than traditional inbred line crosses, improving prospects for identifying the causal genes. We carried out genome-wide association mapping by using 288 mice from a commercially available outbred stock; NMRI mice were genotyped with a high-density single-nucleotide polymorphism array to map loci influencing high-density lipoprotein cholesterol, systolic blood pressure, triglyceride levels, glucose, and urinary albumin-to-creatinine ratios. We found significant associations ( However, mapping resolution is typically too coarse to identify the causal genes. Several breeding strategies, including heterogeneous stocks, advanced intercross lines, and the collaborative cross (CC), can produce populations with increased recombination and improved mapping resolution , low levels of linkage disequilibrium (LD), and absence of population structure as the most promising choices for mapping studies.Linkage analysis using crosses between inbred mouse strains is a powerful method for detecting genetic loci underlying quantitative traits  studies with human populations  risk factors, but their study included relatively few single nucleotide polymorphisms  compared with the > 100,000 genetic markers typically used in human GWA studies.Outbred populations have been used previously to refine the location of QTL detected in other mapping studies (Our GWA study using 288 outbred NMRI mice genotyped with the Mouse Diversity Array (am to 6 pm) at 20-24°.Three hundred 4- to 6-week-old, male NMRI mice were purchased from Taconic (Taconic Europe) and individually housed in solid-bottom cages with free access to water and standard rodent chow . The vivarium was maintained on a 12-hr light/dark cycle (6 Tail-cuff blood pressure was measured in 8-week-old mice using a CODA-6 noninvasive blood pressure monitoring system (Kent Scientific) as previously described (e(ACR + 1). The lipid traits (HDL-C and CHL) and the blood pressure traits  were highly correlated among themselves (r > 0.97), and although we analyzed each of the individual traits, results were essentially identical and we report here only our analysis of HDL and SBP, as representative of these groups of traits.Blood samples were obtained from each mouse by submandibular puncture after a 4-hr fast. Plasma samples were frozen at −80° for later measurement of total cholesterol (CHL), high-density lipoprotein cholesterol (HDL-C), triglycerides (TG), and glucose (GLU) using a Beckman Synchron CX5 Chemistry Analyzer. All traits except ACR were approximately normally distributed. The ACR was highly skewed, with many mice having an ACR of zero. We tested a variety of ACR transformations, but all lead to similar conclusions. We report the result for the log-transformed variable logACR = loghttp://cgd.jax.org/tools/mousedivgeno/). A total of 581,672 SNP genotypes were obtained for each of the 290 animals. Of these, 244,840 SNPs (42%) were polymorphic. Two samples were identified with 99% identity of their SNP genotypes and were removed from subsequent analysis, which was carried out on the remaining 288 mice. We computed the MAF and tested Hardy-Weinberg equilibrium for each polymorphic SNP and retained 103,872 SNPs with MAF > 2%, Hardy-Weinberg equilibrium χ2 < 20 and missing values < 40%. The small proportion (1.3%) of missing genotypes that remained were imputed using fastPhase  was calculated for all pairs of SNPs within a 50-Mb sliding window across the genome. Locally weighted scatter plot smoothing (LOWESS) was used to compute the median r2 as a function of distance between pairs of SNPs. The information content of each SNP was computed as the symmetric Shannon entropy, (pln(p) + (1 − p)ln(1 − p)), where p is the MAF of the SNP. In addition to the NMRI population, we computed information content of the full set of 581,672 SNPs genotyped in 79 strains of the BxD recombinant inbred panel and in the eight founder strains of the collaborative cross (heatmap function in R 2.10.0 (R Development Core Team 2009).The squared correlation coefficient  score is reported. Fixed effect covariates can be included in genome scans using any of these statistical tests, which enabled implementation of conditional scans and forward stepwise search by including previously selected marker genotypes as covariates.We carried out single-locus association genome scans on diallelic SNPs using each of three statistical tests. We computed a linear trend test (1df) by regressing the trait on genotype scores −1, 0, 1 corresponding to AA, AB, and BB genotypes, respectively. The trend test assumes additive genetic effects at a locus. We also conducted analysis of variance  that allows for both additive and dominant effects at a locus. Finally we used the EMMA software to fit a mixed linear model at each SNP  scores. This was repeated 100 times. We fitted a generalized extreme value distribution to these scores and derived significance thresholds from the quantiles of this distribution . Trait values were sampled from a multivariate normal distribution using mvrnorm in R with correlation structure defined by the kinship matrix and the genetic and residual variances were as estimated for HDL. We removed the selected SNP from the data and performed a genome scan with EMMA. The distance between the SNP with highest –log(p) and the target SNP was recorded. In cases where a group of adjacent SNPs had tied P values, we computed the median distance between the location of association peak and the target SNP. We repeated this process 1000 times, and computed the distribution of distances from the peak to the target SNP. A small proportion of association peaks were observed on different chromosomes from the target SNP. These events were recorded but were excluded from the distance calculation.To assess the genome-wide average precision of mapping in this population, we performed a simulation study using the observed genotype data. We randomly sampled a SNP from the genome and simulated trait values assuming that this SNP was the causal locus. We simulated an effect size corresponding to the same percentage of total variance explained as the HDL QTL on Chromosome 1 (reported in the section http://cgd.jax.org/datasets/datasets.shtml). The squared correlation coefficient (r2) between SNPs was used as a measure of LD. We observed a sharp decay of LD with increasing physical distance between SNPs . The mean percentage of identical SNPs (of the 44K filtered set) between any pair of animals was 74%, with a range from 69 to 91%.Population structure due to stratification or to family relationships within a sample can adversely affect mapping studies if not accounted for in the analysis  occurred on the same chromosome as the simulated QTL in 99.3% of simulations. When the peak was on the same chromosome it was within 1.34 Mb in 95% of simulations, within 0.52 Mb in 80% of simulations, and within 0.17 Mb in 50% of simulations . LD blocks are larger in our NMRI sample than is usually seen in a human population sample. There are also substantial regions of long-range LD, which is typical of laboratory mouse populations  for all 581K SNP markers in our NMRI population, in 79 BxD recombinant inbred strains, and in the eight founder strains of the Collaborative Cross (CC) . The aveFigure S3). The genome-wide 5% threshold for logACR ranged from 7.76 to 7.79 for EMMA and the simple trend test, but the ANOVA thresholds were substantially greater (12.45 using permutation). We attribute this to the combination of extreme logACR values with rare heterozygous genotypes that arise in many permutations of the data. The trend test is robust to this effect, but it risks missing associations with large dominant components.We used two methods to assess significance thresholds for GWA mapping, simulation and unrestricted permutation. We applied these to each of three methods for measuring association: the trend test, ANOVA test, and mixed model. The estimated genome-wide significance thresholds for glucose, HDL cholesterol, systolic blood pressure, and triglycerides were similar across all of these combinations. Values ranged from 5.12 to 5.90, but no single method or trait was consistently higher or lower than another . The excFigure S4, A and B). The most striking findings were two highly significant loci associated with HDL. There was an association with SBP on proximal Chromosome 10 at 7 Mb that exceeded the genome-wide 0.05 thresholds for the simple trend and ANOVA tests, but fell below the threshold for the EMMA test. The logACR trait was the most variable of the five traits, although still highly concordant across test statistics. For this trait, we observed loci on Chromosome 5 at 147 Mb and Chromosome 11 at 88 Mb that exceeded the 0.05 threshold for either simple trend test or the ANOVA test. There were a number of subthreshold loci, in particular for logACR, that stood out from the background and may be of interest.We performed GWA mapping using each of three test statistics, a simple trend test, ANOVA, and a trend test within a mixed model that accounts for family structure (EMMA). Results obtained using these tests across all five traits examined here were highly concordant  were also significantly associated with total cholesterol levels (not shown). The Chromosome 1 locus at 173 Mb spans a region encompassing 16 genes . Numerous mouse crosses have linked HDL to this region and Apoa2 has been identified as the gene underlying the QTL  was associated with high HDL-C levels compared with the C allele . On Chromosome 5, the region of strongly associated SNPs contains 7 genes, including Scarb1 . This region has also been linked to HDL in multiple crosses, and Scarb1 (encoding SRB1) was identified as the primary candidate gene . The peak SNPs at 173 Mb (rs31551271) and 181 Mb (rs30672856) were correlated (r = 0.36), although they are not in the same LD block . To establish whether these represent independent associations we repeated the genome scan analysis using EMMA with the peak SNP markers from Chromosome 1 and Chromosome 5 (rs36333480) as covariates. No new QTL were identified and the support for an independent QTL at 181Mb was reduced to a level consistent with chance . We also fit multilocus regression models with different combinations of the three QTL for HDL (Table S1). The Chromosome 1 locus at 181 Mb explains 10% of the total variance in HDL when considered on its own. However, after adjusting for the Chromosome 1 locus at 173 Mb, the QTL at 181 Mb accounts for only 2.5% of total variance. With the addition of the Chromosome 5 locus, this contribution decreases further, to 0.3% of total variance. Thus, the Chromosome 1 locus at 181 Mb may represent a spurious association in which the combined effects of two loci with genuine associations combine to create a “ghost” signal.In addition to the main peak at 173Mb on Chromosome 1, we observed a second distinct and significant peak at 181 Mb . This reP-values for these traits indicates that there may be an excess of small P-values, in particular for logACR . We identified the five strongest associations for each of the traits and compared them with published QTL for the same traits  that includes 316 genes. A cross between C57BL/6J and C3H/HeJ mice previously linked HDL to this locus with a 95% CI between 57.00 and 88.50 Mb (including 854 genes). Assuming the same causal gene for the GWA and the QTL cross, we can narrow the search for candidate genes to the overlapping region from 79.87 to 88.50 Mb containing 177 genes. We can use high-density SNP data (Hnf1b) is a strong candidate because genetic deletion specifically in hepatocytes and bile duct cells significantly raises plasma cholesterol levels , to the Zentral Institut fur Verzuchstierzucht in Hannover, and finally to Taconic. The bottleneck at the NIH likely reduced the genetic variation greatly. Most existing outbred populations, including NMRI, were derived from classical laboratory inbred strains and as such will have significant blind spots and limited haplotype diversity (Apoa2 locus. They also report secondary association signals at 173.6Mb and 173.7Mb, substantially proximal to our locus at 181Mb. This region of Chromosome 1 has a complex LD structure in our NMRI sample (Apoa2 are genuine or spurious.Spurious QTL detection in GWA studies can occur for a variety of reasons (I sample  and amonMultiple testing presents a statistical challenge for both mouse and human GWA studies. The Bonferroni correction widely applied to human GWA analyses imposes a substantial multiple testing penalty, effectively limiting the ability to detect loci with small effects to reduce the detection of spurious loci. In our analysis, we used a novel permutation technique to calculate significance thresholds through simulation. Although permutation tests have been shown to be potentially misleading in the presence of family structure (Precision of QTL mapping is not well understood in human GWA. We used a simulation approach to estimate mapping precision in our NMRI population and established that we can localize a QTL with large effect size to within 1.34 Mb of the greatest association peak. This result represents a genome-wide average and there may substantial local variation in mapping precision. This approach could be applied over a range of QTL effect sizes in any genotyped population sample including human GWA studies. Our assessment of mapping precision is tailored to the particular QTL found in this study. QTL of smaller effect size or in the context of a complex genetic background may be mapped with less precision.This study demonstrates that GWA analysis can be successfully applied to outbred mice populations to identify genetic variants underlying complex traits. GWA studies can complement classical linkage analyses using inbred mouse crosses to refine QTL and identify causal genes, and future studies using outbred populations with greater genetic diversity should be even more powerful for identifying causal genes. However, the promise of currently available commercial outbred populations is limited by low genetic diversity and the requirement for sample sizes substantially larger than the approximately 00 animals used in this study.


Genomic selection uses dense single nucleotide polymorphisms (SNP) markers to predict breeding values, as compared to conventional evaluations which estimate polygenic effects based on phenotypic records and pedigree information. The objective of this study was to compare polygenic, genomic and combined polygenic-genomic models, including mixture models . The data consisted of phenotypes and SNP genotypes  of 2,188 mice. Various growth, behavioural and physiological traits were selected for the analysis to reflect a wide range of heritabilities (0.10 to 0.74) and numbers of detected quantitative traits loci (QTL) (1 to 20) affecting those traits. The analysis included estimation of variance components and cross-validation within and between families.Genomic selection showed a high predictive ability (PA) in comparison to traditional polygenic selection, especially for traits of moderate heritability and when cross-validation was between families. This occurred although the proportion of genomic variance of traits using genomic models was 22 to 33% smaller than using polygenic models. Using a 2.5% mixture genomic model, the proportion of genomic variance was 79% smaller relative to the polygenic model. Although the proportion of variance explained by the markers was reduced further when a smaller number of SNPs was assumed to have a substantial effect on the trait, PA of genomic selection for most traits was little affected. These low mixture percentages resulted in improved estimates of single SNP effects. Genomic models implemented for traits with fewer QTLs showed even lower PA than the polygenic models.Genomic selection generally performed better than traditional polygenic selection, especially in the context of between family cross-validation. Reducing the number of markers considered to affect the trait did not significantly change PA for most traits, particularly in the case of within family cross-validation, but increased the number of markers found to be associated with QTLs. The underlying number of QTLs affecting the trait has an effect on PA, with a smaller number of QTLs resulting in lower PA using the genomic model compared to the polygenic model. Recently, high-density single nucleotide polymorphism (SNP) arrays for a broad range of species have been developed, including humans, mice, plant species such as barley, wheat or maize as well as major livestock species, such as cattle, pigs, sheep and chickens. In the past, selective breeding in plant and livestock species was based on phenotypic information combined with extensive pedigrees using best linear unbiased prediction. The use of high density SNP arrays opened the opportunity of using genomic information to estimate genomic breeding values for individuals . EstimatThe high cost of genotyping, especially for the high density SNP arrays, limits the extent to which routine genotyping can be implemented in practice. Additionally, many of the SNPs contribute little to the genetic variance of a trait, as was found for example for human height variation  or complThe aim of this study was to assess the efficiency of genomic selection using mouse data and how it is affected by a) the heritability of the trait, b) the number of QTLs affecting the trait, c) the type of trait  and d) the number of SNP markers in the model allowed to have a substantial effect. Various models are fitted (including polygenic and/or genomic effects), and cross-validation performance within and between families is compared.Tables Analyses of weight traits based on model 1), using polygenic effects only, showed slightly lower heritabilities  were 22 to 31%, 23 to 33% and 25 to 30% lower, respectively, than those using the polygenic model (1) (Tables In model (3), additionally fitting polygenic effects essentially captured part of the genetic variance that was not accounted for by the genomic effects. The total variance attributed to genetic effects (polygenic and genomic) was in line with the polygenic variance found in model (1). Phenotypic proportions of the variance of the genomic effects using model (3) were consistently lower than in model (2). The phenotypic proportions of the variance of the genomic effects were 33 to 44%, 37 to 52% and 44 to 50% lower for weight, behavioural and physiological traits, respectively, than the phenotypic proportions of the variance of the polygenic effects obtained from model (1). For these traits, the phenotypic proportions of the variance of the polygenic effects accounted for 40 to 48%, 31 to 50% and 50 to 80%, respectively, of the heritability estimated using model (1). The use of different mixtures in model (3) resulted in a 75 to 92%, 60 to 70% and 75 to 80% decrease in phenotypic proportions of variance of the genomic effects compared to the corresponding proportions of polygenic effects from model (1) for the respective traits. The phenotypic proportions of the variance of the polygenic effects for weight, behavioural and physiological traits accounted for 73 to 80%, 60 to 61% and 81 to 100%, respectively, of the phenotypic proportions of the variance of the polygenic effects from model (1).rd allele, resulted in small changes in proportions of the variance of the genomic effects with lower mixture percentages.Using model (3), in general, a lower mixture percentage led to a decrease in phenotypic proportions of the variance of the genomic effects and to an increase in the phenotypic proportions of variance of the polygenic effects in all traits. Comparing W6 and W6m, treating missing alleles as a separate 3Tables In contrast, using between family cross-validation, model (1) resulted in substantially lower PA than models (2) and (3) for most traits. This was especially visible for traits with moderate to high heritabilities (e.g. for W6: PA of 0.15 vs. 0.24 or for TF: PA of −0.04 vs. 0.19 using model (1) and (2), respectively; Tables TA was the only trait to show significant differences in PA for within as well as between family cross-validation using model (2) with different mixtures. PA was stable at first with the low mixture models, but with mixtures below 7.5%, PA decreased substantially compared to its highest value (0.27 vs. 0.35). W6 showed a similar pattern for between family cross-validation, with a drop-off for mixtures below 7.5% (from 0.27 to 0.20). Both W6 and W10 showed a trend for a decrease in PA for within family cross-validation for mixtures below 7.5% in model (2). TA was the only trait to show a tendency for a reduction in PA with a decrease in mixture percentage, for both within (from 0.43 to 0.41) and between family cross-validation (from 0.34 to 0.28) using model (3). All other traits showed no significant decrease in PA with lower mixture percentages. Different modelling of missing genotypes as used for W6m compared to W6 showed almost no difference in PA.As an illustration of the statistical relevance of particular markers, ratios of posterior to prior odds based on two 2.5% mixture models are shown in Table rd allele did not change their estimates, the number of markers with increased evidence to be associated with a QTL was much lower for W6m than for W6.In contrast to the variance estimates and PA, for which treating missing alleles as a separate 3Figures 2 = 0.74), but as low as 0.27 for a trait with a low heritability . However, the relationship between heritability and PA was far from linear, as can be seen when comparing for example TF and I75, where the latter trait had a lower heritability but a higher PA using within family cross-validation. This might indicate that other factors besides the heritability have an influence on PA of a model.In general, higher heritabilities resulted in an increase in PA of genomic selection for all traits. Similar results were found for a different set of traits from this dataset ,13, withIn addition to heritability, the influence of the number of QTLs on PA of a trait was also investigated. As pointed out earlier, the number of SNP markers to be associated with QTLs is higher than the number of QTLs so that we found more markers to have an substantial effect on QTLs than found by Valdar et al. . Across There was a clear tendency for traits with fewer SNP markers associated with QTLs to have a lower PA in the case of between family cross-validation. The only exception was HC, which had the lowest PA but not the lowest total number of markers associated with QTLs. However, this trait had a relatively high number of markers classified with the lowest levels of evidence for QTLs compared to the other traits, which indicate their low effect size. For within family cross-validation the tendency was weaker.rd allele reduced the number of detected SNPs associated with QTLs. This reduction had no influence on PA.Simulation studies, e.g. by Zhong et al. , KizilkaAnalysis of variance components based on models (2) and (3) indicated that behavioural traits showed in general much lower variability attributable to cage effects. The larger variability of cage effects for weight and physiological traits was also found by Valdar et al.  and variThere is a vast statistical literature on model comparison criteria using Bayesian and frequentist perspectives. In this work we focus on the use of genomic models to predict genetic values of individuals or to predict future observations. In such a context an obvious criterion of model comparison is their predictive ability. This was studied using cross-validation. Using this method, all three models performed equally well using within family cross-validation. Extensive pedigree information reduced the advantage of genomic information which provided only a small benefit relative to polygenic selection. However, with less close family ties, as is the case with between family cross-validation, genomic information became substantially more valuable, in agreement with other studies ,18. ThisAdding polygenic effects to a genomic model influenced the estimated variances by picking up the part of the genetic variance that was not captured by the genomic effects model. However it had little influence on PA. Legarra et al.  and De lA reduced number of markers assumed to have a substantial effect on the trait had an influence on estimates of variance but had no significant effect on PA for most traits. Mixture models explained less of the variance attributed to genomic effects, but resulted in better estimates of individual SNP effects. As a consequence, the PAs between models differed little. Within trait, there was a clear relationship between the mixture percentage and the number of SNP markers associated with QTLs, but no clear association with the PA. TA was the only trait to show a significant decrease in PA for within as well as between family cross-validation, but only in cases where the mixture proportion dropped below 7.5%. Weight traits showed almost the same trends for some mixture models, but for most traits no change in PA occurred even at a mixture proportion of 2.5%. Even though estimates for PA were not significantly different from each other, there seemed to be an optimum mixture percentage, with highest values obtained often around mixtures of 40%.Su et al.  found siDue to the large costs of genotyping, low density SNP arrays or methodologies that reduce the numbers of animals to be genotyped are of great importance. Research in genome-wide association studies has found that a two-stage design with pre-selection of SNPs between steps can reduce costs substantially without reducing the power of the study ,23. AnotGenomic selection generally performed better than traditional polygenic selection, as indicated by an increase in PA. The increase in PA was most pronounced in the case of between family cross-validation. Larger increases in PA were found for traits with lower heritabilities, but the underlying number of QTLs affecting the trait had an important effect. Traits with a small number of QTLs showed lower PA using the genomic model compared to the polygenic model. Behavioural traits showed a lower variance of cage effects than other traits, but no difference in efficiency of genomic selection compared to traits with a similar heritability. Models including both polygenic and genomic effects captured more of the genetic variance, but did not improve PA. The dataset was restricted to genotyped animals only; incorporation of non-genotyped animals may show different results as a result of for example lower errors of estimation of fixed effects and higher accuracy of prediction of polygenic effects .Reducing the number of SNP markers assumed to have a substantial effect in a mixture model did not significantly change PA for most traits, particularly in the context of within family cross-validation. The mixture approach showed that models using different percentages of SNPs affecting the trait performed efficiently even with low percentages, which may be of greater importance in the future with increasing sizes of SNP arrays.In the present work, the a priori probability that a marker effect has a detectable effect was treated as a known parameter. In common with other results from the literature, this did not have a clear effect on the PA of the models. However as shown in Figure Data on 2,188 geno- and phenotyped mice provided by the Wellcome Trust Centre for Human Genetics were used to analyse the efficiency of genomic selection in seven traits. The data were freely available  and the 2 < 0.5 within 2 Mb and < 0.2 within 8 Mb [After removing uninformative markers, 10,496 SNPs were retained for the analysis. All animals had a call rate above 95% and 99% of all SNPs had call rates higher than 99%. Missing alleles were imputed at random based on the Hardy-Weinberg equilibrium conditional on the observed allelic frequencies of genotyped SNPs. The random numbers were generated based on a uniform distribution. The extent of linkage disequilibrium between pairs of markers was low with an rhin 8 Mb  .rd allele with low frequency (W6m).Traits were chosen across a range of heritabilities, type  and number of QTLs Table , based oAll traits were treated as normally distributed and analyzed incorporating fixed effects and covariates based on the models reported by Valdar et al. . Fixed eThree basic groups of models were used to compare changes in variance components and PA as a result of using genomic information. One model used only polygenic effects (1), a second model used only genomic effects (2), and a third model fitted both effects (3). For models (2) and (3), seven different sub-models were considered based on the percentage of markers that was assumed to have a substantial effect. This included a non-mixture model using 100% and six mixture models, ranging from 70%, 40%, 10%, 7.5%, 5% to 2.5% of the SNPs assumed to have a substantial effect. In the following, these sub-models will be labelled according to the mixture percentages. All analyses were performed using a Bayesian approach and implemented with Markov chain Monte Carlo methods  using thμ fits a general mean and the vectors b, c, u and e fit thefixed,cage I is the identity matrix and A the additive genetic relationship matrix. X1, X2 and Z are incidence matrices relating the vectors b, c and u with y. This is the mixed model which is most commonly used to predict traditional breeding values in animal breeding programmes. For the model using genomic effects, model (1) was changed to a Bayesian multi-marker association model as follows:where Qas fits the genomic effects, with a the vector representing effects associated with marker alleles s a scaling factor modelling the variance explained by each marker and Q the design matrix linking alleles with markers [s as follows for the non-mixture models:where  markers . Priors TN denotes a truncated normal distribution. For mixture models the following scaling factors s were used:where π0, and the second distribution models the markers that have a substantial effect at a proportion π1. The proportions of markers π1 were varied across mixture models ranging from 100 to 2.5%. Variances for the first distribution where the first distribution models the markers with on average little to no effect at a proportion u accounts for genetic variation which could not be explained by the genomic markers a.where the effects are as defined earlier. Here the polygenic variance of Estimates for the variance of polygenic effects PA was calculated as the Pearson’s correlation between a predicted observation and the corresponding realized observation. Realized observation was calculated as the phenotype corrected for fixed effects and covariates, while the predicted observation was the estimated breeding value, as was done by Legarra et al. . To predTwo different routines for splitting the data were used: within family and between family cross-validation. For within family cross-validation, full sib families were randomly split between training and validation set such that each set contained at least one animal from a family. For between family cross-validation, families were split such that no full sib family would have animals in both datasets simultaneously. As a result, for between family cross-validation no close genetic connectedness due to full sib families was available between training and validation data. In the case of within family cross-validation, full sibs with phenotypic data linked the breeding values of the training and validation data.As an illustration, the relative importance of individual markers was quantified via the computation of Bayes Factors, conditional on either model (2) or model (3). The correct inferences about the statistical relevance of particular markers could involve, first, calculation of the posterior probability of each model. Secondly one could report Bayes factors conditional on the model with largest posterior probability, or averaging over all models. This task was judged to be computationally too burdensome and was not undertaken in this study. As indicated in Table π1 the a priori probability that the marker has a substantial effect. Results were plotted per trait for all markers, whereby a PPOR > 3.2 can be interpreted as substantial evidence for the marker to have an increased effect, a PPOR > 10 as strong evidence, and a PPOR > 100 as decisive [where decisive .The authors have no competing interests.DK conducted the statistical analyses of the data, discussed the interpretation of the results and prepared and drafted the manuscript. DS suggested the use of mixture models, helped with the interpretation of the results and contributed to the final manuscript. GS assisted with the statistical analysis and provided interpretations of the results. LJ provided assistance to use the software for the statistical analysis and provided the idea how missing genotypes should be fitted. CA helped with the interpretation of the results and the writing of the manuscript. RR coordinated the research, initiated the project, identified the data and its analysis and helped with the interpretation of the results and writing of the manuscript. All authors read and approved the final manuscript.


Motivation: For the analysis of rare variants in sequence data, numerous approaches have been suggested. Fixed and flexible threshold approaches collapse the rare variant information of a genomic region into a test statistic with reduced dimensionality. Alternatively, the rare variant information can be combined in statistical frameworks that are based on suitable regression models, machine learning, etc. Although the existing approaches provide powerful tests that can incorporate information on allele frequencies and prior biological knowledge, differences in the spatial clustering of rare variants between cases and controls cannot be incorporated. Based on the assumption that deleterious variants and protective variants cluster or occur in different parts of the genomic region of interest, we propose a testing strategy for rare variants that builds on spatial cluster methodology and that guides the identification of the biological relevant segments of the region. Our approach does not require any assumption about the directions of the genetic effects.Results: In simulation studies, we assess the power of the clustering approach and compare it with existing methodology. Our simulation results suggest that the clustering approach for rare variants is well powered, even in situations that are ideal for standard methods. The efficiency of our spatial clustering approach is not affected by the presence of rare variants that have opposite effect size directions. An application to a sequencing study for non-syndromic cleft lip with or without cleft palate (NSCL/P) demonstrates its practical relevance. The proposed testing strategy is applied to a genomic region on chromosome 15q13.3 that was implicated in NSCL/P etiology in a previous genome-wide association study, and its results are compared with standard approaches.Availability: Source code and documentation for the implementation in R will be provided online. Currently, the R-implementation only supports genotype data. We currently are working on an extension for VCF files.Contact:heide.fier@googlemail.com In the search for disease susceptibility loci (DSLs), genome-wide association studies (GWAS) have been a successful instrument for the identification of replicable genetic associations . They caet al. (2011) have proposed a method that compares the sharing patterns of rare alleles between cases and controls. Recently, general statistical frameworks have been developed  will not provide efficient power. Similarly, non-parametric tests that directly rely on the shape of the distance distribution functions (e.g. Kolmogorov–Smirnov test) will concentrate on the difference in the skewness of the distance distribution functions. However, they ignore information about the actual physical distances between the rare variants.One alternative approach to directly compare the two weighted distance distribution functions is the application of a non-parametric two-sample test on the variability of the distance distribution functions. The Ansari–Bradley test statistic can then be expressed asThe Ansari–Bradley test assumes the same location parameter for the tested two independent distribution functions and tests for differences in the ratio of scales. The scale of a distribution function describes its spread, i.e. the scale of a normal distribution is defined by its variance.Because we apply two different weighting schemes on each sample, we obtain two test statistics for the Ansari–Bradley test: one test statistic for the distance distribution functions weighted on the distribution of variants in cases and another one for the distance distribution functions weighted on the distribution of variants in controls.We defines) of the weighted distance distribution functions for cases and controls is equal to one.For both weighting schemes, we independently test whether the ratio of scales (We select the maximum of both test statistics based on our hypotheses (1) and (2) as our final test statistic.A rejection of the null hypothesis implies an association of the tested rare variants in the region with affection status. Because of the likely presence of tied observations in the distance distribution functions, we use an implementation of the standard Streitberg/Roehmel shift algorithm to retrieve exact distribution functions for our test statistics .P-value is estimated as the proportion of permutation test statistics, which are more “extreme” than the actually observed test statistic for the real data.The significance of the test statistic is obtained based on permutations. In each replicate, case–control status is randomly assigned to each proband in such a way that the total number of cases and controls of the original study is maintained. The genotypes of the probands are kept fixed, maintaining the LD structure of the region in the permutation sample. The For the application of our approach to dosage data, i.e. those datasets that contain genotype probabilities instead of allele counts, we recommend calculating the expected allele count for each subject and variant Using simulation studies, we evaluate the performance and power of the Ansari–Bradley test based on the weighted distance distribution functions. We also apply our analysis approach to a sequencing dataset for non-syndromic cleft lip with or without palate to demonstrate its practical relevance.−8 and simulated 5000 haplotypes with 500 000 base pairs. Subsequently, we selected 30 SNPs with a predefined upper MAF cutoff. Based on two randomly chosen haplotypes, we used an additive disease model with a disease prevalence of 0.15 to derive our genotypes. We assigned an invariant risk ratio of 3.0 to each SNP that has a causal influence on the affection status. We repeated the last step for each specification until we received a sample of 500/500 cases and controls or 750/750 cases and controls.For the generation of the genetic data in the simulation study, we implemented the model as described in the simulation study by We applied different simulation scenarios to examine the type 1 error and power of our proposed methods.In the following, we refer to the proposed rare variant test statistics based on the allelic distances as distance-based measure (DBM).Moreover, we compare the proposed test statistic with some of the existing statistical methods that relate rare variants to a dichotomous phenotype: the CMC approach  that assWe denote the test statistic of For the simulations, we first differentiated between two different settings that relate to the physical distribution of the rare variants in the derived samples. In the clustered scenario (Clustered = Yes), all variants that have a disease-causing effect are sampled as a sequence with close physical close position to each other, whereas the remaining non-causative/protective variants and their physical positions are randomly sampled outside this sequence. In the non-clustered scenario (Clustered = No), the physical position of all selected variants is randomly assigned. The degree of clustering of the simulated variants, i.e. the distances between the associated loci, was thereby chosen according to the observed degree of clustering for the real dataset that we used for the application of our method (Section 3.2).P-values used for the type 1 error evaluation and for the power estimates are based on 1000 permutations.Next, we varied the sample size between 500/500 cases and controls or 750/750 cases and controls. In all derived different scenarios, we examined two different upper MAF thresholds, namely 1% and 0.5%, to evaluate the sensitivity of the presented measures to different MAF cutoffs. We used 1000 replicates to evaluate the type 1 error and 500 replicates to estimate the power of each approach. All showed estimates result from two-sided testing. The α = 0.05 and α = 0.01—to evaluate the type 1 error. The simulation study results suggest that our approach maintains the type 1 error.For the power estimates of the methods, we included one additional specification in the outlined scenarios. In a first setting, we assumed that, for all 10 DSLs, the rare allele increases the disease risk. In a second setting, we assumed the simultaneous presence of deleterious and protective effects, i.e the rare alleles of seven DSLs are disease causing, whereas the rare alleles of three DSLs have a protective effect.Based on 500 replicates, The power estimates for the non-clustered scenario show that our constructed DBM had a better performance than the collapsing approach (CMC), the two methods based on weighting schemes  and the SKAT and C-Alpha test, when the effect direction of the causative rare variants is the same.In the case of mixed-effect directions of the causative variants, the SKAT and C-Alpha test showed more power in one of the four outlined scenarios compared with the DBM method.The replication-based measure (RB), however, outperformed all other compared methods  in all specified simulation runs in the non-clustered scenario. For a rather small MAF cutoff (MAF < 0.005), the power advantage of the RB method compared with our DBM for the non-clustered scenario became similar though. In general, the simulation studies suggest that our approach achieves power levels that are comparable with the power levels of current methodology, even in scenarios where there is no clustering of variants.Because all compared methods except the DBM method are not sensitive to location clustering of the variants, the power estimates of CMC, Price, MB, RB, SKAT and C-Alpha did not differ considerably in the clustered and non-clustered scenario.Our constructed distance-based measure (DBM), however, is sensitive to physical closeness of variants, and thus showed far more power in a clustered scenario than in a non-clustered scenario. This power gain had the consequence that in the clustered scenario our distance-based measure (DBM) showed the highest power estimates in all simulation runs compared with the other methods .The power advantages of the DBM method compared with the replication-based measure (RB) ranged from 1 to ∼35% when only risk variants are present in the simulated genomic region. The power advantage of the DBM measure was thereby greater for the smaller MAF-cut off. When both risk and protective variants are defined in the simulation runs, our newly introduced measure showed even more power compared with the other methods. In one simulated setting, the DBM measure had a power advantage of >60% compared with the next best performing method (RB). It is important to note, however, that the power estimates of all outlined methods were reduced in simulation runs where variants with opposed effect directions were included.In addition, we also re-ran some of our simulations with a constant genetic attributable risk to confirm our qualitative conclusion about the performance of the different methods (data not shown).We applied the discussed approach to a sequencing study on non-syndromic cleft lip with or without cleft palate (NSCL/P). The dataset was generated by a follow-up sequencing of 96 cases and 96 controls in gremlin-1 (GREM1), a candidate gene located in a genomic region at 15q13.3 that was identified as a suggestive NSCL/P locus in a GWAS by P-values of our derived distance-based test statistic (DBM) compared with the other outlined collapsing and weighting methods. For all compared methods, the P-values are based on 1000 permutations.For our proposed distance-based approach (DBM), we select two different MAF cutoffs (1 and 5%) and compared them with the other methods . It can be seen that our newly introduced measure (DBM) finds a highly significant association of the sequenced 15q13.3 region at both defined upper MAF cutoffs, whereas the other methods  fail to detect a significant association at a 5% significance level. Before the application of our method to real data, one should perform simulation studies to determine a suitable window size as for the other mentioned rare variant association tests, given the sample size and the assumption of the disease parameters, i.e. prevalence, effect size, etc. For the application of our variant position-based test, the window size should be chosen according to the spatial distribution of the variants on the chromosome, so that variant clusters are not separated.So far, existing statistical methodology for association analysis has ignored the physical locations of the variants. In this communication, we have proposed a class of methods to test the association of rare variants to a dichotomous trait that incorporates the underlying spatial distribution structure of the rare variants. Our method is based on statistical clustering methodology. Instead of collapsing or combing the genotypes of rare variants in the genomic region of interest, our test statistic takes advantages of physical distances/locations of the alleles at the rare variant loci and detects rare variant patterns that are different between cases and controls. As a result, we obtain a new class of association tests for rare variant analysis that can aid the localization of the biological relevant segments in the analyzed genomic region. As for any rare variant approach, subpopulation-specific patterns in the variant distribution can bias the analysis results of our test statistic. Although the findings of It is important to note, however, that our method is best suited for high coverage sequencing data to detect and test the spatial structure of variants. SNP data that were obtained from GWAS SNP chips, because of the pre-defined SNP locations on such chips, offer only limited information on the spatial distribution of variants in a genomic region. Moreover, the presented method also has limitations in testing aggregated, but positional unconnected, genome regions, like non-coding regions.For now, we focus on a very intuitive test statistic that compares the two distance distributions between cases and controls, using a Ansari–Bradley test statistic. Currently, we are working on an extension of the approach that allows the integration of covariates in the test statistic and to generalizations to quantitative traits.Funding: The project described was supported by Award Number  from the National Institute of Mental Health and Award Number  from the National Heart, Lung, and Blood Institute.Conflict of Interest: none declared.


F distribution was derived and verified using computer simulations. We obtained equivalent formulas for the cost of phenotype measurement error. Effects of differences in measurements were examined in a genome-wide association study (GWAS) of two grading scales for cataract and a replication study of genetic variants influencing blood pressure. The mean absolute difference between the analytic power and simulation power for comparison of phenotypic means and variances was less than 0.005, and the absolute difference did not exceed 0.02. To maintain the same power, a one standard deviation (SD) in measurement error of a standard normal distributed trait required a one-fold increase in sample size for comparison of means, and a three-fold increase in sample size for comparison of variances. GWAS results revealed almost no overlap in the significant SNPs (p<10−5) for the two cataract grading scales while replication results in genetic variants of blood pressure displayed no significant differences between averaged blood pressure measurements and single blood pressure measurements. We have developed a framework for researchers to quantify power in the presence of measurement error, which will be applicable to studies of phenotypes in which the measurement is highly variable.Measurement error of a phenotypic trait reduces the power to detect genetic associations. We examined the impact of sample size, allele frequency and effect size in presence of measurement error for quantitative traits. The statistical power to detect genetic association with phenotype mean and variability was investigated analytically. The non-centrality parameter for a non-central  In genome-wide association studies (GWAS), association between large number of single nucleotide polymorphisms (SNPs) and a trait measurement is computed and SNPs with strong associations will be replicated in a separate cohort. Non-differential measurement error in both genotyping and phenotyping reduces the power and hence increases the type II error to identify true associations in discovery cohorts. This decreases the efficiency of GWAS to produce findings in discovery that are less likely to be replicated in subsequent studies. Errors in genotype have been reduced through technological advances and stringent quality controls in SNP genotyping. Measurement and misclassification errors in case-control studies and measurement errors in exposure variables have been well studiedPerforming power and sample size calculations allows researchers to manage cost of genotyping effectively. With recent discoveries made using web-based questionnaire for data collection In this study, firstly we quantified the power to identify genetic variants that affect the means and variability of quantitative traits in GWAS of unrelated individuals in the presence of measurement error, where measurement error was defined as the additional variation introduced to a “true” underlying phenotype. Secondly, we demonstrated the impact of measurement error on the pipeline of GWAS analysis in population-based studies. We presented real data analysis based on two phenotypes: age-related cataract and blood pressure to illustrate the impact of measurement error on GWAS discovery and on genetic replication studies.ith individual, We used the following model to describe the phenotype:p, the minor allele frequency (MAF). p via a Binomial distribution.The marker locus satisfies the Hardy-Weinberg equilibrium (HWE). Hence the genotype frequencies are computed based on SNP effects are additive. Without loss of generality, we let With measurement error The power for linear regression can be determined using the non-central F distribution, with non-centrality parameter (NCP)  follows :(2)Without measurement errors, ith individual, Following the framework described by Visscher and Posthuma The SNP has effect on phenotype variance but not the trait mean.Phenotype is standard normally distributed in absence of heterogeneous variance.We assume that fined as :(3)p. For the comparison of phenotype means, the phenotypes were simulated using p = 0.2, n = 15,000, p = 0.2, n = 30,000, To verify our findings and assess the power of genetic association testing in the presence of measurement error, we carried out simulation studies under various scenarios. First, we simulated the genotypes We defined cost of phenotype measurement error as the percentage increase in sample size required to maintain a constant analytical power for an increase in measurement error. Following the framework of Edwards et al. Similarly, for comparison of phenotype variances, we used The Singapore Malay Eye Study (SiMES) and Singapore Chinese Eye Study (SCES) are population-based cross-sectional epidemiological studies on eye diseases for residents of Singapore. Details of the study design and methodology have been reported and published elsewhere In the SiMES cohort, nuclear cataract was assessed using two methods: 1) the Lens Opacities Classification System III (LOCS III) e and DBPe) and used for association testing in comparison with the “true” values (SBP and DBP).In the Chinese cohort, blood pressure was measured according to a protocol used in the Multi-Ethnic Study of Atherosclerosis p value <10−6) and (3) MAF <1%. Detailed quality control procedures for SCES samples genotyped on OmniExpress chips were provided in the supplementary materials . A total of 620,901 SNPs were genotyped in each cohort. An additional 635 samples in SCES was genotyped using Illumina Human OmniExpress BeadChips with a total of 729,698 SNPs. Detailed quality control procedures for sample and SNPs were described elsewhere aterials . After qe, SBP and SBPe in each cohort. In brief, linear regression analysis was performed assuming an additive model, adjusted for age, age-squared and body mass index (BMI), with medication corrected BP as the dependent variable. To account for batch effect of data from separate chips in SCES, meta-analysis was performed using an inverse-variance fixed effects model and a Bonferroni adjusted cut off of p value = 0.0055 (0.05/9 tests) was used to control Type I error at 5%.For genome-wide analysis of nuclear cataract in SiMES, we used the nuclear cataract value from the worse eye, where a larger value indicates higher severity. Each phenotype was standardized by subtracting the mean and dividing over the SD of the phenotype. Association testing was performed on standardized nuclear cataract phenotype for comparison of means and squared-standardized nuclear cataract phenotype for comparison of variances. For genetic replication analysis, we analyzed 9 variants which showed significant associations with BP in East Asians The PLINK software (version 2.0) To verify our findings, we compared the analytical power with the simulated power. The mean (SD) of absolute difference between the analytical power and simulation power for comparison of means and variances was 0.00169 (0.00195) and 0.00418 (0.00398) respectively. The maximum absolute difference for comparison of means and variances was 0.00941 and 0.0197 respectively.C could be approximately equal to For small effect sizes, henotype .p<10−5) from both grading scales in the GWAS of nuclear cataract in a comparison of phenotypic means. None of the SNPs overlapped.A total of 2,349 samples from SiMES with both genotype and phenotype data of Wisconsin System and LOC III grading were included for genome-wide testing. The measurements of nuclear cataract in SiMES varied substantially for some individuals , especiae was high , compared to the presence of misclassification errors (of case-control status) for GWAS. We note that only as the measurement error exceeded 0.4 and 0.6 SD of the phenotype for comparison of means and variances respectively, the decrease in power became substantial. In current times, measurements prone to large errors have mostly been improved through technological advancements, or taking of multiple measurements and averaging them. While measurement error is not easily quantifiable in practice, we provide a framework to estimate measurement error using repeated measurements .In the National Cooperative Gallstone Study, it was reported that 7% and 17% of the variation in observed triglycerides and cholesterol values were attributable to errors respectively Our measurement error model has the same power as a classical measurement error model, where the error is in the independent variable instead of the dependent variable. The impact of measurement error under the classical measurement error model has been well studied in the area of econometrics and statistics To reduce measurement error, simple methods such as trimming and winsorizing have been used to screen outliers In this work, we chose to compute power based on the simple linear regression framework and additive allele effects. We recognize that there are other tests available for testing association in GWAS Our results have important implications in practice. The methods of assessing the power of the sample size calculation in GWAS, which do not account for potential measurement errors, may optimistically over-estimate the power or equivalently under-estimate the sample size required. In the present study, we recommend the computation of sample size and power for GWAS of traits that have low repeatability, or differ between different grading scales and machinery, by a magnitude of more than 0.6 and 0.4 SD of true phenotype for comparison of means and variances respectively. A pilot study with multiple measurements is recommended to estimate the measurement error using our proposed method. This is to ensure accurate sample size calculation before GWAS. Finally, we note that the statistical power incorporating measurement errors is straightforward to compute using any software that provides values under the F distribution probability density function and the R code is available at request from the authors.Text S1Derivation of squared correlation coefficient for comparison of phenotypic means and variability.(DOC)Click here for additional data file.Text S2Detailed quality control procedures for SCES samples genotyped on OmniExpress chips.(DOC)Click here for additional data file.Text S3Estimation of measurement error using repeated measurements.(DOC)Click here for additional data file.