There is growing interest in the role of rare variants in the variation of complex traits due to increasing evidence that rare variants are associated with quantitative traits. However, association methods that are commonly used for mapping common variants are not effective to map rare variants. Besides, livestock populations have large half-sib families and the occurrence of rare variants may be confounded with family structure, which makes it difficult to disentangle their effects from family mean effects. We compared the power of methods that are commonly applied in human genetics to map rare variants in cattle using whole-genome sequence data and simulated phenotypes. We also studied the power of mapping rare variants using linear mixed models (LMM), which are the method of choice to account for both family relationships and population structure in cattle.We observed that the power of the LMM approach was low for mapping a rare variant (defined as those that have frequencies lower than 0.01) with a moderate effect (5 to 8 % of phenotypic variance explained by multiple rare variants that vary from 5 to 21 in number) contributing to a QTL with a sample size of 1000. In contrast, across the scenarios studied, statistical methods that are specialized for mapping rare variants increased power regardless of whether multiple rare variants or a single rare variant underlie a QTL. Different methods for combining rare variants in the test single nucleotide polymorphism set resulted in similar power irrespective of the proportion of total genetic variance explained by the QTL. However, when the QTL variance is very small , these specialized methods for mapping rare variants and LMM generally had no power to map the variants within a gene with sample sizes of 1000 or 5000. We observed that the methods that combine multiple rare variants within a gene into a meta-variant generally had greater power to map rare variants compared to LMM. Therefore, it is recommended to use rare variant association mapping methods to map rare genetic variants that affect quantitative traits in livestock, such as bovine populations.The online version of this article (doi:10.1186/s12711-016-0238-5) contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) have been successful in identifying common variants that are associated with complex diseases and quantitative traits. However, the common variants that have been identified thus far account for only a small fraction of the estimated heritabilities –3. TheorRare variants are poorly captured by the commonly used single nucleotide polymorphism (SNP) chips, because SNPs on these chips typically have a much higher minor allele frequency (MAF) than rare variants and, thus, are generally in low linkage disequilibrium (LD) with these. Recent technological advances allow us to study individual genomes at the base-pair resolution , includiMethods for GWAS based on common SNP variants are well established . HoweverSeveral classes of statistical methods have been developed for the analysis of rare variants for ‘case–control’ designs and quantitative traits in humans for both randomly sampled and related individuals –19. A shOne broad class of such methods is known as the “burden test” , 20, 21.The second broad class of methods comprises variance component tests, such as that implemented in the C-alpha  and sequp value optimized nuisance parameter score test extended to relatives) for related individuals [The third category of methods combines burden tests and variance component tests to exploit the strengths of both approaches. This is implemented in the software SKAT-O for unrelated individuals  and in Mividuals . These mSeveral studies have mapped rare variants that contribute to complex diseases in humans by using deep exome sequencing , 28, 29.The above-mentioned methods for rare variant association mapping were developed for human studies for which samples are obtained at random from a population or data that originate from small families, e.g. trio and sib-pair analyses. In contrast, bovine datasets usually include large half-sib families, and intensive artificial selection in cattle may pose special issues that are related to data analysis. For example, rare variants may be confounded with family structure, making it more difficult to disentangle their effects from family mean effects. In addition, the availability of large half-sib family sizes in cattle has the advantage that rare variants may be observed at a higher frequency within extended families compared to the population as a whole. The suitability of the above-described statistical methods that were developed to map rare variants for quantitative traits in humans still remains unexplored for data structures such as those of cattle and other livestock species. Thus, the objective of our study was to investigate power and type I errors of several approaches used to map rare variants in bovine data. Our hypothesis is that the power of the specialized methods that were developed to detect rare variants in the human genome will be higher than that of a linear mixed model approach, which is currently the method of choice to map common variants in the bovine genome. Thus, we propose method(s) for rare variant mapping in livestock populations, which should contribute to the development of models that are geared towards exploiting rare variants in genome-assisted breeding.The statistical methods that we tested for rare variant mapping were famBT , famSKATy is a vector of phenotypes, X is a design matrix for fixed covariates including the intercept, γ is a vector of unknown covariate effects, Z is an incidence matrix relating phenotypes to the corresponding random polygenic effect, u is a vector of random polygenic effects that follows a multivariate normal distribution A is the additive genetic relationship matrix and e is a vector of random residuals, M is a n × m matrix that encodes the genotype at the m tested variant loci and n is the number of individuals with mij representing the allele dosage  of the minor allele at the j-th variant of individual i, and β is a vector of (possibly correlated) random effects of the m variants, ρ = 0 and ρ = 1 correspond to models famSKAT and famBT, respectively. This method for detecting rare variants is referred to as MONSTER [ρ i.e. ρ = 0, MONSTER is equivalent to famSKAT and when ρ = 1, MONSTER is equivalent to famBT.When written in more conventional animal breeding notation, the MONSTER model becomes: MONSTER . A grid H0 that H1 that p value from its expectation under the null hypothesis, was calculated for all statistical methods considered to detect rare variants.To detect associations between a trait and a genomic region of interest, we tested the null hypothesis  MONSTER . To acce MONSTER , which fWe compared MONSTER, famBT and famSKAT to two methods that are used for association mapping of common variants: a linear mixed model  and a siy is the vector of phenotypes, 1 is a vector of ones, μ is the general mean, m is a vector of allele dosages (ranging from 0 to 2) that associate records to the marker effect, g is the scalar additive effect of the SNP, Z is an incidence matrix relating phenotypes to the corresponding random polygenic effect, u is a vector of random polygenic effects that follows a multivariate normal distribution A is an additive relationship matrix and σa2 is the polygenic variance, and e is a vector of random environmental deviates that follows a normal distribution e2 is the error variance and I is an identity matrix. The model was fitted by restricted maximum likelihood (REML) using the software DMU [H0 that g = 0 was assessed using a t-test. The null hypothesis was tested with 1000 replicates and the results are presented as the null model. The genomic control coefficient [p-value was below a significance threshold after correction for multiple-testing. We used two different multiple-testing correction approaches that are described in section “Comparison of different methods used to map rare variants in the simulation”.The linear mixed model (LMM) carries out a SNP-by-SNP analysis. Complex familial relationships are the primary confounding factor in GWAS of livestock populations. In cattle, LMM, which model the effects of relationships among individuals through polygenic effects, can control the false positive rate caused by family structure and population stratification , 35. Herware DMU , and thefficient  was usedμ is the intercept, y is the vector of phenotypes, G is the genomic relationship matrix that is built based on high-density (HD) SNP genotypes, I is an identity matrix, m is a vector of the imputed allele dosages (ranging from 0 to 2), and η is a vector of random residual deviates with variance Single variant association analysis using a LMM for full sequence variants is computationally demanding, i.e. it requires a computation time of date SNP . Therefodate SNP . BrieflyIn total, the genotypes of 27,119 Holsteins animals were available for this study from the Illumina 54 k SNP array version 1 or 2 . The number of SNPs remaining after quality control was equal to 43,415, for more details see . HoweverENSBTAG00000018852 located between 1,116,669 and 1,212,429 bp that comprised 635 annotated SNPs in its transcribed region; the 222 rare variants (with a MAF < 0.01) within this gene were grouped into different SNP sets according to their MAF; the average pairwise LD (r2) for these variants was equal to 0.149 with an average distance of 83 bp between variants; and (2) the ENSEMBL Gene ID: ENSBTAG00000035858 located between 610,854 and 933,224 bp that included 3015 annotated SNPs and 309 rare variants (MAF < 0.01); the average pairwise LD (r2) for these variants was equal to 0.74 with an average distance of 106 bp between variants.Approaches for rare variant mapping are gene-based, thus the results cannot be easily averaged across multiple genes. Therefore, based on the number of rare variants and level of LD between variant sites, two genes on bovine chromosome 10 were selected for this study: (1) the ENSEMBL Gene ID: Phenotypes were simulated as the sum of three components, i.e. a polygenic effect, a QTL effect computed as the sum of the simulated effects of the underlying rare variants, and a random error. The polygenic effects were simulated based on pedigree records. The effects of rare variants were simulated as random effects. Four scenarios with respect to the MAF of the causal variants were considered. Rare variants were grouped into four classes based on MAF for the sampled individuals i.e.: 0.01 ≤ MAF < 0.02; 0.005 ≤ MAF < 0.01; 0.001 ≤ MAF < 0.005; and MAF < 0.001. Two different approaches for assigning effects to rare variants were followed: within a MAF class either multiple rare variants contributed to the total QTL effect or only one rare variant contributed to the whole QTL variance. In the scenarios with multiple causal variants, half of the rare variants within each MAF class were assigned an effect.α) was then calculated by the following equation and each causal rare variant was assigned an effect with a certain weight (as defined next):Vqtl is the proportion of genetic variance explained by the QTL multiplied by the total genetic variance , M is the genotype dosage matrix including the loci which have a QTL effect. The weights were assigned in order to add QTL effects on the simulated phenotypes. Note that this formula considers the genotype variance at the QTL, as well as the co-variance between the QTL, and that it yields one value for α that is used for all QTL. Therefore, the total QTL effect for each animal was calculated as: αM.Three levels of heritability for the trait were considered i.e. 0.3, 0.5 and 0.8. In addition, three levels of QTL variances were considered. The variance explained by the QTL  was equal to 0.1, 0.5 or 1 % of the total genetic variance when the heritability was equal to 0.5. In the scenarios with multiple causal variants, the sum of the variance explained by individual causal variants was set equal to the predefined total QTL variance. The QTL effect  and four SNP sets based on the following MAF classes of rare variants: 0.01 ≤ MAF < 0.02; 0.005 ≤ MAF < 0.01; 0.001 ≤ MAF < 0.005; and MAF < 0.001). Thus, if the p value for a tested SNP set with simulated QTL was less than 0.05/5, it was considered to be significant. For EMMAX and DMU, the p value for simulated QTL was corrected by the total number of SNPs tested. For example, if the pvalue for the simulated QTL was less than 0.05/635, it should be considered as significant for Gene ID: ENSBTAG00000018852. However, all the variants tested here are located within a gene and therefore are not independent because of the LD between them. Therefore, we used an alternative multiple-testing correction method based on calculating the effective number of independent SNPs for total number of SNPs according to [ENSBTAG00000018852 and the corresponding eigenvalues explained 99.5 % of the SNP data variation. Based on these criteria, if the p value for the simulated QTL was less than 0.05/17 for the single variant analysis using EMMAX or DMU, it was considered as significant. The standard errors for each scenario were calculated from bootstrapping based on 100 re-samplings from the 100 simulation runs.The power of each method was estimated as the proportion of runs that significantly detected loci that were simulated to be causal. A significance level of 0.05 after Bonferroni correction was used for each scenario. The rding to . Based oλ (genomic control) values for MONSTER, famBT, famSKAT, EMMAX_AMAT, and EMMAX_GMAT were less than 1, indicating that the p values closely followed the expected distribution under the null hypothesis. Therefore, these methods showed no evidence of inflation of the p values under the null model. However, some of the observed χ2 values for DMU_AMAT were far too large, which indicated very high false-positive values . First, the power values for all rare variant mapping methods across the four MAF classes  were very similar under one of the scenarios. For the scenario with a moderate heritability  in all scenarios  were similar compared to the specialized methods for rare variant mapping   Figs. , 3, 4. Wps Figs. , 3, 4. Wps Figs. , 3. In gps Figs. , 3, 4. Wps Figs. , 3, 4 bups Figs. , 3, 4.The objective of our study was to compare the power of several gene-based methods to detect rare variants using simulated phenotype data and imputed whole-genome sequence variants for a bovine population with a complex pedigree structure.Methods that are specialized for the detection of rare variants in a population of individuals with family relationships  yielded more power than linear mixed models  for the detection of QTL with multiple rare causal variants. The linear mixed model which is the method of choice for association mapping of common variants was less powerful for the detection of QTL with multiple rare causal variants Figs. , 3, 4.χ2) for data simulated under the null model (no rare variant contributing to the phenotypic variance) followed closely the expected distribution under the null hypothesis for all methods except DMU_AMAT  under the null model for DMU_AMAT. This is probably because an extremely low frequency allelic variant will remain confined to a few families or individuals. If, by chance, these families or individuals have extreme phenotypes, that effect will be attributed to the allele resulting in a false positive association. The lower the MAF, the greater the chance that the minor allele is confined to a few families or individuals. Therefore, after filtering out the loci with a very low MAF (MAF < 0.001), the observed χ2 followed closely the expected χ2 for DMU_AMAT  than that of the linear mixed models , no method had more than 5 % power (i.e. type I error threshold) for the detection of rare variants with a sample size of 1000 individuals Fig. . As expeENSBTAG00000035858 gene in the main scenarios  was very low when only one rare variant was simulated as the QTL. Therefore, the power of famSKAT (ρ = 0) was greatest while that of famBT (ρ = 1) was greatest when the statistical method’s assumptions matched the genetic architecture of the trait. However, the differences in power between MONSTER, famBT and famSKAT were very small across all scenarios. Therefore, when applying these methods on real data for mapping rare variants, it is reasonable to consider all three methods since the genetic architecture of the trait under study is usually unknown. In summary, in cattle, it is recommended to use rare variant association mapping methods to identify low frequency genetic variants especially when multiple rare variants are causal and contribute to the trait. Once identified, these rare variants could be exploited for whole-genome prediction of breeding values in the future.The power of rare variant association mapping methods  depends on the genetic architecture of the trait because they differ in their assumption about the underlying variants, direction of their effects as well as the correlation structure between rare variants. This was also shown by the simulation on the Imputation accuracies of rare variants are lower than those of common variants and this could have a large impact in association analyses for rare variants on real data . We usedMutations that change the protein structure or lead to a non-functional protein can have a strong phenotypic impact and may therefore be detectable. However, rare variants with subtle effects may be difficult to identify, even if the sample size is large. Therefore, the gene-based approaches used in our study should be considered for genome-wide mapping of rare variants. Besides, computational cost is an important factor to consider when performing genome-wide rare variant mapping. In our analyses, it took ~11 min to perform rare variant mapping for a sample size of 1000 and ~52 min for a sample size of 5000. Considering that there are ~22,000 annotated genes in the bovine genome, this still implies a huge computational effort when considering all the genes. Therefore, it is important that the algorithms for gene-based mapping are further optimized, but it may also be useful to target rare variants in candidate genes only to save computational time.Our findings showed that combining rare variants in a test SNP set with MONSTER, famBT and famSKAT yielded more power to map QTL than linear mixed models for bovine data. We also found that these methods could overcome the confounding of extreme phenotypes in the family mean when mapping rare variants compared to a one-step linear mixed model approach . In facthttp://www.ncbi.nlm.nih.gov/bioproject/PRJNA238491).The data used in this study originated from the 1000 Bull Genome Project (Daetwyler et al.  Nature G


Use of whole-genome sequence data is expected to increase persistency of genomic prediction across generations and breeds but affects model performance and requires increased computing time. In this study, we investigated whether the split-and-merge Bayesian stochastic search variable selection (BSSVS) model could overcome these issues. BSSVS is performed first on subsets of sequence-based variants and then on a merged dataset containing variants selected in the first step.We used a dataset that included 4,154,064 variants after editing and de-regressed proofs for 3415 reference and 2138 validation bulls for somatic cell score, protein yield and interval first to last insemination. In the first step, BSSVS was performed on 106 subsets each containing ~39,189 variants. In the second step, 1060 up to 472,492 variants, selected from the first step, were included to estimate the accuracy of genomic prediction. Accuracies were at best equal to those achieved with the commonly used Bovine 50k-SNP chip, although the number of variants within a few well-known quantitative trait loci regions was considerably enriched. When variant selection and the final genomic prediction were performed on the same data, predictions were biased. Predictions computed as the average of the predictions computed for each subset achieved the highest accuracies, i.e. 0.5 to 1.1 % higher than the accuracies obtained with the 50k-SNP chip, and yielded the least biased predictions. Finally, the accuracy of genomic predictions obtained when all sequence-based variants were included was similar or up to 1.4 % lower compared to that based on the average predictions across the subsets. By applying parallelization, the split-and-merge procedure was completed in 5 days, while the standard analysis including all sequence-based variants took more than three months.The split-and-merge approach splits one large computational task into many much smaller ones, which allows the use of parallel processing and thus efficient genomic prediction based on whole-genome sequence data. The split-and-merge approach did not improve prediction accuracy, probably because we used data on a single breed for which relationships between individuals were high. Nevertheless, the split-and-merge approach may have potential for applications on data from multiple breeds.The online version of this article (doi:10.1186/s12711-016-0225-x) contains supplementary material, which is available to authorized users. Genomic selection was introduced in many livestock breeding programs during the last decade. One of the main reasons for its rapid development is the availability of 50k single nucleotide polymorphism (SNP) chips for all major livestock species, including cattle , pigs 22, and pon ≪ p (n for number of recorded phenotypes and p for number of estimated SNP effects) problem is much greater with imputed sequence data than with e.g. the 50k-SNP chip, because p increases considerably, while n remains the same. In addition, computation time increases proportionally to the sharp increase in p.At the same time, simulation studies suggested, rather optimistically, that the use of (imputed) whole-genome sequence data could result in considerably increased accuracy of genomic prediction , 6. An iThe issues involved in genomic prediction using sequence data, as described above, could be, at least partly, solved by reducing the number of SNPs by removing those that are not associated with the trait of interest. This can be achieved by performing a genome-wide association study , 18, or n ≪ p problem that is encountered when all SNPs in the sequence data are simultaneously fitted in a single genomic prediction model.The objective of this study was to investigate the accuracy of SAM Bayesian variable selection applied to whole-genome sequence data. SAM modelling involves a series of initial analyses on subsets of SNPs, to select a final set of SNPs that are in strong association with the trait of interest. Our hypothesis is that the SAM Bayesian variable selection model is able to alleviate the severe The data included de-regressed proofs (DRP) and effective daughter contributions  for 555The BovineHD genotypes of the bulls were imputed to whole-genome sequence using the sequenced individuals from the 1000 Bull Genomes Project Run 4 as reference population. This multi-breed reference population comprised 1147 sequenced animals with on average an 11-fold coverage of which 311 were Holstein bulls, but all the individuals were included in the reference population because earlier studies showed that a multi-breed sequenced reference population can be beneficial for imputation accuracy, especially for variants with a low minor allele frequency (MAF) –23. PolyEditing steps of the imputed sequence data involved removing variants for which all three genotypes were not observed and thus reduced their number from 13,968,906 to 12,254,506 variants  between them, which reduced model performance as observed from the strongly inflated SNP variance component. To alleviate this problem, the following additional edits were performed. Throughout the whole genome, for any group of variants with a squared correlation of 1 between genotypes in the reference population, only the “rightmost” variant was retained, which drastically reduced the number of variants from 12,254,506 to 4,249,573  subsets of 40,090 or 40,091 variants were formed, where subset x contained variant x, n + x, 2n + x, etc. The first 33 subsets contained 40,091 variants and the last 73 subsets contained 40,090 variants.Starting with these 4,249,573 variants, to further reduce the levels of LD within the subsets, subsets were formed using an alternative strategy. Variants were first sorted based on their MAF, which was used as a very simple proxy for high LD, considering that high LD between two loci can only be achieved if the loci have similar MAF , 27. BasInitial analyses on these subsets revealed that, in spite of sorting variants on MAF to allocate those in high LD across subsets, the performance of the model for several subsets still suffered from levels of LD that were too high. To alleviate this, for all subsets, the variant groups that had a squared correlation between genotypes higher than 0.95, only the “rightmost” was retained. For a limited number of subsets, the performance of the model was still poor, thus we repeated the same editing step again with a lower threshold of 0.90 for 16 subsets, and again with a threshold of 0.85 for two of those 16 subsets. Finally, the combined sorting of variants based on MAF and checking for LD within subsets reduced the number of variants from 4,249,573 to 4,154,064. See Table Within each of the 106 subsets, a Bayesian stochastic search variable selection model (BSSVS) was applied for each of the three traits. The BSSVS model can be described as:In BSSVS, the effect for locus The conditional posterior density of ollowing , and theFinally, the conditional posterior distribution of the indicator The conditional posterior densities of The Gibbs sampler was implemented using right-hand-side updating . For eacBased on the results of the analyses within subsets, variants were sorted based on their posterior probabilities, i.e. the posterior means of the QTL-indicators To compare the SAM procedure based on imputed sequence data to other strategies, all predictions with the merged subsets were either performed with or without adding all 50k SNPs from the BovineSNP50 chip . In total, 41,682 SNPs on the commonly used 50k-SNP chip were included in the dataset after imputation to whole-genome sequence, and were used in all the scenarios that included the SNPs of the 50k-chip. Predictions were also performed using only the 50k SNPs or all 4,154,064 variants that included the 41,682 SNPs of the 50k-chip. As a final alternative, genomic estimated breeding values (GEBV) for the selection candidates were computed as the average of the GEBV obtained within each of the 106 subsets. This can be considered as an average of the predictions generated from randomly well-spaced and informative genome-wide 50k-like sets of variants.Because some of the analyses on the merged datasets and some of the alternative strategies described above involved considerably more variants than the analyses for the subsets, all analyses on the merged datasets and the alternative strategies were performed by running a Gibbs chain of 300,000 iterations with a burn-in of 50,000. For all merged datasets, the parameter n ≪ p problem is expected to be much less severe than for an analysis that involves all the variants, simply because the number of variants (p) within each subset is much smaller. In addition, both the creation of subsets of variants and the editing carried out to remove variants in complete or high LD, are expected to have a positive impact on model performance within the subsets, in terms of convergence. To assess model convergence, effective sample sizes of the SNP variance component One potential benefit of the SAM BSSVS approach, as indicated above, is that within the subsets the ollowing . In addiTo evaluate prediction accuracy of all applied models, the animal data were split into 3415 reference bulls, all born before 2001, and 2138 validation bulls born between 2001 and 2008. For all the models described previously, only the phenotypes of the 3415 reference bulls were used. The targeted prediction for validation bull To investigate the impact of using the different final datasets on the detection of QTL, which is the ultimate goal when using sequence data for genomic prediction, the posterior probabilities of all the variants of all models were evaluated. This was done by displaying the Manhattan plots with Bayes factors greater than 1. Bayes factors were computed as:For each of the 106 subsets, the estimated effects of variants were used to predict GEBV for the 2138 validation animals. These prediction accuracies were generally quite close to the accuracies obtained with the 50k-SNP chip, although some subsets yielded slightly lower accuracies, and a few subsets even considerably lower accuracies . This demonstrates that a Gibbs chain based on 100,000 iterations with 50,000 as burn-in was sufficient for any of these analyses.To better understand the ability of the model to select variants in QTL regions across the different datasets, we made Manhattan plots for all Bayes factors greater than 1. First, we considered analyses based on 50k SNPs, merged data from 1060 to ~470,000 variants, or all 4,154,064 variants  complete LD is very important for applications of Bayesian genomic prediction models that explicitly estimate a SNP variance component using sequence data, since it may reduce the performance of these models. Based on our results, pruning within the subsets based on an LD threshold of 0.9 is recommended. Whether this threshold is sufficient can be easily monitored by checking the variance of the GEBV in the training data, where inflated values indicate impaired model performance and probably decreased prediction accuracy.Our results showed that the SAM Bayesian variable selection model provides a procedure to consider all sequence-based variants in the prediction model, while at least part of the analysis can be performed in parallel. At the same time, the performance of the model in terms of achieved effective sample size of the estimated SNP variance component was, within the subsets, reasonably similar to that of the analysis based on the 50k SNPs. However, for the merged datasets, increasing the number of included variants required an increasingly longer Gibbs chain to achieve the same effective sample size. The accuracy achieved based on the merged data was at best similar to that based on the 50k SNPs, and only slightly larger when the average GEBV across the subsets was used to predict the validation bulls.Results of simulation studies showed that the impact of using whole-genome sequence data on the accuracy of genomic prediction depends, at least partly, on the characteristics of the simulated data. Gains in accuracy were reported to be either large when causal variants had a low MAF  or the nUsing all variants, either simultaneously or by computing average GEBV across all subsets, resulted in GEBV that were considerably less biased than the 50k GEBV. The GEBV of the merged subsets were the most biased i.e. had the most inflated variance. These results can be explained as follows. Selection of variants and the subsequent prediction based on the merged dataset were both based on the same phenotypic data. Variants for which effects were overestimated in the first step, are more likely to be selected into the merged dataset, than other variants. As a result, estimated variant effects and estimation errors are correlated, and the effects of the selected variants will tend to be overestimated in the second step as well , which rn ≪ p problem, or because a more correct identification of the variants that have strong associations simply did not improve the prediction for the considered validation animals. These topics related to model performance will be discussed in the next section.Several reasons may explain the generally observed lack of improvement in prediction accuracy when using imputed sequence data: (1) impaired accuracy of imputed genotypes relative to e.g. 50k genotypes; (2) causal mutations may have a much lower MAF than most of the variants on commonly used SNP arrays, and may therefore be more easily filtered out of the data; and (3) imputation accuracy of sequence variants with a low MAF was shown to be, in general, poorer than that of common variants , 39, whiIn our study, the validation population consisted of animals from generations after those from which the training animals originated, e.g. 84 % of the validation animals had their sire included in the training dataset. If only the 341 validation bulls without their sire in the reference population were considered, similar results (not shown) were obtained, probably because this subset of bulls still had strong relationships with the reference population. The relatively strong relationships between validation and training animals may explain why there was no benefit from including e.g. the 1060 sequence-based variants that had a strong association to the traits in addition to the 50k SNPs, although the Bayes factors suggested that this particular analysis performed slightly better to detect loci that were strongly associated with the trait of interest. It should be noted that this scenario is very similar to the approach of Brøndum et al. , in whicn ≪ p problem when using whole-genome sequence data. On the one hand, our results clearly showed that reducing the number of variants based on the SAM approach resulted in a considerable increase in effective sample sizes of the Gibbs chain. On the other hand, given that the accuracies did not change when the Gibbs chain was increased from 100,000 to 300,000 samples and all 4,154,064 variants were included (results not shown), one can question the importance of the effective sample size of the SNP variance component when many variants in high LD are included in the model. In this case, there is probably a very large number of different sets of estimated variant effects that all yield very similar results in terms of GEBV.One of the specific aims of our application of the SAM approach, was to alleviate issues due to the severe The issue of high LD, which may extend across long distances and therefore over many variants, can be, at least partly, solved by preselecting variants. Attractive approaches to do this, are either to perform the SAM strategy proposed here, or a GWAS  across mIn conclusion, the SAM approach applied to whole-genome sequence data did not improve prediction accuracies in our study, probably because training and prediction took place within a single breed in which relationships between animals are high. This is also in agreement with the results of MacLeod et al. . NeverthOne of the features of variable selection models is that they propose a priori variances that lead to differential shrinkage across loci. Overall, the differences between any of the prediction models belonging to the so-called “Bayesian Alphabet” type , are dueAs the number of included variants increases, it may become necessary to adapt the model settings to the specific characteristics of the data. In the majority of the analyses, we considered a priori that 99.9 % of the variants of all the datasets had a small effect. In reality, this number may be quite different across the range of datasets considered. An alternative strategy is to assume that the absolute number of variants with a large effect remains the same regardless of the number of variants included, and to adapt ordingly . We testentclass1pt{minimaWhen using whole-genome sequence data, the level of LD between close variants is very high. After additional editing, the number of variants in the dataset decreased by 65 % by pruning for or lower . Anotheror lower , which mor lower .Our results confirmed that the SAM procedure combined with Bayesian variable selection models provided a procedure that can use whole-genome sequence in genomic prediction models while limiting the overall computing time. Assuming that all analyses of the split datasets can be performed in parallel, the total computation time was 124 h, i.e. 5 h for the split analysis and 119 h for the analysis of the merged data, considering the scenario in which 212,000 selected variants were included in the final analysis. The computing time increased linearly as the number of variants included increased, and as a result the analysis of all 4,154,064 variants with a Gibbs chain of 300,000 iterations took 111 days. Processing fewer variants simply results in less computation time for a single iteration of the Gibbs chain. At the same time, our results showed that pre-selection of variants leads to faster convergence, thus to decreased length of the Gibbs chain.We showed that the SAM approach, combined with the BSSVS model, was able to perform genomic prediction efficiently using whole-genome sequence data. Effectively, it splits one large computational task into many much smaller ones, and thereby makes use of parallel processing. As a result, the whole procedure can be completed in less than two days, considering that only a few thousand variants from the sequence data are included in the final merged dataset, instead of 111 days when all sequence-based variants are included simultaneously. If the average of the GEBV across subsets is used, with parallel processing of the analyses, computation time can be shortened to 5 h. In addition, the SAM procedure improved the mixing properties of the Gibbs chains in the analysis, simply by reducing the total number of variants included in any of the analyses. In particular, it is important to prune variants, within the subsets, that have complete or high levels of LD, i.e. for which


G × E in psychiatry may explain why environmental risk factors have big impact in some individuals but not in others, and conversely why relatives that are genetically at risk for disease do not all develop disease. Here we discuss two novel methods that use an aggregate genome-wide measure of genetic risk to detect G × E and estimate its effect in the population using data currently available and data we anticipate will be available in the near future. The first method exploits summary statistics from large-scale genome-wide association studies ignorant of the environmental conditions and detects G × E in an out-of-sample risk-profiling framework. The second method relies on larger samples and is based on a mixed linear model framework. It estimates variance explained directly from single nucleotide polymorphisms and environmental measures. Both methods have great potential to improve public health interventions focusing on risk-based screening that is informed by both genetic and environmental risk factors. The importance of gene-by-environment interaction (G × E) in psychiatry has intuitive appeal and is often discussed. However, the dearth of data to investigate G × E means that empirical evidence is modest. Here we consider how the era of genome-wide genotyping opens new approaches for G × E research. G × E in disease aetiology implies environmental factors control disease outcome conditional on genetic predisposition, and conversely, genetic factors control disease outcome conditional on environmental exposure. It explains why genetic and environmental factors can have a big impact in some individuals but not in others. G × E research aims to identify non-marginal genetic and environmental effects, that is, effects of a specific genetic  risk factor that does not act in the population as a whole when averaging over all other variables but only act conditional on an environmental (or genetic) variable.et al.Interpretation of G × E research requires careful consideration of the hypotheses tested, first recognising that presence of statistical interaction depends on – and may be induced by – the scale of measurement. In the past 15 years, the majority of G × E researches have used a molecular genetic approach focusing on candidate genes and specific environmental risk factors. Researchers hypothesised environmental factors controlled disease outcome only if a single genetic mutation was present . For complex genetic diseases including psychiatric disorders, the effect of a specific genetic variant is usually very small effect and hence the prior probability that a specific genetic variant interacts with a specific environmental factor is also very small. Therefore, the majority of published G × E studies have suffered from lack of replication, low-power, a publication bias towards positive results and major methodological concerns  promised new hope but early studies were also underpowered  but act more additively on a susceptibility to disease scale   can be used as proxy estimate of genetic effects in a G × E study in which individuals have both genome-wide genotypes and measures for environmental risk factors. GRPS are quantitative scores calculated for each individual and are an estimate of an individuals' genetic risk for disease. GRPS were first applied to schizophrenia GWAS data where they provided evidence for a substantial polygenic component to the risk of schizophrenia involving many loci of very small individual effect  from the GRPS sample (or ‘target sample’) are included in the discovery sample. GRPS are constructed in two steps: firstly, individual effect sizes of risk alleles  from linear-mixed models (Yang Y), the full logistic regression equation will be:G is the multi-locus GRPS, E is the environmental moderator variable and G × E is the interaction term between G and E. Under this model significant genetic and environmental effects already imply G × E on the disease (Y) scale, but a significant G × E term implies G × E on the underlying liability to disease. In this framework, multiple GRPS and multiple environmental factors can be included in the analyses to allow for hypothesis-driven identification of G × E effects. For example, GRPS can be based on SNPs that are selected based on functional annotation or physical position in the genome.The GRPS and the environmental variable of interest can now be included as individual terms as well as a product term in a risk-profiling framework. Fitting nested (increasingly more restricted) models allows testing for significance of the GRPS, the environmental factor of interest, and their interaction effect. For a disease trait  (2014)  shows that if individuals in independent target samples are ranked on GRPS then the odds of disease in the 10th decile is 7–20-fold (varying between samples) greater than the odds of disease in the first decile.et al.et al.A G × E application may consider, for example, neonatal vitamin D level  , g, ge and ε are vectors of length n of the aggregate effects of all the SNPs from all of the individuals, the genotype–environment interaction effects from all of the individuals, and the residual effects, respectively. The variance of y is the sum of the genetic variance, the interaction variance and the error variance. For example, when the environmental condition is binary, Ag is the genetic relationship matrix (GRM) estimated from all SNPs and elements in Age = Ag for all pairs of individuals sharing the same environment and elements in Age = 0 for the pairs of individuals in different environments.The estimation of variance explained by aggregate SNP effects, sometimes called SNP heritability (see the Introduction section) is based on a mixed linear model framework. In this framework, genetic variance is estimated from genetic similarity among pairs of individuals who are not related in the classical sense. The basic idea behind this method is that for a polygenic trait, pairs of individuals who show higher genetic similarity also show higher resemblance at the trait level. Genetic similarity for each pair of individuals  is measured from all the SNPs and the aggregated SNP effects are treated as random variables in a mixed linear model (Yang g) reflects the genetic variation that is captured by common SNPs and the estimate of the G × E effects (ge) reflects the proportion of the variance attributable to G × E. Through application of restricted maximum likelihood estimation (REML), the proportion of genetic and/or G × E variance to the total variance can be estimated. Significance of the parameters can be tested by likelihood ratio tests comparing the likelihood under the full and reduced models.The estimate of the aggregate SNP effects  is problematic, exacerbated by potentially different lifetime disease prevalences under the two environmental conditions, which may be unknown or difficult to estimate. We advise to use the bivariate approach to test for significance of the G × E term, rather than interpreting the estimates of SNP-heritability in the two environments, since the correlation is not affected by the ascertainment imposed on the disease in the two environments. A magnitude of the interaction variance can be estimated in the univariate mixed linear model. Analysis under both the univariate and bivariate G × E frameworks is recommended to gain further insight into the estimated interaction.Application of the mixed model method requires data sets in which all individuals are measured for genome-wide genotypes and the environmental risk factor. In large data sets the genetic and G × E terms can be partitioned by fitting multiple GRMs based on specific notations such as functional pathways, similar to fitting multiple GRPS × E interaction terms in the risk profiling framework.http://www.complextraitgenomics.com/software/gcta/)  ignorant of the environmental conditions. Since the dearth of data sets informative for both genetic and environmental measures has been a limiting factor in G × E research, the risk-profiling framework is likely to be more widely applied and allows statistical power to be leveraged from larger samples not measured for the environment. In the risk-profiling framework, identification of true interaction effects largely depends on the prediction accuracy of the genetic and environmental factors. Prediction accuracy of GRPS is driven by precision with which the individual SNP effects are estimated in the ‘discovery sample’ in which large sample size generates higher precision. Combined efforts in the psychiatric genetics community (PGC) have achieved 34 241 schizophrenia cases, and 45 604 controls in 2014 (2014) resulting in high precision of the estimation of individual SNP effects and consequently large prediction accuracy of the GRPS. Precision of the environmental measures largely depends on the measure of interest. By nature, some environmental variables are measured with greater precision  than others . Large discovery sample sizes and well-defined environmental variables in the target samples will increase precision and prediction accuracy in the risk-profiling framework. Interpretation of results must consider the likely representation of unmeasured environmental risk factors in the discovery sample.In both frameworks, the genetic architecture underlying the disease is a determinant in the statistical power of a study, this factor is however beyond our control. For example, larger sample sizes are required when common SNPs explain less variance , which can be due to, for example, common SNPs being not in sufficient linkage disequilibrium (LD) with the causal variants or total heritability being low. In the risk-profiling framework, prediction efficacy  depends on the sample size of the discovery sample whereas the ability to detect variance explained that is significantly larger than zero depends on the size of the target sample. The same applies to variance explained by G × E. When sufficient samples are available and the researcher can apply both methods, the mixed linear model framework is to be preferred. It estimates the variance explained directly from individual-level genotype data, accounting for the correlation structure between the SNPs.G × E studies that estimate genetic risk from genome-wide genotypes are in their early days since there are few data sets of sufficient size informative for both genetic and environmental factors. Much larger sample sizes, however, are expected to become available in the coming years allowing application of both frameworks to a wide variety of psychiatric diseases, either with direct measures of genetic risk and environment or through proxy-measures of both entities.n = 4304 individuals), Salvatore et al. (n = 1162). They also demonstrated interaction between the GRPS and two environmental factors: parental knowledge and peer deviance. Genetic factors related to alcohol problems were more pronounced under conditions of low parental knowledge and high peer deviance.Using genetic summary statistics on alcohol problems in young adults from the Avon Longitudinal Study of Parents and Children  in a sample of 2082 healthy individuals. This result does not exclude the possibility of a causal relationship but shows that at least part of the association between schizophrenia and cannabis use may be due to a shared genetic aetiology.When environmental measures are not available in a case-control sample, association between genetic factors underlying the disease and the potential environmental moderator can be studied in samples with healthy individuals. Power et al.  used GRP. et al., to explet al.et al.An approach to study G × E when measures on environmental risk factors are not directly available is to use epigenetic markers as proxies for the environment. Epigenetic markers associated with for example smoking behaviour  and was significantly different from zero but not from one. The results were not suggestive of G × E interaction and suggested that many schizophrenia risk alleles are shared across ethnic groups.An example of a G × E study in a linear mixed model framework is a bivariate analysis of schizophrenia in which the two traits represent two different populations: European and African descent . Augmenting these genetic risk predictors with environmental moderators should increase prediction accuracy. Diagnostic use of multi-locus genetic risk predictors is a long-term goal that might come closer once informed by environmental predictors. Real progress in G × E research requires concerted effort of collection of informative data sets.


Any inference concerning the significant hypotheses must account for the impact of the selection procedure itself, for otherwise the estimates will be hopelessly biased  shows comparatively little shrinkage under replication, due to the phenomenon that the winner's curse has little effect on hypotheses with extreme test statistics  portion to predict effect sizes for the ranked hypotheses. Similar procedures have been proposed , but our1.4.The analysis of a vector on rates  and genementclass2pt{minim2.The basic projack has several key elements: (i) construction of an 2.1.For many problems, the original data can be divided into an The projack approach works by performing split-sample analysis of a single matrix, and we construct an appropriate matrix as follows, using a kind of jackknife pseudo-value. Define the mentclass2pt{minim2.2.Due to ranking bias, re-ordered jackknife. We note that for the idealized data structure, and if the effect sizes are constant, i.e., Using a single held-out column for our prediction is inefficient, so we proceed by performing the re-ordering procedure for each mentclass2pt{minim2.3.projack, for Prediction by Re-Ordered Jackknife and Cross-Validation, The re-ordered jackknife has only slight bias, as each of the re-orderings is based on mentclass2pt{minim2.4.We propose a choice of not shrink outlying values, as these values largely maintain their original ranks in the re-ordered jackknife. Simulations for Figure } Figure . In summ2.5.Here we illustrate the difficulty in providing unbiased rank effect estimates by analyzing null GWAS data. We used simulated association data using genotypes from the HapMap JPT3.For a number of problems, a single vector of This algorithm for the independent projack is not immediately obvious, and results from a consideration of a hypothetical matrix We recommend performing the simulations at least 1000 times, in order to minimize stochastic variation. Each simulation step of the independent projack corresponds to a single random 3.1.We return to the psoriasis example described in Section 1, using the independent projack and competing methods. For the independent projack, we augmented 3.2.Here we decribe additional simulations, using 875 samples from the 1000 Genomes project, as described in For genotype data, due to the presence of linkage disequilibrium, SNPs nearby the causal SNPs will also exhibit association with the trait. For causal SNP Figure entclass1pt{minimaentclass1pt{minima4.We have attempted to describe the important aspects of the ranked estimation problem. Our proposed solution is a frequentist general resampling method for prediction of ranked effects and estimation of normal means, without explicit smoothing or Bayesian inference. The projack is ready to be used as a low-bias estimator/predictor of ranked effects in large-scale multiple testing settings. Further work remains in fully understanding the tradeoffs between bias and variance, although choices of 5.This study is supported in part by NIH R01MH101819 and NSF DMS-1127914. Funding to pay the Open Access publication charges for this article was provided by institutional funds at North Carolina State University.Supplementary DataClick here for additional data file.Supplementary DataClick here for additional data file.


We estimated the proportion of h2 captured by common SNPs for DILI to be between 0.3 and 0.5. For co-amoxiclav induced DILI, chromosome 6 explained part of the heritability, indicating additional contributions from common variants yet to be found. We performed simulations to assess the robustness of the h2 estimate with limited sample size under low prevelance, a condition typical to studies on idiosyncratic pharmacological traits. Our findings suggest that common variants outside of HLA contribute to DILI susceptability; therefore, it is valuable to conduct further GWAS with expanded case collection.Recent genome-wide association studies identified certain human leukocyote antigen (HLA) alleles as the major risk factors of drug-induced liver injuries (DILI). While these alleles often cause large relative risk, their predictive values are quite low due to low prevalence of idiosyncratic DILI. Finding additional risk factors is important for precision medicine. However, optimal design of further genetic studies is hindered by uncertain overall heritability of DILI. This is a common problem for low-prevalence pharmacological traits, since it is difficult to obtain clinical outcome data in families. Here we estimated the heritability ( Given the relatively small sample sizes obtainable in pharmacogenetic studiesWhile there are some successes identifying major risk factors of DILI , no SNPs were identified in DILI across all drugs, nor have any been validated when flucloxacillin and coamoxiclav are excluded in this collection. This is likely due to limited power of detecting modest SNP effects with the relatively small cohort size. Understanding the heritability of these conditions is one step toward understanding genetic architecture of pharmacogenomic risk, and may provide valuable information for designing future studies.Genome-wide association studies (GWAS) usually assume that common diseases are attributable to allelic variants present in more than 1–5% of the populationThis approach is particularly attractive to apply in the context of pharmacogenomics studies, where ascertainment of family data is difficult or even impossible. Given the implicit assumption that adverse drug reactions (ADRs) are subject to substantial genetic control in pharmacogenomics studies, it is important to present evidence of the size of the genetic component (or heritability) for the trait under investigation.Heritability estimates for complex traits are typically determined through twin studies. However, these approaches have limited utility in the context of susceptibility to ADRsh2 captured by all genome-wide common SNPs, chromosome 6 genome-wide SNPs and genome-wide SNPs without chromosome 6 for DILI. Results for liver injuries induced by co-amoxiclav and flucloxacillin are summarized in h2all = 0.48 ± 0.313, h2chr6 = 0.478 ± 0.076, h2NOchr6 = 0.18 ± 0.40). Whereas with co-amoxiclav induced DILI patients, chromosome 6 explained part of the heritability , indicating contributions from additional common variants are yet to be found. Estimates for h2 may be underestimated due to GCTA algorithm constraints so that SNP-heritability on the observed scale could not be greater than 1. Even so, this finding suggests that continuous collection of DILI cases is valuable for the potential of discovering additional associations with common genetic variants.We estimated the proportion of h2 captured by common SNPs for T1D to be, on average, 0.51 ± 0.23 with a sample size of 75 and 0.46 ± 0.15 with a sample size of 200. These estimates are similar to estimations made with the entire dataset of 1963 cases and 2938 controls . Moreover, estimates calculated from sample sizes of 75 and 200 cases gave similar results, with both indicating that chromosome 6 explains part of the heritability (the h2chr6 estimate is 0.19 ± 0.15 with 75 cases and 0.12 ± 0.058 with 200 cases). For a sample size of 75, however, the standard deviation for our h2chr6 estimate is close to the mean. This indicates that calculations are not stable with smaller sample sizes, underscoring the uncertainty about flucloxacillin-induced DILI. Estimates for h2chr6 calculated using this particular T1D dataset may also be underestimated due to inadequate SNP density in the MHC region in this particular data set.The heritability of T1D is estimated from pedigree studies to be 0.9999h2 is 0 for both flucloxacillin induced and co-amoxiclav induced DILI controls coded as cases. Results are summarized in Lastly, we observe that the estimated While further investigation is required to confirm the robustness of the GCTA algorithm for low prevalence traits such as DILI, this work highlights the potential value of its application. Here we were able to apply the algorithm to investigate the contribution of common variants on the chromosome level. Such investigations can provide insight into disease mechanism and into inter-individual variation. Moreover, for ADRs in particular, we are able to provide previously unobtainable estimates of heritability. Such estimates will help optimize designs of future studies for identifying additional genetic contributions to these conditions.Findings suggest that collecting and genotyping more co-amoxiclav induced DILI cases is valuable for discovering additional associations. While further investigation is required to confirm the robustness of the GCTA algorithm for low prevalence traits like DILI, this work highlights the potential value of its application. Particularly for pharmacological traits, we can provide previously unobtainable estimates of heritability. Such estimates will help optimize designs for future studies.DILI datasets were from case-control studies of individuals taking flucloxacillin (77 cases and 288 population controls)2h2 captured by common SNPs for DILI. We also assessed the robustness of the GCTA algorithm with datasets of moderate sample sizes and low prevalence.The GCTA algorithm measures the effect of common variants with genome-wide SNP data using a mixed model approachh2 from iSAEC DILI genome-wide data , chromosome 6 data, and genome-wide data without chromosome 6. We also estimated h2 for all individuals (co-amoxiclav or flucloxacillin induced DILI), for individuals with co-amoxiclav induced DILI, and for individuals with flucloxacillin induced DILI. For individuals with co-amoxiclav induced DILI we evaluated northwest Europeans only and southern Europeans both together and separately. All analyses were performed separately. For each population and dataset, unless otherwise noted, we calculated h2 adjusting for prediction errors due to global structure and local structure. We used principal components analysis (PCA) to adjust for prediction errors due to global structure. Two principal components were included as regression covariates in the mixed model. We also used an optional functionality of the GCTA tool to adjust for prediction errors due to imperfect linkage disequilibrium. All analyses were performed for DILI prevalence estimated to be 0.00012We used the GCTA algorithm to estimate h2 for subsets of cases and controls from a Type I Diabetes (T1D) dataset. We choose to use a T1D because the histocompatibility complex (MHC) region on chromosome 6 has major genetic contribution to risks of both DILI11h2 from genome-wide data , chromosome 6 data, and genome-wide data without chromosome 6 for cases and controls with a 1:3 ratio, where the number of cases were 75 and 200 to reflect sample sizes similar to iSAEC DILI sample sizes. Estimates for h2 were averaged over twenty random selections of cases and controls for these sample sizes. The prevalence of T1D is estimated to be 0.008 h2 estimates. We also report h2 estimates and standard errors with the full WTCCC T1D dataset and the GCTA parameter for prevalence set at 0.0005 and 0.008. Given the WTCCC data were collected from a homogenous population, however, we do not adjust for prediction errors due to global structure.To evaluate the robustness of the GCTA algorithm with datasets of moderate sample sizes, we conducted a positive control and negative control experiment. We performed simulations for our positive control experiment. Simulations involved estimating h2 for DILI controls coded as cases with WTCCC controls. This analysis was performed with northwestern European controls from the flucloxacillinin induced and co-amoxiclav induced DILI datasets. The prevalence of DILI was set to be 0.0005.For a negative control experiment we tested for measurement errors by estimating C.L.O. and Y.S. designed the study, analyzed and interpreted the data, and wrote the manuscript. C.L.O. performed the experiments. G.H. interpreted the data and critically revised the manuscript for important content. All authors approved the final version of the manuscript.