Variation in environment, management practices, nutrition or selection objectives has led to a variety of different choices being made in the use of genetic material between countries. Differences in genome-level homozygosity between countries may give rise to regions that result in inbreeding depression to differ. The objective of this study was to characterize regions that have an impact on a runs of homozygosity (ROH) metric and estimate their association with the additive genetic effect of milk (MY), fat (FY) and protein yield (PY) and calving interval (CI) using Australia (AU) and United States (US) Jersey cows.n = 6751 US; n = 3974 AU) and CI  were used in a two-stage analysis. A ROH statistic (ROH4Mb), which counts the frequency of a SNP being in a ROH of at least 4 Mb was calculated across the genome. In the first stage, residuals were obtained from a model that accounted for the portion explained by the estimated breeding value. In the second stage, these residuals were regressed on ROH4Mb using a single marker regression model and a gradient boosted machine (GBM) algorithm. The relationship between the additive and ROH4Mb of a region was characterized based on the (co)variance of 500 kb estimated genomic breeding values derived from a Bayesian LASSO analysis. Phenotypes to determine ROH4Mb and additive effects were residuals from the two-stage approach and yield deviations, respectively.Genotyped cows with phenotypes on MY, FY and PY  was found for CI and ROH4Mb for the US population. Multiple potential epistatic interactions were characterized based on the GBM analysis. Lastly, the covariance sign between ROH4Mb and additive SNP effect of a region was heterogeneous across the genome.We identified multiple genomic regions associated with ROH4Mb in US and AU Jersey females. The covariance of regions impacting ROH4Mb and the additive genetic effect were positive and negative, which provides evidence that the homozygosity effect is location dependent.The online version of this article (doi:10.1186/s12864-015-2001-7) contains supplementary material, which is available to authorized users. An individual’s inbreeding coefficient is defined as the probability that any randomly chosen allele at a homologous locus carried by the individual is identical-by-descent (IBD) and equals the coancestry between its parents , 2. FollHigh levels of inbreeding result in a reduction in fitness and overall performance at the phenotypic level, due to individuals carrying a large number of deleterious recessive mutations and/or the reduction in frequency of the superior heterozygotes . This reLonger ROH segments (>5 Megabases (Mb)) instead of short (> 0.5 Mb) and moderate (> 1.5 Mb) segments have been shown by simulation to have a higher correlation with the homozygous mutation load when the effective populations size is low  . This haCharacterizing the homozygosity across the genome and its impact on inbreeding depression in dairy cattle is advantageous due to the large number of cows that are currently being genotyped and the large number of fitness (e.g. fertility) and performance (e.g. milk yield) traits being measured. Specifically, characterizing these regions with the Jersey breed is worthwhile given the higher levels of inbreeding and smaller effective population size when compared to the Holstein breed , 22. Then = 6751 US; n = 3974 AU) and an increased calving interval , which is the interval between consecutive calvings and a measure directly linked to fertility. Phenotypic information for the AU population was provided in the form of yield deviations and equivalent variable for US population were calculated after adjusting their phenotypes (e.g. Milk yield) for fixed effects. The ROH status of a SNP  was defined based on whether the SNP was within an ROH of at least 4 Mb in length (ROH4Mb). A two-stage analysis was performed within each population to estimate the effect of the ROH4Mb status of a SNP on milk yield and fertility traits. The first stage involved generating residuals from an animal model that accounted for the additive effects captured by the estimated breeding value (EBV) of the individual. The second stage involved using the residuals from the first stage as a phenotype and regress these on the ROH4Mb status utilizing a single marker regression and gradient boosted machine (GBM). Significance was declared by using a permutation test based on 2500 samples [n = 2,500 samples) [Two cow populations born in the US and AU were utilized to identify regions that when homozygous cause a reduction in milk (MY), fat (FY) and protein yield  .Fig. 1AnThe single marker regression and GBM analysis identified multiple regions that have a significant effect when contained within a ROH of at least 4 Mb across multiple traits and populations. A complete list of the regions along with their significance level is outlined in Table Multiple regions of the genome were found to display potential interactions based on their frequency as descendent pairs. A complete list is outlined in Table We further characterized the relationship between the additive and ROH4Mb effects of a SNP. Estimates of the additive marker effect of each SNP were obtained using a whole genome marker regression on the yield deviations, using the Bayesian LASSO of Park and Casella . The ROHThe relationship between the additive effect, ROH4Mb effect and their covariance is outlined for MY in Figs. A single marker regression and an ensemble learning method, GBM, were utilized in the current analysis to characterize regions that have an impact on inbreeding depression based on a ROH metric. In order to determine how similar the results were for the single marker regression and GBM analysis, a rank correlation based on SNP used across both analysis was estimated within each trait and population. The variables utilized in the correlation were the significance value for single marker regression and the variable importance score for GBM. The rank correlation across traits and population ranged from 0.48 to 0.65. A rank correlation of less than unity is not surprising given that the importance score from the GBM analysis captures both the ROH4Mb effect of the SNP and its epistatic interactions with all other SNP.There were no regions in common across the USA and AU populations that had a significant impact on inbreeding depression. Interbull correlations  of EBVs p-value across all SNP for the US population was below 0.1 for 10 out of 15 SNP (66.7 %), although only 3 SNP would be significant at the 0.05 level based on the Bonferroni multiple correction factor. In our analysis, the residuals from the 2 stage analysis were corrected for the individuals’ EBV. It is worth noting though that some of the residual may still contain an additive genetic component, thus creating a partial confounding in subsequent analyses. The average accuracy of the estimated breeding values (EBV) in our data was 0.76 and 0.42 for PY and CI, suggesting that the EBV correction does provide a reasonably good measure of the additive breeding value of the individual. In order to confirm that additive effects from SNP information were not within the residual from the two-stage analysis, the correlation between yield deviations that were corrected for the additive SNP effects estimated from the LASSO model and the residual from the two-stage were computed for the US population. The correlations between the two measures for protein yield and calving interval was 0.94 and 0.99 and is displayed graphically in Additional file In order to determine if regions obtained from the two-stage analysis show some degree of dominance using the actual (raw or unadjusted) phenotype an estimate of the additive and dominance effect of SNP declared as being significant were estimated. Actual phenotypes were only available for the US dataset and therefore only SNP that were declared significant within the US population were utilized. The dominance The animals used in the study had multiple production records and therefore the regions characterized in the currently study result in a reduction in performance and/or fitness of the animal, but are not lethal or individually do not have a large impact on fitness. Furthermore, individuals that are homozygous in these regions actually have a chance of being allowed to stay in a herd, unlike when lethal or large effect mutations exist, due to the animal having a small likelihood of being born alive. Furthermore, it has been argued that the ability for a population to purge deleterious homozygous mutations is greater for large effect and/or lethal mutations and is not as effective for mutations with minor effects . From thWe identified regions with a putative multiplicative effect for all traits. A further network analysis was able to identify networks shared between two interacting SNP. The existence of ROH4Mb by ROH4Mb interaction between two loci would generate non-linear epistasis in the form of diminishing  or reinforcing  epistasis . A few rGHR), which has been associated with milk yield and composition [The relationship between the additive and ROH4Mb effects based on their GEBV covariance was characterized across the genome for multiple traits. The regions on BTA3 (47.25–54.15Mb), BTA7 (24.26 – 49.00Mb), BTA20 (23.71–34.98Mb) and BTA26 (9.34 – 20.71Mb) have been previously found to be under positive directional selection , 28–32. position  and has position , 30. TheWith the current study we have shown that regions that impact inbreeding depression are variable across populations. The causes of this heterogeneity are manifold: potential lack of power, from a different number of founder individuals, to varying numbers of influential sires in the previous generations, different mating programs or selective goals over time. Interestingly in the current study the majority of the regions identified were at a low frequency. This is important since the power to estimate effects when the frequency of the region is low is reduced and most regions of small effects would be missed by only using a single population. Due to this, a population may not show an effect based on the current set of animals utilized, but over time the frequency may increase and the power will be sufficient to estimate it. Therefore if a region has been shown to be sensitive to long stretches of homozygosity in other populations then long stretches of homozygosity in a population under study should be further investigated. This is also one of the primary limitations of using medium density genomic data, given that the majority of variants impacting inbreeding depression are probably carried at low frequency and these would be in low LD with the ones used in SNP assays. Nevertheless, identifying regions across multiple countries capitalize on the fact the ROH regions differ across populations as confirmed by Howard et al.  using tha priori knowledge on the impact of a region when it is contained within a long stretch of homozygosity can be utilized in mating schemes in order to constrain homozygosity at specific regions while allowing homozygosity at other regions. Previous research has used methods that constrain relationships averaged across the genome [Furthermore, the e genome –38, althGenomic regions across multiple traits were found to be associated with ROH4Mb on BTA13, BTA23 and BTA25 for the US population and BTA3, BTA7, BTA17 for the AU population. Furthermore, multiple potential epistatic interactions were characterized. The regions on BTA3, BTA7, BTA20 and BTA26 displayed a large positive covariance between the ROH4Mb and the SNP effect and these regions have been previously found in signatures of selection studies. This provides evidence that the effect of a region being homozygous is dependent on the genomic location. Future work should investigate the effectiveness of incorporating location specific inbreeding effect into mating designs using simulated and real data.No animal care approval was required for the present manuscript because all records came from field data. Phenotype and pedigree information on US Jersey and AU Jersey cows were provided by the American Jersey Cattle Association  and the Australian Dairy Herd Improvement Scheme , respectively. For the US dataset, the phenotypes used were the same in both populations and included standardized 305 day lactation milk (MY), fat (FY) and protein yield (PY) and calving interval . For the AU dataset, yield deviations were already estimated and in order to make comparisons similar yield deviations were constructed for the US population that was based on the same model using ASReml , as outlijklm = μ + HYSi + parityj + monthk + age + eijklm (Model 1)yijklm refers to either standardized MY, FY, PY, or CI, μ is the intercept, HYSi is the fixed effect of herd-year-season of calving, parityj was the fixed effect of parity, monthk was the fixed effect of month of calving, and age was the regression of age at first calf. Residuals were the only random effects in the model. For cows with multiple lactation records, the average of yield deviations generated from Model 1 were used. Yield deviations were standardized to have a mean of 0 and a variance of 1 to ensure that the results were not affected by systematic differences between the two populations.where yn = 8235) and AU Jersey cows (n = 4075) were provided the American Jersey Cattle Association  and the Australian Dairy Herd Improvement Scheme , respectively. A complete description of the SNP panels used and SNP editing is outlined by Howard et al. [2) of less than 97.5 % were removed. The SNP that passed quality control and were in common across the two populations  were used for the analysis.Genotypic information on US Jersey cows  and CI  were used.Across both stages, only animals that had both phenotypic and genotypic information for milk production traits , with A representing the additive relationship matrix derived from a pedigree that traced back at least 4 generations. The pedigree was constructed based on a recursive algorithm to compute the inverse of A assuming a non-inbred population [A was based on section 4.3 in Henderson [D  to take on only three values A was constructed based on the Meuwissen and Luo [ijk, was weighted by wijk for the kth individual according to Garrick et al. [ijk was:where ypulation . The algenderson , which a and Luo  algorithk et al.  to accouh2 refers to the heritability, r2 refers to the repeatability and l refers to the number of records. The h2 and r2 values used for all three milk yield traits were 0.25 and 0.43, respectively. The h2 and r2 values used for CI were 0.08 and 0.17, respectively.where A single marker regression approach was applied using the following model:ij = μ + ROH4Mbj + eij (Model 3)yij refers to the yield deviation for MY, FY, PY, or CI and μ is the intercept, ROH4Mbj is the ROH4Mb status for SNPj and eij is the random residual. One of the drawbacks with GWAS is deriving the correct threshold to use, so that the number of false positives arising through multiple testing is minimized. Our approach was to use a permutation test to empirically derive a statistical threshold and consequently reduce the number of false-positives due to multiple hypotheses being tested [where yg tested . A permuMachine learning algorithms such as gradient boosting machines (GBM) that generate a decision tree provide a convenient and computationally efficient way to explore high order interactions. We used GBM to explore the degree of ROH4Mb by ROH4Mb interaction that occurs across traits. The GBM algorithm, which was introduced by Friedman , produceIn the current study, the “gbm” R package  was usedThe identification of epistatic interactions between the ROH4Mb status of a SNP was carried out using the methodology outlined by Yao et al. . Based on = 2,500 samples) [The significance of the frequency of a descendent pair and variable importance value was declared based on a permutation test (samples) . Within In order to determine the relationship across the genome for the additive genetic effect and ROH4Mb status, the Bayesian LASSO of Park and Casella  was usedP-value < 0.001) SNP based on the single marker regression and had a significant SNP-by-SNP interaction for the GBM analysis were investigated further using cow positional candidate genes using Bos Taurus assembly  for functional characterization. Candidate genes were chosen based on their location relative to the SNP with the largest significance. Furthermore, a gene network work analysis was undertaken using GeneMANIA [Regions that had contiguous significant (eneMANIA  in order


Genome-wide linkage studies have identified the 9q22 chromosomal region as linked with colorectal cancer (CRC) predisposition. A candidate gene in this region is transforming growth factor β receptor 1 (TGFBR1). Investigation of TGFBR1 has focused on the common genetic variant rs11466445, a short exonic deletion of nine base pairs which results in truncation of a stretch of nine alanine residues to six alanine residues in the gene product. While the six alanine (*6A) allele has been reported to be associated with increased risk of CRC in some population based study groups this association remains the subject of robust debate. To date, reports have been limited to population-based case–control association studies, or case–control studies of CRC families selecting one affected individual per family. No study has yet taken advantage of all the genetic information provided by multiplex CRC families.We have tested for an association between rs11466445 and risk of CRC using several family-based statistical tests in a new study group comprising members of non-syndromic high risk CRC families sourced from three familial cancer centres, two in Australia and one in Spain.QLS; p = 0.41).We report a finding of a nominally significant result using the pedigree-based association test approach , while other family-based tests were non-significant, but with a p-value <; 0.10 in each instance. These other tests included the Generalised Disequilibrium Test , parent of origin GDT Generalised Disequilibrium Test  and empirical Family-Based Association Test . Related-person case–control testing using the “More Powerful” Quasi-Likelihood Score Test did not provide any evidence for association (MTGFBR1*6A allele and CRC risk in these families. The weak support for an increase in risk in CRC predisposed families is in agreement with recent meta-analyses of case–control studies, which estimate only a modest increase in sporadic CRC risk among 6*A allele carriers.After conservatively taking into account considerations for multiple hypothesis testing, we find little evidence for an association between the  PTCH1, XPA, GALNT12 and TGFBR1[TGFBR1 , but with largely inconclusive results [Several genome-wide studies -3 have pnd TGFBR1. Follow  results -7.TGFBR1) gene is an attractive candidate as TGF-β signalling plays an important role in the control of a range of biological functions associated with colon carcinogenesis including tissue homeostasis, angiogenesis, inflammation, proliferation and cellular differentiation and has and has also been implicated in both the suppression and promotion of CRC , contains a deletion of three GCG triplets from the sequence of exon 1, resulting in the expression of a mutant receptor protein with six consecutive alanine (TGFBR1*6A) rather than nine consecutive alanine (TGFBR1*9A) residues. This is a hypomorphic mutation encoding a TGFBR1 variant protein with reduced TGF-β growth inhibition-signalling activity. The TGFBR1*6A allele has been proposed to act as a low-penetrance susceptibility allele for a number of malignancies [TGFBR1 allelic expression. Allele specific expression (ASE) of TGFBR1 in peripheral blood lymphocytes has been observed, with decreased expression associated with the *6A allele and two other SNPs in linkage disequilibrium [The transforming growth factor β receptor type 1  negative disease [Although some studies have suggested that the l cancer ,8,11, mol cancer -17. A rel cancer . A furthl cancer . One of l cancer . In the l cancer ,20. In b disease .TGFBR1*6A with hereditary CRC using any family-based association test (FBAT) [There have been no reports to date that have explored the likelihood of an association of t (FBAT) -24, or ft (FBAT) . The famt (FBAT) , as the t (FBAT) . It is at (FBAT) .TGFBR1 locus. We genotyped an expanded set of families for rs11466445 and used FBATs and the “More Powerful” Quasi-Likelihood Score Test (MQLS) to test for association with diagnosis of colorectal neoplasia . We report that after applying several family-based association tests we only found a nominally significant result using the PBAT rapid algorithm (p = 0.028), with another three FBAT algorithms all non-significant, but each yielding a p-value <; 0.10. There was no evidence of an association using the MQLS case–control model (p = 0.41).We recently completed a new genome-wide linkage study  using noThe study was reviewed and approved by the Human Research Ethics Committees of the three participating centres: Flinders Medical Centre, Adelaide, The Royal Melbourne Hospital, Melbourne and Institut Català d’Oncologia, Barcelona, with informed consent obtained from all participants.A total of 414 individuals , from 146 CRC families were recruited from clinics in Melbourne, Adelaide and Barcelona and informed consent was obtained from all participants. We restricted our study to non-syndromic high risk CRC families, defined as those containing at least one affected person who has one or more first-degree affected relatives and where the known causal mutations had been excluded. In each case, the diagnosis was confirmed by medical and pathology reports. FAP and MUTYH were excluded clinically and HNPCC or Lynch syndrome was excluded by testing for microsatellite instability (MSI) (as measured by tumour-associated length variation in microsatellites BAT-25 and BAT-26) and/or immunohistochemistry indicating loss of hMLHI, hMSH2, hMSH6 and hPMS2 encoded proteins. Affected status was defined as diagnosis with either colorectal adenocarcinoma (CA) or one or more advanced adenomas (AA), where AA was defined as three or more synchronous or metachronous adenomas and/or adenoma (s) with villous morphology, and/or with severe dysplasia, and/or diameter ≥ 10 mm. Diagnoses were confirmed by pathology reports.Unaffected individuals were family members who were either over 70 years of age with no history of CA or AA or were 50 years of age or older and had, within the last 5 years, recorded a colonoscopy result negative for neoplasia. As the age of onset is fairly late with a mean age of onset is 55.4 years Table , the cohTGFBR1 rs11466445 variant status was determined by PCR amplification using primers Fwd 5’-GAGGCGAGGTTTGCTGGGGTGAGG-3’ and Rev 5’-CATGTTTGAGAAAGAGCAGGAGCG-3’. PCR amplification was performed in a 25 μL reaction containing 50 ng genomic DNA using the Platinum Taq DNA polymerase with the addition of 3 × enhancer solution and followed the manufacturer’s protocol for GC-rich fragments (Invitrogen). Amplified fragments were separated by electrophoresis on a 10% polyacrylamide gel (Biorad) post-stained with gel-red (Jomar Diagnostics). Genotypes were assigned according to fragment sizes. A product size of 121 bp corresponded to the most common allele, *9A, whereas a product size of 112 bp corresponded to the *6A allele  was used [QLS, an improvement on the quasi-likelihood score test WQLS[QLS can incorporate unaffected controls and controls of unknown affection state. It also makes use of the affection state of relatives with missing genotype data by using their affection status to weight the family. The rationale being that an affected person who has additional affected relatives is more likely to be carrying a genetic predisposition.For case–control testing the “More Powerful” Quasi-Likelihood Score Test  LOD score is 0.293. By using IBD information it is possible to control for linkage using the GDT. Unlike the FBATs, the MQLS case–control test does not control for linkage and allows both linkage and association to contribute to the test statistic.The use of null hypotheses of “linkage and no association” in the FBAT and PBAT software was conservative. While the families show genetic linkage with cancer diagnosis in a region of chromosome 9  with a 1-LOD support interval of ~127.97–140.0 Mb [We found 315, 95 and four people to be homozygous for the rs11466445 *9A allele, heterozygous and homozygous for the *6A allele, respectively, with a *6A allele frequency (AF) of 0.124. The four people carrying the *6A/*6A genotype were dispersed across two families, each having one discordant pair . An exact test found the genotype to be in Hardy-Weinberg equilibrium  and there were no observed Mendelian inconsistencies. The allele frequencies of the *6A allele in the affected and unaffected family members  were slightly higher than observed in a case–control British study of hereditary CRC  .In the first instance, we tested for an association with colorectal neoplasia using the Generalised Disequilibrium Test (GDT). Given the large differences in pedigree sizes in this present study and the high number of possible intra-pedigree discordant pairings between genotyped people, the generalised relative pairs weighted by family size approach implemented by the GDT software, provides a good fit with the data. One caveat of using discordant pairs, however, is that in complex disease some people inheriting a risk allele do not develop the disease, or develop it rather late in life and this needs to be taken into account. As some of the pedigrees are multi-generational, we used inheritance by descent (IBD) data to inform the GDT analysis. Testing for association between the rs11466445 *6A allele and colorectal neoplasia in 208 discordant relative pairs by the GDT algorithm produces a p-value of 0.085  and ignore unaffected sibling data. This parent of origin test for the 15 parent–child pairs in the study was consistent with the full GDT result  with a null hypothesis of linkage and no association, with robust sandwich variance estimates (Table QLS) which accounts for relatedness between subjects using a corrected variance. Unlike the FBATs, the MQLS can make use of the genotyping information of the 24 singletons in the study and can use the people with unknown affection status as controls. The result was insignificant (Table QLS is not robust to population heterogeneity and will inflate type I error rates (the incorrect rejection of a true null hypothesis) in instances of population stratification. Given the convincingly non-significant result we did not investigate this further.We used the “More Powerful” Quasi-Likelihood Score Test .Testing with the rapid PBAT algorithm gave a nominally significant result under an additive genetic model (p = 0.028). Under the GDT, GDT-PO and FBAT approaches we did not find a significant association, but all the p-values were consistently borderline, with p-values <; 0.10. Unlike the FBAT approaches, we found no evidence of an association using MThe differences in p-values between the methods, under the same hypotheses and genetic models are due to the formulation of the test and also the treatment of family structures, which leads to differences in groupings informative for the test statistic.The GDT, a robust generalisation of the intuitively simple transmission-disequilibrium test (TDT), examines transmission disequilibrium between pairs of discordant relatives. The variant GDT-PO test, considers only parent–child discordant pairs. As relatively few parent–child pairs were genotyped in this study, the test will have much reduced power. However, given the age of the parents, the result should be more robust to misspecification of phenotype. The FBAT and PBAT algorithms are highly related and examine transmission disequilibrium from parents to affected offspring.TGFBR1 alleles and having affected offspring. The use of only affected offspring in the association statistic makes it robust to phenotype misspecification of affected people as unaffected. In the case of a missing parent, or parents, the test conditions on the sufficient statistic for the genotype distribution in each family; where a parent genotype is expressed as a set of likelihoods conditioned upon known offspring genotype(s). The design of the FBAT necessitates that extended pedigrees are split into nuclear families, which can introduce bias due to correlation. The FBAT also requires specification of the genetic model. The PBAT rapid algorithm differs from FBAT in that extended pedigrees are broken up into clusters of trios who share the same parents. The rapid algorithm in PBAT tests only the minor alleles and offers the ability to generate p-values using a robust Monte Carlo permutation based method instead of the asymptotic Normal distribution [QLS test is very different to the others, and is a regression model rather than a family-based association test. It considers both within- and between-family associations using a linear regression of genotypes on affection status with correlations for relatedness modelled as a kinship coefficient random effect.For the FBAT statistic, informative families are those with at least one parent heterozygous for the two ribution . It alsoThe closeness in p-values between all the family-based methods demonstrates the finding is not particularly sensitive to different assumptions underpinning these various algorithms. More broadly, given the difference in informative pairs/families in each FBAT method and nature of the algorithm, the general agreement across methods suggests this marginal evidence of an association is not a spurious result.However, the nominally significant PBAT result should perhaps be treated with some caution. While the p-value was generated using a robust empirical Monte-Carlo based method, it is possible the partitioning of people into clusters of trios may inflate type I error. As the 22 informative nuclear families are broken into 26 informative clusters of trios, there is a degree of correlation between some clusters that is unaccounted for by the approach. Conversely, there is reason to think that such correlation may not greatly influence the p-value. The similarity in p-values between the GDT and the FBAT, which also splits extended pedigrees, suggests the difference in handling of extended pedigree structure between the methods did not overly affect the association test result in this instance.In essence, a method (PBAT) which examines transmission to affected relatives but breaks pedigrees up for computational reasons is significant, while a method (GDT) that examines discordant relative pairs that does not adjust pedigree structure is non-significant. It is unclear how the different pairings or pedigree structure between these methods is contributing to the difference in p-value. In simulations, the GDT test was found to have more power over the FBAT in the majority of nuclear family and extended pedigree structures tested . HoweverOnly one SNP was tested for association with CRC, however, the genotype data was reformulated into several tests and genetic models with different treatment of the genotype data and family structures. Correction for these multiple tests can be applied, but such correction assumes independence of the tests. As these tests are very dependent, such a correction is highly conservative. Given the number of tests made of this single hypothesis, the PBAT association will become non-significant after correction for multiple tests.All reported association studies of rs11466445 have been of a case–control design . Even stTGFBR1 *6A allele to be significantly associated with CRC while the latter did not. The authors of a recent review considering the *6A allele association and ASE studies together concluded that the effect of the allele on CRC predisposition is, at best, very subtle [Collectively, current evidence suggests the *6A allele is a relatively minor contributor to CRC prevalence. A modest 12% and 8.5% increase in CRC risk, respectively, was found by two meta-analyses across large populations ,19. The y subtle .TGFBR1 locus, suggests that rs11466445 does not contribute significantly to the collective genetic predisposition towards CRC in these families.Our finding here of little evidence for an association with 6*A in CRC predisposed families supports the conclusions of recent meta-analyses and a review, which find the effect of the 6*A allele on CRC risk is modest. This weak evidence for association, together with the modest linkage signal in the region of the QLS: “More Powerful” quasi-likelihood score test; MSI: Microsatellite instability; PBAT: Pedigree-based association test; QLS: Quasi-likelihood score.6*A: Six alanine allele; AA: Advanced adenoma; ASE: Allele specific expression; CA: Colorectal adenocarcinoma; CRC: Colorectal cancer; FBAT: Family-based association test; GDT: Generalised disequilibrium test; GDT-PO: Parent of origin generalised disequilibrium test; HNPCC: Hereditary non-polyposis colorectal cancer; IBD: Identity-by- descent; MThe authors declare that they have no competing interests.LJL performed all the genotyping and experimental lab work, prepared data for analysis and helped with the manuscript; GSB performed experimental lab work; JPR, BT and IWS analysed the data; GPY, FM, IB and GC coordinated the original collection of the samples. JPR, BT and GNH wrote the manuscript; TJL contributed programme support and insightful critique; GNH conceived and designed the current study. All authors participated in data interpretation and critical revision of the manuscript. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2407/14/475/prepub


Using the whole genome sequencing data and the simulated longitudinal phenotypes for 849 pedigree-based individuals from Genetic Analysis Workshop 18, we investigated various approaches to detecting the association of rare and common variants with blood pressure traits. We compared three strategies for longitudinal data: (a) using the baseline measurement only, (b) using the average from multiple visits, and (c) using all individual measurements. We also compared the power of using all of the pedigree-based data and the unrelated subset. The analyses were performed without knowledge of the underlying simulating model. Whole genome sequencing (WGS) makes it possible for investigators to extend association studies to rare variants. Rare variants, which have minor allele frequencies (MAFs) of less than 1% to 5%, might play an important role in the etiology of complex traits and account for missing heritability unexplained by common variants . HoweverThe longitudinal study design, which collects repeated measurements on the same subject over time, has been routinely used in epidemiologic and clinical research. The repeated measurements can reduce error and thus increase statistical power compared with the single measurement. There have been increasing applications of such a design in genome-wide association studies (GWAS) with a focus on common variants. The analytical strategies include using the measurement at a single time point , using tIn the era of next-generation sequencing studies, the family-based design has the unique advantages of protecting against population stratification, detecting genotyping errors, and facilitating accurate imputation, all of which are challenging issues to cope with in the studies of rare variants using unrelated subjects. However, it is well known that enrolling and sequencing additional family members will not increase statistical power as much as that can be achieved by the same number of unrelated subjects. The degree of power gain from the added family members depends on the extent of the within-family correlation and the size of each family. Thus, it is of interest to assess this power gain in each specific study.Genetic Analysis Workshop 18 (GAW18) provided WGS data (sequencing plus imputation) in a pedigree-based sample with longitudinal measurements for systolic blood pressure (SBP) and diastolic blood pressure (DBP). In this study, we implement methods to exploit longitudinal and family structures and apply these methods to examine the associations of aggregated rare variants, as well as common single-nucleotide polymorphisms (SNPs), with SBP and DBP. We compare the power of the methods using the baseline measurement only, using the averaged value over repeated measurements, and using the full information of longitudinal data. We also contrast the power of the methods using all of the pedigree-based data with that using the unrelated subset.http://www.r-project.org) version 2.15.1.In this study, we focus on the first replicate of simulated SBP and DBP and the genetic data from sequencing and imputation only on chromosome 3 because of limited computation resources. The analyses were performed without knowledge of the underlying simulating model. We obtained 849 individuals from 20 pedigrees, among which 142 are unrelated. All individuals have SBP and DBP measurements at three time points with no missing data, as well as age, gender, smoking status, and antihypertensive medication status. Note that we preadjust the SBP and DBP measurements by the antihypertensive medication status . We define common variants as those with MAFs 5% or greater and obtain 403,098 SNPs on chromosome 3. We jointly analyze rare variants by mRNA transcripts, which are the functional products of genes. We exclude transcripts whose total rare allele frequency  is less than 0.01 and end up with a total of 813 transcripts represented by accession numbers. Given a common single-nucleotide polymorphism (SNP) or a transcript for the phenotype, we consider using (a) the baseline, (b) the time-averaged, and (c) the repeated measurements; for study subjects, we consider using (a) the entire pedigree-based sample and (b) the unrelated subjects only. All statistical analyses were carried out in R T the genotypes of the m variants, and Xit = T the q covariates including the intercept and possibly time-varying ones. Under the family-based design and when subject i belongs to family p, we modify the aforementioned notation to be pitY, Gpi and Xpit.Assume there are http://snp.gs.washington.edu). We consider the following functional categories: missense, missense-near-splice, splice-3, splice-5, stop-gained, stop-lost, and stop-lost-near-splice. Note that the functional annotation is specific to each transcript. The burden score of the ith subject at a given transcript is defined as the sum of genotypes of the selected variants: We focus on variants with MAF less than 5% and that are putatively functional . Specifically, using the chromosomal location (NCBI built 37.1) provided by the GAW18 data, we search for functional annotation of 812,234 SNPs with MAFs 5% or less on chromosome 3 using the GVS server  age in the baseline (averaged) phenotype model.where i at time t, it is written asTo account for the correlation of measurements from the same individual, we use the linear mixed-effects model. For subject i bis a random effect that follows i bare mutually independent; and Xit consists of the intercept, gender, smoking status, and the time-varying age. By including age into Xit, we assume that the traits change linearly with time. Both visual inspection of the individual-level trait trajectories and statistical testing of the age coefficient support the linear modeling (results not shown). Because i binduces a squared correlation of i. Note that i bis shared by different measurements of subject i so that the induced correlations are the same.where ith subject in the pth pedigree, we formulate thatTo account for the phenotype correlation among subjects from the same family, we also adopt a linear mixed-effects model. For the pi gis a random effect representing genetic similarity among family members, pi gis independent of Xpi is the same as Xi in (1). In addition, we assume that i and i'. Unlike i bin (2), which is shared among correlated units (time), there is a random effect pi gfor each unit (subject) here, and their covariance matrix is specified so that correlations among different pairs of family members are different.where Model (3) can be readily extended to accommodate repeated measurements. We include the repeated measurements in (3) as follows:Xpit contains the time-varying age, gpi is introduced previously, bpi follows the same distribution as bi in model (2), and gpi and bpi are independent of each other. Unlike in (2), pi bhere characterizes the additional correlation between repeated measurements after adjusting for the genetically induced portion. To see this, we consider the reduced model without bi:where t and t'. However, the covariance between measurements For both (4) and (5), the covariance between different family members is p-values of top SNPs using (4).Although model (4) is more flexible than (5), the chromosome-wide scan based on (4) is not feasible within the given timeframe and available computational resources. We thus adopt a two-stage strategy that first scans chromosome 3 using (5) and then refines the 2 <0.2) restricted to those with MAFs 5% or greater using the unrelated subjects. Then we project the SNP loadings of unrelated subjects to their relatives to calculate the eigenvectors of the entire sample of families.GAW18 data consist of Mexican Americans from San Antonio, a population that may have an admixed ancestry of whites and Native Americans. To account for possible population stratification, we include top principal components (PCs) of SNP genotypes as covariates in the above regression models. We first obtain independent SNPs . Note that the use of model (4) does not alter the aforementioned order based on power, although it tends to slightly improve on the use of model (5). Using the Bonferroni correction, the genome-wide significance threshold is 1.3 × 10-7, at which the top five SNPs can be declared as genome-wide significant by any method. Note that we only focused on chromosome 3, so what we are assessing is in fact chromosome-wide significance. For testing the association between rare variants and SBP, the 6 tests also have controlled type I error . Again, compared with the unrelated subset, the relatives added considerable information on the associations of the top three transcripts. All three types of SBP generated comparable power with all individuals, and the three consensus top transcripts are described in Table -5, at which the three top transcripts can be declared as genome-wide significant by any method. All of the identified common and rare variants map to the gene MAP4, which spans from 47,892,180 to 48,130,769 on chromosome 3.Figure The results of testing the genetic association with DBP show similar patterns as with SBP (data not shown). In particular, using the averaged DBP yielded better power than using the repeated measurements. Tables We investigated three approaches to exploiting longitudinal phenotype data and assessed the power gain of adding family members in the context of WGS studies. Most GWAS have focused on the population-based design, which maximizes the power per genotyped subject. Our results demonstrated that including family members can also significantly boost the power. Most GWAS have ignored the longitudinal nature of the phenotype data, which are available from many prospective cohorts. The use of the longitudinal data can provide a more accurate measurement of the phenotype and thus serves as a powerful tool in genetic association studies. With more clinic data being available through the electronic medical record (EMR) system and more clinic populations with genotypic data, the search for disease-associated common and rare variants can be more fruitful by improving the phenotyping via longitudinal information.It appears somewhat counterintuitive that using the time-averaged measurement is more powerful than using the repeated measurement in the analysis of the GAW18 data. This is possible because, in the presence of linear time effect, the averaged measurement does not lose any information compared with the repeated measurements but simply reduces error. When more complex longitudinal structures exist, the repeated measurements retain full information and are expected to outperform the averaged measurement.A family-based design can allow us to test association and linkage simultaneously. In this paper, we focused on the association analysis only. We modeled the association in the fixed-effect parameters and accounted for family relatedness using the random-effect parameters, whose covariances among family members are formulated through the kinship coefficient. Our models can be readily extended to linkage analysis by including another set of random-effect parameters whose covariances depend on the proportion of alleles shared identical by descent at the marker locus between a relative pair .The authors declare that they have no competing interests.YJH and YVS designed the overall study and drafted the manuscript. QH conducted statistical analyses. All authors read and approved the final manuscript.


To raise the power of genome-wide association studies (GWAS) and avoid false-positive results in structured populations, one can rely on mixed model based tests. When large samples are used, and when multiple traits are to be studied in the ’omics’ context, this approach becomes computationally challenging. Here we consider the problem of mixed-model based GWAS for arbitrary number of traits, and demonstrate that for the analysis of single-trait and multiple-trait scenarios different computational algorithms are optimal. We implement these optimal algorithms in a high-performance computing framework that uses state-of-the-art linear algebra kernels, incorporates optimizations, and avoids redundant computations,increasing throughput while reducing memory usage and energy consumption. We show that, compared to existing libraries, our algorithms and software achieve considerable speed-ups. The OmicABEL software described in this manuscript is available under the GNUGPL v. 3 license as part of the GenABEL project for statistical genomics at http: //www.genabel.org/packages/OmicABEL. The evolution of current molecular techniques expands our capacity to access different components in the omics space, and new prominent omics emerge . The study of the genetic control of different omics brings the promise of new fundamental and applied biological discoveries; however, such analyses pose “big data” challenges.Current biomedical research is experiencing a large boost in the amount of data generated. In particular, investigations involve human cohorts comprising hundreds of thousands of participants as part of nation-wide biobanking initiatives; furthermore, by using both arrays that include hundreds of thousands of single nucleotide polymorphisms (SNPs), and more recently, exome and whole-genome re-sequencing, the genomes of these participants are being characterized at an increasing level of detail, bringing the number of features assessed to tens of millions. At the same time, technologies for high-throughput assessment of different molecular “omics” phenotypes in large study cohorts are becoming more and more affordable. These molecular phenotypes characterize different classes and sub-classes of biological molecules, their functional modifications and relationships. Examples include hundreds of thousands of epigenetic modifications  and phenotype(s) of interest is studied, with significant associations highlighting the genomic regions harboring the functional variants involved in the control of the trait. While initially GWAS were mostly used to study common diseases, with the rising availability and affordability of omics phenotypes, this methodology is now also applied to investigate the omics space13, providing important insights into both the mechanisms underlying the genetic regulation of particular biological systems, and the determinants of human health and disease16.Genome-Wide Association Studies (GWAS) is an established tool for analyzing the genetic control of complex traits18, which allow for modeling of correlations between phenotypes of relatives. The LMMs are among the most flexible and powerful methods to account for the genetic (sub)structure that inevitably occurs even in carefully designed large population-based studies. However, the increase in power and precision achieved through the use of mixed models comes with considerable costs in terms of computing time.In this work, we address the computational challenges posed by big-data GWAS. These challenges arise when size of sample under analysis is very large or when  thousands of omics phenotypes are studied. We consider analyses facilitated by the use of linear mixed models (LMMs)25 represent a breakthrough compared to older methods, and allow analyses of a limited number of traits in reasonably sized samples even on personal computers. Still, current algorithms and software may be prohibitively expensive for analysis of large samples when dealing with omics data, since the time needed for a multi-trait analysis is essentially that of a one-trait study multiplied by the number of traits. Under this scenario, the analysis of even relatively small samples sizes leads to extremely long wait times. Therefore at the moment, the LMM-based GWAS analysis of large cohorts (tens to hundreds of thousands of participants), and even small (thousands of participants) studies involving omics measurements, represents a considerable problem. This limitation compromises the analyses availability, the data-to-knowledge turnaround time, and leads to excessive energy spending.Recent advances in GWAS using mixed modelsWith this work, we aimed to address the aforementioned problems for big-data LMM-based GWAS. To do so, we took advantage of properties specific to the LMM formulation of GWAS, and analyzed a number of possible algorithms applicable to the analysis of large data. By combining sophisticated linear algebra and optimization techniques, we produced a fast and scalable software. Our software facilitates GWAS of tens of thousands of samples and hundreds of thousands of omics phenotypes, without the need for super-computing facilities.n studied individuals as a point in ann-dimensional space, which comes from a multivariate Normal distribution. The expected mean is modeled using a standard regression model asE[Y] =Xβ, whereX is the design matrix which includes the genotypes of interest and other covariates, andβ are fixed effects. The variance-covariance matrix is defined asM =σ2 · (h2Φ + (1− h2)I); here,σ2 is the total variance of the trait,h2 is the heritability coefficient,I is the identity matrix, and Φ is the matrix containing the relationship coefficients for all pairs of studied individuals. GWAS are performed by consecutively including SNPs in the analysis model  and computing the association statistics for the included SNP, thus iteratively applying the model throughout the genome.In a nutshell, LMM models the phenotypes of a group of21, and proceeds with analysis in two steps: for each trait considered, we first estimate the matrix of (co)variances between phenotypes, and then we use it when estimating the SNP effects  problems. The key to fast analysis algorithms is the realization that such problems are correlated, both along them and thet direction; in big-data GWAS, any approach that ignores such correlations cannot be feasible in terms of time-to-solution.26. The core idea is to first decompose a target matrix-based problem in terms of library-supported kernels, and then apply algorithmic and algebraic optimizations. Since the decomposition is not unique, CLAK returns not one but a family of possible solutions, all mathematically equivalent, but exhibiting different space and time complexity.Aiming at supporting computational scientists in the design of efficient software, two of the authors recently developed CLAK, an algebraic system that replicates the reasoning of human experts for the automatic discovery of linear algebra solvershol and CLAK-Eig ; through this factor, each SNPX and each traity is then linearly transformed, giving raise to a sequence of Ordinary Least Squares problems of the formb := (TXX)-1TyX. While such problems are solvable with standard techniques, CLAK-Chol takes advantage of the fact that the covariates are fixed for all SNPs, hence lowering the computational complexity. In single-trait analyses, it is also possible to exploit the fact that the matrixM is symmetric and positive definite. Although asymptotically the Cholesky factorization is equivalent to an eigen-decomposition, in practice it requires 10 times fewer operations. Moreover, instead of using the eigenvectors (a full matrix) to rotate the SNPs, the Cholesky factor (a triangular matrix) allows us to transform them at half the cost. For more details, see the work we have previously published27 describing the CLAK-Chol algorithm.The idea underlying CLAK-Cig is based on three insights: 1) For a given study, the relationship matrix Φ is constant across both SNPs and traits; 2) since the variance-covariance matrixM is built by merely shifting and scaling relationship matrix, its eigenvectors are the same as those of Φ, and its eigenvalues are obtained by shifting and scaling those of Φ; 3) the inverse ofM is easily expressed by inverting the diagonal matrix containing its eigenvalues . Together, these insights suggest that the eigen-decomposition of Φ can be computed once and for all, and most importantly, the eigenvectors of the relationship matrix can be used to rotate all the SNPs and traits only once. After the data is rotated, the computation of the mixed model based GWAS can be carried out by means of a grid of inexpensive Weighted Least Squares problems.The design of CLAK-Eig is determined by three operations: the rotation of the SNPs, the rotation of the traits, and the solution of the Weighted Least Squares problems. The dominant term depends on the size of population (n), number of SNPs (m), and number of traits (t). Whenn > t (orn > m), the overall time complexity comes from the rotation of the SNPs (or the traits), and amounts toO(n2m) (orO(n2t)); if instead botht andm are larger thann, then the dominant term comes from the Least Squares problems, and is linear in population, SNPs and traits:O(nmt)  for a case of multiple trait analysis.Once the initial eigen-decomposition of Φ is available, the complexity of CLAK-EO(nmt) . Note th22 in multi-trait analyses, CLAK-Eig achieves a lower computational complexity. As shown int > n), which is probably the most typical for current and near-future omics studies, the time complexity of CLAK-Eig is linear on the number of markers, traits, and samples; by contrast, all the other methods have quadratic complexity with the sample size. In the second case (n > t), which takes place for smaller ‘omics’ and also will become more common with the increasing affordability of omics technologies and hence larger sample sizes, the cost of CLAK-Eig is determined by the sample size and the number of SNPs, and its complexity is a factort lower than other methods.Compared with current state-of-the-art algorithmsig and CLAK-Chol, the space complexity is mainly determined by the square of the sample size; also, a minimum of one trait, one SNP, and thep covariates must reside in memory. In total, our methods only require enough memory to accommodaten2+(2+p)n entries. If multiple SNPs and/or traits fit in main memory at once, —e.g., dozens or hundreds of them—the computational throughput of our methods improves noticeably. In this case, the space requirement becomesn2+(k+p)n, wherek is the number of SNPs and traits resident in memory. As examples, for sample sizes of 10,000, 20,000 and 40,000, then2 space requirement translates to 1, 3, and 12 GBs, respectively. More details on space complexity are provided inFor both CLAK-Eig and CLAK-Chol, we implemented these algorithms in the OmicABEL software package. In doing so, we tailored our implementations to save intermediate results across adjacent problems; we also re-organized the calculations to fully benefit from both the efficiency of highly optimized linear algebra kernels, and the parallelism offered by modern computing platforms.To demonstrate the practical advantages of CLAK-ESince the size of the datasets involved in GWAS is considerably larger than the memory capacity of current processors, input and output data can only be stored in disk devices. Aware that the penalty for accessing information residing on disk is enormous—several orders of magnitude greater than the cost for performing one arithmetic operation—it is imperative to handle these big-data efficiently. By means of asynchronous transfers between memory and disk, our algorithms achieve a perfect overlap of computation and data movement. As long as the relationship matrix fits in the main memory, and regardless of the size of the data sets—both in terms of SNPs and phenotypes—, the processor never idles waiting for a transfer to complete, thus computing at maximum efficiency.hol and CLAK-Eig as implemented in OmicABEL with that of several well-established packages: EMMAX19, FaST-LMM22 (two-step approximation), and GWFGLS (implementation of the mmscore method of ProbABEL21 in the MixABEL-package29). In the experiments, we considered three different scenarios, varying one among sample sizen, number of SNPsm, and number of traitst, while keeping the other two values constant , all methods exhibit a quadratic behavior, and CLAK-Chol is the only algorithm that completed all tests within 25 hours , the speed-up over the next-fastest software (FaST-LMM) is 8.3: 205 vs. 25 hours; whenn = 1,000, the speed-ups over GWFGLS, FaST-LMM and EMMAX are 24, 32 and 68, respectively: 86, 112 and 240 vs. 3.5 minutes.In the first scenario  shows a linear dependence on the number of genetic markers for all software packages. Again, CLAK-Cctively , when thig’s linear time complexity with respect to sample size, SNPs and traits, its advantage becomes most apparent: when thousands of traits are considered, CLAK-Eig outperforms GWFGLS, FaST-LMM and EMMAX by a factor of 1012, 1352, and 2789, respectively . The (estimated) time required for these analyses is presented inctively , bringinmicABEL (CLAK-Eig) to study 107,144 metabolomic traits in a sample of 781 people from a genetically isolated population of the Vis island (Croatia). These data are part of the EUROSPAN data set reported in the works of30, in this work, 328 such measurements served as a base to compute all pair-wise ratios, resulting in 107,584 traits, which were analyzed for association with 266,878 SNPs. More details about the data are provided inWe applied the OmicABEL software and a computer with 40 cores, we were able to finish the analysis of more than 100,000 traits in only 8 hours.Previously, it took several weeks to accomplish the original analysis of only few hundreds “original” traits. However, using our O11 to be significantly associated with levels of circulating sphingolipid concentrations. The best results obtained for these SNPs when using the original and derived traits are reported. The implicated traits were also analyzed by using other approaches: the full likelihood ratio test based LMM22 (as implemented in MixABEL::FMM), Grammar-γ25 (as implemented in the GenABEL-package29), and the two-step approach21 (as implemented in MixABEL::GWFGLS). Fromλ obtained when analyzing the selected traits with different methods. More details of the analysis of this human metabolomics data set are provided in32, metabolome12, glyco(protein)ome7 and other types of omics data. Results of these studies are used to uncover the link between these molecular phenotypes and high-level complex traits, including human diseases16.In contemporary human genomics, methods and tools face the additional challenge posed by the sheer size of the datasets. Big data are produced from the investigation of large human cohorts including hundreds of thousands of participants; these massive samples facilitate the identification of small effects and lead to important biological insights. Large data also come from the field of functional (gen)omics, which aims at establishing the functional roles of genetic variants; hence GWAS are increasingly applied not only to study complex traits in large cohorts, but also to understand the regulation of human and animal transcriptome18. Most current LMM-based methods for GWAS24 exhibit linear dependency of the compute time on the number of genetic polymorphisms and traits studied, but at least quadratic dependency on the sample size. A notable exception from the latter “at-least-quadratic” rule is the GRAMMAR-Gamma method25 and a method based on low rank approximation of the similarity matrix22 - with the latter exploiting the ideas similar to EIGENSTRAT approach33 and the methods assuming the adjustment of the model for top Principal Components of the kinship matrix variation. However, the computational advantage of these methods comes at the cost of mathematical approximation. For example, the GRAMMAR-Gamma method, while extremely fast, and showing excellent results for human studies, is less suited for analyses of samples with uneven genetic structure; adjusting for top principle components (and EIGENSTRAT) is known to provide incomplete correction for stratification in case of complex kinship. Increasing sample sizes and availability of molecular omics phenotypes lead to “big data challenges” and the computational throughput of LMM’s starts being more and more of an issue, which at present sometimes cannot be resolved without resorting to supercomputing facilities. In recent years, linear mixed model was accepted as a powerful tool for whole-genome analysis of genetic associationshol and CLAK-Eig algorithms and software tools (OmicABEL package) to address LMM-based GWAS. Specifically, our CLAK-Chol will be useful for investigation of complex traits in very large  samples, while CLAK-Eig will be a useful tool for the investigation of genetic control of different omics, potentially including hundreds of thousands or even millions of features.With this work, we address the problem of mixed-model based whole-genome analysis of genetic association for an arbitrary number of traits. We describe the CLAK-Chol approach, we are not aware of similar, Cholesky-based solutions proposed before. The CLAK-Eig approach behind our solutions bear similarities, and actually reduces to previously suggested methods (e.g.28) when the number of traits is one. It is also worth mentioning the Matrix eQTL software34, which, while not implementing the LMM, in many respects exploits the problem-specific properties of multi-trait GWAS in the ways similar to ours.As for our CLAK-C1 for about 3 minutes; by contrast, using a common 40-core compute node node see,Note S2hol solution outperforms advanced current methods (e.g. FaST-LMM) by about one order of magnitude for large-sample-size problems. It is worth mentioning that the latter speed-up becomes possible because we show that for single-trait GWAS problems our CLAK-Chol algorithm is superior to CLAK-Eig, but other current methods are actually implementing solutions similar to our CLAK-Eig algorithm to address the single-trait GWAS problem.In case of single-trait analysis, our results are somewhat less impressive, and our CLAK-C20; similarly, the fast decaying and possibly sparse structure of the kinship matrix can be exploited to lower the number of mathematical operations. Caution must be exercised in the interpretation of findings resulting from GWAS analyses as they may generate false positives if the multiple testing problem is not addressed adequately. A conservative strategy to determine whether an association is statistically significant would be to apply a Bonferronni correction, that is, in our example analysis of 107,144 traits, the conventional genome-wide significance thresholdp-value of 5 · 10-8 should be replaced by 4.7 · 10-13. This is the common approach applied in the metabolomics studies (see30). On the other hand, this threshold would probably be too conservative, given that many of the measurements may be highly correlated. Several methods have been introduced recently37, which may help to overcome this problem; however, this topic lays outside the scope of the current work.Further optimizations of our solutions are possible, for instance by exploiting the structure of the kinship matrix. A “compressed MLM” approach was proposed for decreasing the effective sample size of datasets by clustering individuals into groupsmicABEL could be used for the identification of trans-eQTLs, one should be aware of the specifics of the analysis of this type of data  and a body of methods developed (e.g. methods to account for influences of hidden factors39).For the analysis of specific omics data, our methods (and software) might require some modifications. For example, in the genetic regulation of human transcriptome, large attention is dedicated to cis-eQTLs, computationally a relatively simple task. In contrast, our implementation is tailored to perform full GWAS for every trait analyzed. While O40. One of the common scenarios include the construction of millions of features, and their filtering for further joint analysis—a task which can be also effectively addressed by our methods. Finally, our algorithms can be easily extended, e.g. to search for interactions.We foresee that the primary use of our algorithms and software is within the domain of analysis of complex traits in very large samples and for the genetic analysis of “omics” data. However, potentially, there are other uses. The same set of methods and tools can be used for scanning through other omics in e.g. search for biomarkers for a complex trait or in order to determine functional relations between different omics. For example, one may be interested in doing epigenome-wide scans relating the epigenome to a complex trait . Under this use, the genomic inputs would be replaced by epigenomic data. Advanced statistical and machine learning methods, such as penalized regression, can make use of joint analysis of up to several hundreds of thousands of predictorsmicABEL software.We demonstrated that different computational algorithms are optimal for the problems of single- and multi-trait Mixed-Model based GWAS, and implemented these algorithms in a freely available OmicABEL software implementing computational methods described in this manuscript is available as part of the GenABEL project for statistical genomics athttp://www.genabel.org/packages/OmicABEL. The web-page provides the link to OmicABEL tutorial, giving examples of its use.The Ohttps://r-forge.r-project.org/scm/viewvc.php/pkg/OmicABEL/?root=genabelhttp://dx.doi.org/10.5281/zenodo.1099941GNU GPL v. 3 This is a very well written report on a very important topic of very high impact in the actual of omics and multi-level omics data, allowing beyond sheer analysis (which in large data sets is very demanding indeed in terms of runtime and memory) many more questions answered also for methods research.The methods put forward present a very major step forward for this type of analysis. The methodology is very sound and promising. A tool to actually use is provided, which is also not always the case.The authors are to be commended for this work.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Identification of genetic variants associated with gene expression (eQTLs), methylation (mQTLs) etc is becoming ever more important in understanding the biology of complex genetic disorders.It is desirable, when performing association analyses, to allow for population stratification and/or cryptic relatedness among members of the sample. Mixed models are an effective way of doing this.The high dimensionality of the "omics" data (tens or even hundreds of thousands of measurements) has made the application of mixed model association approaches computationally prohibitive up to now. In addition to detailing an application of considerable practical utility, the article is also clearly written and mathematically rigorous.This article introduces a new software tool (omicABEL) for performing rapid association analyses between SNP data and high-dimensional "omics" data (e.g. gene expression) using mixed models. This is an extremely important development for the following reasons:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. The manuscript shows a computational approach that enABELs the use of linear mixed mixed models for large pedigrees, large numbers of markers and large numbers of (omics) traits.While the work is interesting, several things need to be clarified before the work can be of interest to the wider community.I assume that the manuscript is aimed at the potential users: researchers in genetics with an interest to analyze their 'big data' in a correct fashion and in a repeatable fashion. The manuscript is compact but possibly too compact in places. I would like the following points to be addressed:Accuracy of estimates and comparison of results. The authors make a big deal about comparing the approaches in terms of computing time. They should also be compared systematically in terms of type I error, accuracy of estimates etc. The computational approximations that are made must come at some cost and as researchers we need to know this cost. There are some token comparisons in the supplementary tables but these deal with heritability and P values. Not with the actual SNP effects which are what we want from these analyses. Some scatter plots between different methods may be helpful.We need more detail about the simulations. You simulate different population sizes but you must clarify the family structures and the family complexity. How many generations? All family sizes equal? etc. Also how you simulate marker data in terms of historical population size, lD structure etc. Likewise for correlation structure among the multiple traits.In many places, variables are used before they are defined. p appears in Table 1 but is only clarified later in the text. The tables are currently not readable on their own and the acronyms and variables should be explained within the tables.  Some parts of result should be in the Materials and Methods.Figure 3C could have a logarithmic Y-axis.Figure 3D could omit line for CLAK-Eig and CLAK-Chol is unlabeled.The abbreviation in Table S3 cer-cer lpc, pls spm pc pe etc. makes no sense to me. They are different trait classes but still the table adds very little. In general, the mathematical notation as well as the language in general needs a bit of work. Some sentences are too long with too many clauses, for example CLAK is not defined at first use. X and y are linearly transformed: should you not introduce new variables for the transformed data?The manuscript has the promise to introduce an interesting new computational approach, but we need more details to make up our mind.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.


EPS8 and MGST1 have been proposed to underlie these signals, the causative status of these genes has not been functionally confirmed. To investigate this QTL in detail, we report genome sequence-based imputation and association mapping in a population of 64,244 taurine cattle. This analysis reveals a cluster of 17 non-coding variants spanning MGST1 that are highly associated with milk fat percentage, and a range of other milk composition traits. Further, we exploit a high-depth mammary RNA sequence dataset to conduct expression QTL (eQTL) mapping in 375 lactating cows, revealing a strong MGST1 eQTL underpinning these effects. These data demonstrate the utility of DNA and RNA sequence-based association mapping, and implicate MGST1, a gene with no obvious mechanistic relationship to milk composition regulation, as causally involved in these processes.The mammary gland is a prolific lipogenic organ, synthesising copious amounts of triglycerides for secretion into milk. The fat content of milk varies widely both between and within species, and recent independent genome-wide association studies have highlighted a milk fat percentage quantitative trait locus (QTL) of large effect on bovine chromosome 5. Although both  DGAT1ABCG2GHRAGPAT6378910EPS8 and MGST1 have been speculated to underlie these effects, the causative status of these genes has not been functionally demonstrated.Milk lipids comprise the predominant energy source of the developing neonate in most mammalian species. There is substantial inter- and intra-species variation in milk fat content2Bos taurus. This includes SNP-array panels used for genome-wide association studies, and like the evolution of human genotyping platforms, the density of these panels has steadily increased over time. Driving this increase in SNP-density is the underlying principal that for association mapping to be effective, SNPs must be in sufficient linkage disequilibrium with causal variants to discern genetic signal13151618Given the economic importance of bovine dairy products and beef as human food sources, considerable genetic resources exist for the study of complex traits in In the current study, we performed a detailed investigation of a major QTL affecting bovine milk fat percentage. Bayesian genome-wide association analysis was conducted in a large population of outbred cows to first estimate the genomic location of the QTL. A reference panel of 556 whole genome sequences was then used to impute sequence-resolution genotype data at the chromosome 5 locus, with association analysis revealing a handful of candidate causal variants for this QTL, and a variety of other milk components. We then utilise high depth mammary RNA-sequence data to examine the expression of candidate causative genes for these effects, identifying a large expression QTL (eQTL) for a single gene that is not only highly correlated with the milk composition QTL, but harbours the top associated variants within its proximal regions.MGST1, ~186 kbp downstream of the LMO3 gene, and ~364 kbp upstream of the DERA gene. When the genome was partitioned into 1 Mbp windows and the combined effects of SNPs within each interval estimated, the chromosome 5 93-94 Mbp window accounted for 2.1% of the genetic variance in milk fat percentage, representing the third largest QTL genome-wide , Jerseys (J), and HFxJ crossbreeds. The percentage of phenotypic variance explained by all fitted SNPs in the Bayes B model was 35.6%. Consistent with previous genome-wide association studies (GWAS) of milk fat percentage37891079ome-wide . Of the Having estimated the location of the chromosome 5 QTL, we then imputed sequence-based genotype data into a 10 Mbp interval centred on the BovineHD0500026662 SNP for a population of 64,244 animals. This population comprised the 42,933 animals used for the original GWAS, and an additional 21,311 animals (of similar breed composition) typed predominantly using the Super GGP BeadChip. The sequence reference panel consisted of 556 animals at an average of 15× genome-wide mapped read depth. These animals were broadly representative of the New Zealand dairy population, where 18,854 of the 64,244 animals targeted for imputation had a sire directly represented in the sequence reference, and an additional 28,564 animals had at least one grandsire represented. Variants were called from sequence alignments using RTG Core2 metric was a robust indicator of imputation accuracy . For the subset of 994 filtered SNPs that mapped to the 10 Mbp imputation interval, 790 were common to the genome sequence-derived dataset. For these 790 SNPs, the overall accuracy of imputation was high  = 0.99; mean MAS = 0.93; 22For association testing, analysis was restricted to a 2 Mbp target interval centred on the top chromosome 5 tag-SNP from GWAS . Filtering to remove multi-allelic and low frequency variants (MAF < 0.005) yielded 13,719 SNPs, 863 indels, 255 multiple nucleotide polymorphisms (MNPs), and 107 ‘mixed’ variants (class combinations) for analysis. Of these 14,944 variants, 14,448 were derived wholly from genome sequence data, with 496 (3.3%) present on one or more of the Illumina BovineHD, BovineSNP50, or Super GGP BeadChip platforms used for physical genotyping. Quantifying imputation accuracy as described above, coincident RNA-seq variants in this 2 Mbp interval had a median MAS = 0.99, and mean MAS = 0.97 . Although P-values for this cluster of variants spanned many orders of magnitude , though notably, tagging of the QTL signal was relatively poor for BovineSNP50 chip variants . Based on the MGST1 gene structure derived from mammary RNA-seq data, the cluster of 17 top-associated SNPs were all non-coding variants spanning a 10 kbp interval from intron 1 to 4 kbp upstream of the transcription start site  as a potential causal mutation for this effectet al.MSGT1 variant identified from Bayesian GWAS in the current study (BovineHD0500026662), though the authors also acknowledged a potentially independent signal located nearer EPS8EPS8 in our dataset, and notably, the candidate mutation g.94553580T > C proposed to underlie this QTL is polymorphic in our sample (MAF of 0.134 in our genome sequence reference). Imputation of the variant yielded an allelic R2 of 0.88, suggesting the variant was imputed accurately in our population (P = 3.26 × 10−44), fitting the lead g.93945738 MGST1 genotype removed this effect (P = 0.561). These data do not preclude the possibility that another downstream, non-segregating QTL exists, but suggest the EPS8 g.94553580T > C variant would be unlikely to underlie such an effect.Fitting the g.93945738 genotype as a covariate in the association models and rerunning the analysis for the remaining variants removed most of the association signal in the 2 Mbp interval . Althougpulation , and altDGAT1 and AGPAT6 fat synthesis enzymes4MGST1 SNP (632 variants), significant associations were demonstrated for all milk traits tested , with MGST1, COX6B1, and SNORA23 abundantly expressed (>20 fragments per kilobase of exon model per million mapped (FPKM); cis eQTL for the MGST1 and DERA genes  with the milk fat percentage analysis , we used high-depth mammary RNA-seq data representing the same 406 lactating cows used to quantify imputation accuracy. Of the nine annotated genes in the 2 Mbp interval of interest, six were appreciably expressed . Following the same imputation and association analysis pipeline used previously, none of the gap variants approached the significance of the original top 17 variants , we used a sequential re-mapping, gap extension, and MGST1 TSS, and analysis using CNVnator2 = 1) suggested accurate sequence-based calling of the variant . To assess phenotypic consequences of the variant, we conducted association analysis of MGST1 gene expression using this proxy-haplotype, targeting the RNA-seq cohort since 95% of these animals had been physically genotyped using the BovineHD chip. Using a haplotype dosage model identical to those used for SNP-based eQTL mapping, this analysis did not support the deletion as the likely causative mutation for MGST1 expression antelope , but is MGST1 gene underpinning these QTLs, highlighting a major MGST1 cis eQTL that shares the same, highly associated sequence variants implicated in analyses of milk composition. We report detailed sequence curation of the MGST1 locus, uncovering a number of previously obscured variants including an 8.2 kbp deletion variant 5′ of the MGST1 TSS. Despite the outstanding biological candidacy of this variant, this deletion appears unlikely to underlie the gene expression and milk composition QTLs, though we identify alternative candidate causative polymorphisms as a basis for future functional investigation. Most remarkably, confirmation of MGST1 as the causal gene impacting this diverse array of milk composition phenotypes offers little clue as to the mechanism of effect. Although MGST1 is known to directly bind fatty acids, these activities appear to relate to its role as a detoxification enzyme, so the potential impact on milk lipid synthesis and/or secretion is unknown. As such, elucidation of this mechanism may provide insight into new mechanisms of lactation biology, and at a practical level, future work to tease apart the molecular contribution of the candidate variants should provide opportunities for animal selection and/or gene editing.We present a detailed analysis of a pleiotropic milk composition QTL on bovine chromosome 5, demonstrating large effects for milk fat and protein percentage, milk volume, and milk lactose yield. Integrating large scale DNA and RNA sequence datasets, we provide strong evidence for the All animal experiments were conducted in strict accordance with the rules and guidelines outlined in the New Zealand Animal Welfare Act 1999. Most data were generated as part of routine commercial activities outside the scope of that requiring formal committee assessment and ethical approval (as defined by the above guidelines). For the mammary tissue biopsy experiment, samples were obtained in accordance with protocols approved by the Ruakura Animal Ethics Committee, Hamilton, New Zealand . No animals were sacrificed for this study.Primary datasets consisting of relevant genotypes, phenotypes, and sequence data representing all reported populations have been deposited into the Dryad digital data repositoryThe animal populations used for milk production association analysis consisted of 64,142 female dairy cows located on commercial dairy farms throughout New Zealand, forming part of a large phenotypic and genotypic database of animals used for commercial evaluation of sire performance. Differences in the number of animals quoted for analysis of different traits reflect impacts of genotype and phenotype quality filtering criteria applied for the different traits. All animals were born between 1998 and 2011, with > 95% of records derived from animals born after 2004. When ‘purebred’ animals were defined as having a breed proportion of at least 14/16ths, this population consisted of 20,958 Holstein-Friesians, 11,704 Jerseys, 30,979 Holstein-Friesian x Jersey crossbreeds, and 501 animals that were more than 4/16ths other breeds. Other breed proportions that were also present in these animals included Ayrshire, Brown Swiss, Guernsey, Hereford, Milking Shorthorn, and Swedish Red. The concentrations of major milk components were measured as part of standard herd-testing procedures using Fourier transform infrared spectroscopy. Most milk samples were processed by LIC Testlink  using the MilkoScan FT6000 instrument . For association analyses, milk composition records were restricted to first lactation measurements from October to January inclusive. The 406 animals used for RNA-sequencing consisted of 215 animals described in a previous studyGenomic DNA extraction for high-throughput genotyping was conducted using ear-punch tissue samples or blood, processed using Qiagen BioSprint kits (Qiagen) or a MagMAX system (Life Technologies). The former extraction method was performed by GeneMark , with the latter performed by GeneSeek . For whole genome sequencing, DNA was extracted using phenol-chloroform-based protocols, using semen samples from males, and blood or ear punch tissue samples from females. All high throughput genotyping was conducted by GeneSeek , with animals typed across a range of platforms including the GeneSeek Genomic Profiler BeadChip , the Illumina BovineSNP50 BeadChip , or the Illumina BovineHD BeadChip . Most (N = 377) of the 406 RNA-seq animals were typed using the BovineHD BeadChip, with the remainder (N = 29) typed using the BovineSNP50 platform.Whole genome sequencing was conducted on 556 individuals, consisting of 285 animals from an experimental crossbreed pedigree731Bos taurus UMD3.1 genome assembly using BWA MEM 0.7.8Paired-end FASTQ data were aligned to the MGST1 intron 1, reads representing this gap were identified by a sequential re-mapping and gap extension strategy in two unrelated animals. De novo assembly of the reads resulted in a non-reference consensus sequence of 410 bp, which was confirmed by PCR and Sanger sequencing (see ‘PCR and targeted sequencing’ section below). A modified reference sequence was then derived by replacing the 346 gap N’s with the consensus sequence. For each of the 556 genome-sequenced animals, all reads that were unmapped, not mapped as proper pairs, or were properly mapped to a 1 Mbp interval spanning the gap (chr5:93430000-94430000), were then re-mapped to the gap-filled reference using BWATo determine the sequence of the 364 bp reference gap in Sequence-based genotypes representing the 556 reference animals were imputed into the phenotypic population of 64,244 cows  using Beagle v4High-depth mammary RNA-seq was conducted using tissue samples from 406 lactating cows, representing three subgroups biopsied at different points through time. Sampling details for 215 of these animals has been described previouslyMammary tissue samples were obtained by needle biopsy and total RNA extracted by NZ Genomics Limited  using methods described previously7et al.Sequence data representing all 406 animals was mapped to the UMD 3.1 genome using Tophat2 (version 2.0.12)For accuracy assessment of imputed genome sequence data (see ‘Imputation accuracy assessment’ section below), SNP variants were called on the same Tophat2-derived alignments used for expression analysis using SAMtools (v0.1.19), excluding non-primary reads and reads which failed quality filters. Variants were filtered post-calling to retain variants with a) quality scores greater than 100; and b) an average depth per animal of at least five reads. Genotypes for individual animals were set to missing for calls with fewer than 10 reads. This variant set was also filtered to remove SNPs with fewer than 10 alternative alleles called, and fewer than 400 alleles called in total.P = 1 × 10−6 yielded 994 variants and 386 cows for comparison. For imputed sequence data, a MAF filter of 0.005 was applied in accordance with the criteria used for association analysis. This filter yielded 69,160 variants with a 790 variant intersect with the RNA-seq-derived call-set 2)/t, where p is the frequency of the A allele, a is the estimated allele substitution effect, and t is the total phenotypic variation. Similarly, the proportion of genetic variance explained by each SNP was calculated using (2p(1-p)a2)/g, where g is the total genetic variance.Associations between SNPs and the milk fat percentage phenotype were quantified by restricted maximum likelihood (REML) using pedigree-based mixed models in ASReml-RMGST1 sequence gap, re-imputation and filtering using the same criteria above yielded 14,985 variants. Analyses for the other milk composition traits  used a further refined, 50 kbp interval of filtered sequence variants. This interval was centred on the top associated MGST1 sequence SNP g.93945738C > T (chr5:93920738-93970738), yielding 632 variants for analysis. Significance of tests were assessed using a Bonferroni correction for multiple hypothesis testing . For analysis using the 2 Mbp interval of variants, a threshold of P < 3.34 × 10−6 was used, for analysis using the 50 kbp interval, a threshold of P < 7.91 × 10−5 was used.For computational efficiency, association analysis of milk fat percentage was restricted to a 2 Mbp interval centred on the top chromosome 5 tag-SNP identified through Bayesian GWAS (chr5:92945655-94945655). This interval contained 24,283 variants, and additional filters to remove variants with a MAF < 0.005 , and multiallelic variants (N = 532), yielded 14,944 variants for analysis. Following reference assembly refinement and discovery of new variants within the cis eQTL mapping in the 2 Mbp milk fat percentage interval, these models used VST-normalised read counts representing the six nominally expressed genes. A total of 14,971 imputed sequence variants were assessed in 375 PCA-filtered individuals . This variant set was also restricted to biallelic variants with a MAF > 0.005. Similar models were tested for trans eQTL analysis, extending the number of phenotypes tested to all expressed genes , but restricting analyses to the g.93945738C > T SNP only. For cis eQTL analyses, a multiple testing threshold of P < 3.31 × 10−6 was used ; for trans eQTL analyses, a threshold of P < 5.35 × 10−6 was used .Analysis of gene expression traits was conducted using ASReml-RP-value results lists was conducted to provide insight into whether co-locating QTL possessed the same underlying genetic signal. Use of this method has been described previouslyMGST1 expression-associated SNP g.93945738C > T  was used to quantify Spearman’s rank correlation coefficients. Correlation analyses were performed between milk fat percentage and MGST1 expression, and the six other milk composition traits , with Sanger sequencing confirming a non-reference gap sequence of 410 bp. For analysis of the CNV junctions, PCR products were designed to span the breakpoints apparent from whole-genome sequence alignments  and CAGTGTTAACCACATTGTTCTTG (R1) primers  were designments , using tGain or loss of putative transcription factor binding sites at the 15 top SNP loci was predicted using MATCHHow to cite this article: Littlejohn, M. D. et al. Sequence-based Association Analysis Reveals an MGST1 eQTL with Pleiotropic Effects on Bovine Milk Composition. Sci. Rep.6, 25376; doi: 10.1038/srep25376 (2016).