SYPL2, IFT172, TBKBP1) for which our analysis suggests that the eQTL pattern is not consistent with the lipid association, we identify alternative colocalisation results with SORT1, GCKR, and KPNB1, indicating that these genes are more likely to be causal in these genomic intervals. A key feature of the method is the ability to derive the output statistics from single SNP summary statistics, hence making it possible to perform systematic meta-analysis type comparisons across multiple GWAS datasets (implemented online at http://coloc.cs.ucl.ac.uk/coloc/). Our methodology provides information about candidate causal genes in associated intervals and has direct implications for the understanding of complex diseases as well as the design of drugs to target disease pathways.Genetic association studies, in particular the genome-wide association study (GWAS) design, have provided a wealth of novel insights into the aetiology of a wide range of human diseases and traits, in particular cardiovascular diseases and lipid biomarkers. The next challenge consists of understanding the molecular basis of these associations. The integration of multiple association datasets, including gene expression datasets, can contribute to this goal. We have developed a novel statistical methodology to assess whether two association signals are consistent with a shared causal variant. An application is the integration of disease scans with expression quantitative trait locus (eQTL) studies, but any pair of GWAS datasets can be integrated in this framework. We demonstrate the value of the approach by re-analysing a gene expression dataset in 966 liver samples with a published meta-analysis of lipid traits including >100,000 individuals of European ancestry. Combining all lipid biomarkers, our re-analysis supported 26 out of 38 reported colocalisation results with eQTLs and identified 14 new colocalisation results, hence highlighting the value of a formal statistical test. In three cases of reported eQTL-lipid pairs ( Genome-wide association studies (GWAS) have found a large number of genetic regions (“loci”) affecting clinical end-points and phenotypes, many outside coding intervals. One approach to understanding the biological basis of these associations has been to explore whether GWAS signals from intermediate cellular phenotypes, in particular gene expression, are located in the same loci  and are potentially mediating the disease signals. However, it is not clear how to assess whether the same variants are responsible for the two GWAS signals or whether it is distinct causal variants close to each other. In this paper, we describe a statistical method that can use simply single variant summary statistics to test for colocalisation of GWAS signals. We describe one application of our method to a meta-analysis of blood lipids and liver expression, although any two datasets resulting from association studies can be used. Our method is able to detect the subset of GWAS signals explained by regulatory effects and identify candidate genes affected by the same GWAS variants. As summary GWAS data are increasingly available, applications of colocalisation methods to integrate the findings will be essential for functional follow-up, and will also be particularly useful to identify tissue specific signals in eQTL datasets. In the last decade, hundreds of genomic loci affecting complex diseases and disease relevant intermediate phenotypes have been found and robustly replicated using genome-wide association studies GWAS, . At the In this context, a natural question to ask is whether two independent association signals at the same locus, typically generated by two GWAS studies, are consistent with a shared causal variant. If the answer is positive, we refer to this situation as colocalised traits, and the probability that both traits share a causal mechanism is greatly increased. A typical example involves an eQTL study and a disease association result, which points to the causal gene and the tissue in which the effect is mediated http://www.sanger.ac.uk/resources/software/genevar/), but the abundance of eQTLs in the human genome and across different tissues makes an accidental overlap between these signals very likely However, identifying the traits that share a common association signal is not a trivial statistical task. Visual comparison of overlaps of association signals with an expression dataset is a step in this direction :Q variants, typically SNPs but also indels. We make two additional assumptions and discuss later in this paper how these can be relaxed. Firstly, that the causal variant is included in the set of Q variants, either directly typed or well imputed We consider a situation where two traits have been measured in two distinct datasets of unrelated individuals. We assume that samples are drawn from the same ethnic group, i.e. allele frequencies and pattern of linkage disequilibrium (LD) are identical in both populations. For each of the two samples, we consider for each variant a linear trend model between the outcome phenotypes Q variants can be summarised for each trait using a vector of length Q of  values, where 1 means that the variant is causally associated with the trait of interest and at most one entry is non-zero. A schematic illustration of this framework is provided in SNP causality in a region of In this framework, the colocalisation problem can be re-formulated as assessing the support for all configurations (i.e. pairs of binary vectors) in hypothesis FRK gene and LDL, PP3 >90%) and positive  colocalisation results.Our method is Bayesian in the sense that it integrates over all possible configurations. This process requires the definition of prior probabilities, which are defined at the SNP level (Methods). A probability of the data can be computed for each configuration, and these probabilities can be summed over all configurations and combined with the prior to assess the support for each hypotheses Q is the number of variants in the genomic region and d the number distinct associations .While the method uses Approximate Bayes Factor computations ABF, , no iterImportantly, the use of ABF enable the computation of posterior probabilities from single variant association p-values and MAFs, although the estimated single SNP regression coefficients Given the well-understood requirements for large sample size for GWAS data, we used simulations to investigate the power of our approach. We generated pairs of eQTL/biomarker datasets assuming a shared causal variant. We varied two parameters: the sample size of the biomarker dataset and the proportion of the biomarker variance explained by the shared genetic variant. We set the proportion of the eQTL variance explained by the shared variant to 10% and we used the original sample size of the liver eQTL dataset described herein Results are shown in Until recently the assumption that, for a given GWAS signal, the causal variant in that interval had been genotyped was unrealistic. However, the application of imputation techniques To address this question, we used Illumina MetaboChip data and imputed the genotyped regions using the Minimac software . We thenOur results show that when the causal variant is directly genotyped by the low density array, the use of imputed data is not essential . HoweverStatistical power may also be affected by the mode of inheritance of the causal variant. To address this, we simulated cases under a recessive pattern of inheritance. Our results show that if the true model is recessive, but the eQTL signal is nonetheless analysed using the trend test, then we will often also successfully detect a colocalised signal .We compared the behaviour of our proposed test with that of proportional colocalisation testing It has been proposed that gene expression may be subject to both global regulatory variation which acts across multiple tissues and secondary tissue specific regulators We have so far assumed that each trait is associated with at most one causal variant per locus. However, it is not unusual to observe two or more independent associations at a locus for a trait of interest To illustrate this situation, we simulated datasets with two causal variants: one colocalised eQTL/biomarker signal plus a secondary independent “eQTL only” signal . These sN SNPs jointly to accommodate for N distinct associations per trait). However, this approach has two drawbacks. Firstly, the interpretation of the resulting posterior probabilities is more challenging in situations where some but not all of the variants are shared across both traits. More importantly, the typical approach consists of publishing single variant summary statistics, which would prevent the use of standard summary statistics, a key feature of our approach.The natural and statistically exact modification of our approach would compute, for each trait, Bayes factors for sets of SNPs rather than single SNPs . The LocusZoom association plots for each of these loci can be found in HLA-DQ/HLA-DR and TC (R and TC  but thesCEP250), we did not find a significant eQTL signal, pointing to potential differences in bioinformatics processing and/or imputation strategy. In such a situation, both PP3 and PP4 are low and PP0, PP1 and PP2 concentrate most of the posterior distribution.For only one locus  do not have enough evidence to strongly support either colocalisation or absence of colocalisation , but for which our method finds strong support for colocalisation (PP4 >75%). SDC1, TGOLN2, INHBB, UBXN2B, VLDLR, VIM, CYP26A1, OGFOD1, HP, HPR, PPARA. See CMTM6, C6orf106, CUX2, ENSG00000259359.SYPL2, IFT172, TBKBP1) which, based on our re-analysis, do not colocalise with the lipid traits, have a nearby gene with a high probability of colocalisation . This suggests that these genes are more likely candidates in this region. To explore the possibility that secondary signals may colocalise, we applied the stepwise regression strategy described above to deal with several independent associations at a single locus. We performed colocalisation test using eQTL results conditional on the top eQTL associated variant. Two of the loci  showed evidence of colocalisation with expression after conditional analysis . The website was developed using RWUI We developed a web site designed for integration of GWAS results using only p-values and the sample size of the datasets .The database and browser currently include the possibility of investigating colocalisation with liver We have developed a novel Bayesian statistical procedure to assess whether two association signals are colocalised. Our method is best suited for associations detected by GWAS, which are likely to reflect common, imputable, variations with small effects, or a rare variants with large effect sizes. Our aim differs from a typical fine-mapping exercise in the sense that we are not interested in knowing which variant is likely to be causal but only whether a shared causal variant is plausible. The strength of this approach lies in its speed and analytical forms, combined with the fact that it can use single variant p-values when only these are available.http://cran.r-project.org/web/packages/coloc).Our results show that to provide an accurate answer to the colocalisation problem, high-density genotyping and/or accurate use of imputation techniques are key. The quality of the imputation is another important parameter. Indeed, while the variance of the regression coefficient can be estimated solely on the basis of the minor allele frequency for typed SNPs and sample size (and the case control ratio in the case of a binary outcome) We currently assume that each genetic variant is equally likely a priori to affect gene expression or trait. A straightforward addition to our methodology would consider location specific priors for each variant, which would depend for example on the distance to the gene of interest, or the presence of functional elements in this chromosome region Another related issue is the choice of prior probabilities for the various configurations. For the eQTL analysis, we used a  results . In caseSORT1 gene). Several eQTLs will be colocalised, both between them and with the biomarker of interest. In this situation one would typically expect that a single gene is causally involved in the biomarker pathway but the colocalisation test with the biomarker will generate high PP4 values for all genes in the interval.The interpretation of the posterior probabilities requires caution. For example, a low PP4 may not indicate evidence against colocalisation in situations where PP3 is also low. It may simply be the result of limited power, which is evidenced by high values of PP0, PP1 and/or PP2. Moreover, a high PP4 is a measure of correlation, not causality. To illustrate this, one can consider the relatively common situation where a single variant appears to affect the expression of several genes in a chromosome region  eQTL/disease or disease/biomarkers comparisons are all of biological interest and use the same statistical framework. We expect that the fact that the test can be based on single SNP summary statistics will be key to overcome data sharing concerns, hence enabling a large scale implementation of this tool. The increasing availability of RNA-Seq eQTL studies will further increase the opportunity to detect isoform specific eQTLs and their relevance to disease studies. Owing to the increasing availability of GWAS datasets, the systematic application of this approach will potentially provide clues into the molecular mechanisms underlying GWAS signals and the aetiology of the disorders.While this report focuses on finding shared signals between a biomarker dataset and a liver expression dataset, we plan to utilise summary results of multiple GWAS and eQTL studies, for a variety of cell types and traits. In fact, our method can utilise summary results from any association studies. Disease/disease, , and specifying chunks of 1000 SNPs, with an overlap window of 200 SNPs on each side, which improves accuracy near the edges during the phasing step. Each chunk was phased using the program MACH1 with the number of states set to 300 and the number of rounds of MCMC set to 20 for all chunks. Phased haplotypes were used as a basis for imputation of untyped SNPs using the software Minimac with 1000 Genomes European ancestry reference haplotypes  to impute SNPs not genotyped on the Illumina array. Variants with a MAF less than 0.001 were also excluded post-imputation. The data was then collated in probability format that can be used by the R Package snpStats To speed up the imputation process, the genome was broken into small chunks that were phased and imputed separately and then re-assembled. This was achieved using the ChunkChromosome tool (http://genome.sph.umich.edu/wiki/minimac) between both datasets, we applied our colocalisation procedure. We conducted conditional analysis on SNPs with p-values eQTL p-values, effect sizes, and standard errors were obtained by fitting a linear trend test regression between the expression of each gene and all variants 200 kilobases upstream and downstream from each probe. After filtering out the variants with MAF <0.001, monomorphic SNPs, multi-allelic SNPs (as reported in 1000 Genomes or in the Ensembl database) and variants not sufficiently well imputed .The biomarker p-values from the meta-analyses (with genomic control correction) were obtained from a publicly available repository (http://csg.sph.umich.edu/locuszoom/).The regional association plots for the eQTL and Biomarker datasets were created using LocusZoom Q to the functional role corresponding to the five hypothesis P(S) is the prior probability of a configuration, D given a configuration S, and the sum is over all configurations S which are consistent with a given hypothesis h = . Thus, the probability of the data given a configuration is weighted by the prior probability of that configuration.We call a “configuration” one possible combination of pairs of binary vectors indicating whether the variant is associated with the selected trait. We can group the configurations into five sets, Next, to avoid computing the proportionality constant in The ratios in the numerator and denominator of A Bayes Factor for each SNP and each trait 1 and 2 was computed using the Approximate Bayes Factor ABF, . WakefieZ statistic and the shrinkage factor r is the ratio of the variance of the prior and total variance  on V, can be approximated using the MAF and sample size. However for imputed data it is preferable to use the variance outputted in standard regression analysis directly in the ABF equation. For the expression dataset used here, the variance and effect estimates from the regression analysis were used for computation of ABFs  and one biomarker, and each plot shows different sample sizes for the biomarker dataset. The variance explained by the causal variant for both the traits is colour coded. The x-axis shows the estimated PP4 for 1,000 simulations using data imputed from metaboChip Illumina array . The y-a(TIF)Click here for additional data file.Figure S2Simulation analysis with a shared causal variant between two studies, comparing results using imputed versus not imputed data where the causal SNP is not included in one of the datasets. The two datasets used are one eQTL (sample size 966 samples) and one biomarker, and each plot shows different sample sizes for the biomarker dataset. The variance explained by the causal variant for both the traits is colour coded. Column and row headings are the same as in previous figure. The causal SNP is not included in Illumina 660W panel.(TIF)Click here for additional data file.Figure S3The relationship between PP4 and the posterior predictive p-value  from proportional testing. Proportional testing uses the BMA approach, integrating over all possible two SNP models. Each row shows a different scenario, the total number of causal variants in a region is indicated by number of symbols in the plot titles with the type of causal variant indicated by the symbol: full circle - affects both traits; top only - affects one trait; bottom only- affects other trait. For proportional testing, the grey vertical line indicates the threshold ppp of 0.05. Each column shows the total proportion of trait variance for the biomarker explained by all variants in a region, with variance explained spread equally over all variants. In all cases, for the eQTL trait, n = 1,000, 10% of the variance explained by the variant; for the biomarker trait, n = 10,000.(TIF)Click here for additional data file.Figure S4The relationship between PP4 and the posterior predictive p-value  from proportional testing, using subset of SNPs which appear on the Illumina HumanOmniExpress genotyping array. For the eQTL trait, n = 1,000, 10% of the variance explained by the variant; for the biomarker trait, n = 10,000, 1% or 2% of the variance explained by the variant. Column and row headings are the same as in previous figure.(TIF)Click here for additional data file.Figure S5Regional Manhattan plots corresponding to loci listed in (PDF)Click here for additional data file.Figure S6ANGPTL3 locus. The x-axis shows the physical position on the chromosome (Mb) A: −log10(p) association p-values for LDL. The p-values are from the Teslovich et al published meta-analysis of >100,000 individuals. B: −log10(p) association p-values for ANGPTL3 expression in 966 liver samples.LDL association and eQTL association plots at the (TIF)Click here for additional data file.Figure S7Regional Manhattan plots corresponding to loci listed in (PDF)Click here for additional data file.Figure S8Simulation analysis with multiple shared causal variants. The first plot represents cases with only one causal variant in a region, while the following plots illustrate the behaviour of the statistic in the presence of an additional causal variant affecting the variance explained of the eQTL trait. In all scenarios, the first causal variant explains 10% of the variance of the eQTL trait. The second causal variant explains 1%, 5%, or 10% of the eQTL trait. We show the proportion of simulations with the posterior probability (PP3 or PP4) of the indicated hypothesis >0.9. Error bars show 95% confidence intervals . In all cases, for the eQTL sample size is 1,000; for the biomarker trait, the sample size is 10,000.(TIF)Click here for additional data file.Figure S9Simulation analysis with a recessive shared causal variant. The two datasets used are one eQTL  and one biomarker . The variance explained by the biomarker is colour coded and the shape of the dots represent the different mode of inheritance. The simulation procedure and distribution of the statistic are the same as defined in previous figure.(TIF)Click here for additional data file.Table S1Biom pval and eQTL pval report the lowest p-values found for the association with the trait listed and for the liver expression association respectively, with the corresponding SNP name (Biom SNP and eQTL SNP); the column Best Causal reports the SNP within the region with the highest posterior probability to be the true causal variant. The probabilities have been rounded to 1 significant figure.Results using reported loci that colocalise with liver eQTL. Published results of loci correlating with both liver expression and one of the four lipid traits  and posterior probability of different signal (PP3) and common signal (PP4) after applying colocalisation test. Each row lists the results for one probe, and the multiple entries for the same locus and trait represent multiple probes mapping to the same locus. the columns (PDF)Click here for additional data file.Table S2Signal includes genes that are part of overlapping regions and that colocalise at PP4 >75%; the column Region represents the genomic coordinates for the start and stop of the signal; in the column Tesl, “Y” indicates that this signal with any of the genes included has been reported to be an intermediate for any of the four lipid biomarker associations by Teslovich et al. ; the columns Biom pval and eQTL pval report the lowest p-values found for LDL association and for the expression association respectively, with the corresponding SNP name (Biom SNP and eQTL SNP); the column Best Causal reports the SNP within the region with the highest posterior probability to be the true causal variant. The probabilities have been rounded to 1 significant figure.eQTL/LDL colocalisation. Positive (PP4 >75%) eQTL/LDL colocalisation results between the liver eQTL dataset and the Teslovich meta-analysis using the most stringent prior for the probability that one SNP is associated with both traits, (PDF)Click here for additional data file.Table S3eQTL/HDL colocalisation. Positive (PP4 >75%) eQTL/HDL colocalisation results between the liver eQTL dataset and the Teslovich meta-analysis. Column and row headings are the same as in previous figure.(PDF)Click here for additional data file.Table S4eQTL/TG colocalisation. Positive (PP4 >75%) eQTL/HDL colocalisation results between the liver eQTL dataset and the Teslovich meta-analysis. Column and row headings are the same as in previous figure.(PDF)Click here for additional data file.Table S5eQTL/TC colocalisation. Positive (PP4 >75%) eQTL/HDL colocalisation results between the liver eQTL dataset and the Teslovich meta-analysis. Column and row headings are the same as in previous figure.(PDF)Click here for additional data file.Text S1Supplementary materials. Expanded methods, derivations and analyses.(PDF)Click here for additional data file.Text S2Overview of gene function of new colocalisation results associated with blood lipid levels and liver expression.(PDF)Click here for additional data file.


The X chromosome is generally understudied in association studies, in part because the analyst has had limited methodological options. For nuclear-family-based association studies, most current methods extend the transmission disequilibrium test (TDT) to the X chromosome. We present a new method to study association in case-parent triads: the parent-informed likelihood ratio test for the X chromosome (PIX-LRT). Our method enables estimation of relative risks and takes advantage of parental genotype information and the sex of the affected offspring to increase statistical power to detect an effect. Under a parental exchangeability assumption for the X, if case-parent triads are complete, the parents of affected offspring provide an independent replication sample for estimates based on transmission distortion to their affected offspring. For each offspring sex we combine the parent-level and the offspring-level information to form a likelihood ratio test statistic; we then combine the two to form a combined test statistic. Our method can estimate relative risks under different modes of inheritance or a more general co-dominant model. In triads with missing parental genotypes, the method accounts for missingness with the Expectation-Maximization algorithm. We calculate non-centrality parameters to assess the power gain and robustness of our method compared to alternative methods. We apply PIX-LRT to publically available data from an international consortium of genotyped families affected by the birth defect oral cleft and find a strong, internally-replicated signal for a SNP marker related to cleft lip with or without cleft palate. The X chromosome is unique in that males have only one, maternally-derived copy, while females are diploid. As a form of dosage compensation, a random X is inactivated in each cell early in female embryonic development Lyon, . Regionsp-values to test for association; they do not enable estimation of disease-related marker relative risks. The method we will propose is for case-parent triads, but accommodates triads with a missing individual.Most family-based methods available for X chromosome analysis are extensions of autosomal methods. The original transmission/disequilibrium test (TDT) was proposed to detect autosomal SNPs associated with disease in case-parent triads , and provide both robustness against bias due to population stratification and the opportunity to estimate disease-related marker relative risks .In the following sections, we initially describe the SSX-LRT and PIX-LRT for single X-linked SNP markers with complete genotype data. An extension of the approach then enables inclusion of families with missing genotype data. We assess Type I error rates for SSX-LRT, PIX-LRT, and X-LRT and compare power for the SSX-LRT, PIX-LRT, and XTDT by calculating chi-squared non-centrality parameters based on expected counts Agresti, . As an eM, F, and C denote the number of copies of the variant (minor) allele in the mother, father and affected offspring (proband), respectively. We exclude regions on the X that correspond to a homologous region on Y, including the pseudo-autosomal regions and the X-transposed region . Then M ∈ {0, 1, 2}, F ∈ {0, 1}, C ∈ {0, 1} for male offspring, and C ∈ {0, 1, 2} for female offspring. Consider tests of the null hypothesis that there is no association or no linkage against the alternative of association in the presence of possible linkage. Assume there is Mendelian transmission at that locus in the source population. Further assume parental allelic exchangeability in the source population, as in  is an offset term required because there are two ways for M to equal 1 . The parameters α1 and α2 are the log of half the odds that the mother carries 1 copy of the variant when the parents together have 1 and 2 copies, respectively. See Table 1 = α2 = 0, which under exchangeability is distributed as a central chi-squared with two degrees-of-freedom  of the affected offspring , modeled in a log-linear form, multiplying the sex-specific expected counts for each parental genotype pair by the probabilities shown in Table The analysis follows a multinomial for the counts based on both triad genotypes and sex  is proportional to:Here γExpression 3 can be rewritten as:With complete data, the nuisance parameters do not need to be explicitly estimated when calculating the maximum likelihood estimates for the relative risks and the likelihood ratio test statistic. Closed form solutions to the maximum likelihood equations for the relative risks and the corresponding likelihood ratio test statistic under specified genetic models of inheritance are given in Supplement When some genotype information is missing, we use the Expectation-Maximization (EM) algorithm as has been described  test statistics has a chi-squared distribution with two degrees-of-freedom.To form a test based on both families of affected sons and families of affected daughters, we recommend forming a combined test statistic. Let BS and GS (“+1” for relative risk >1 and “-1” for relative risk <1). Under the combined null hypothesis the results will be two independent standard Gaussian statistics. Let BN and GN be the number of triads with a heterozygous mother and an affected son or daughter, respectively. The weighted combined Z statistic is constructed as follows:However, rather than just computing the sum we note that the most plausible departures from the null would involve scenarios where the boys and girls experience the same direction of effect, that is, the variant either increases risk for both or decreases risk for both.  Accordingly, the following construction exploits that directional agreement to enhance power  can also be carried out in the context of the PIX-LRT method to be described.Similar analyses that either simplify the parameterizations or are aimed at testing X-inactivation relationships , and another that models M, F conditional on M+F and the sex of the affected offspring  above. But PIX-LRT will augment that by capturing information from the parents, rather than conditioning away that information (cf. the 12 stratification parameters included in Table M + F) is distributed across the two parents. Under the null hypothesis, for a SNP on the X chromosome, one would expect neither the mother's two chromosomes nor the father's single chromosome to be enriched for either allele. However, suppose the variant is linked to risk of the disease. Because the mother of an affected son was the source of his only X, the mothers of affected sons should be enriched for that variant as compared to the fathers. Because a father of an affected daughter transmitted his only X to his daughter, whereas the mother could transmit either one of her two X's to her daughter, the fathers of affected daughters should be enriched compared to the mothers. These resulting opposing patterns of enrichment within the parents can be exploited by conditioning on the sex of the affected offspring and the number of variant alleles the parents carry (M + F), taking advantage of our parental exchangeability assumption.We begin with some intuition to clarify why there is information in how a fixed number of variant alleles  for the distribution of a chi-squared likelihood ratio test statistic. Under the null hypothesis, the LRT statistic follows a central chi-squared distribution, which has an NCP of 0. The NCP is calculated by treating expected triad counts under the specified population structure as data used to fit the relevant models O'brien, . Values H0: no effect in males or females; (2) Hm0: no effect in males; (3) Hf0: no effect in females.To assess performance when there is admixture present in the population, we calculated the NCP for PIX-LRT, SSX-LRT, XTDT, and X-LRT. Consider two scenarios, each with two subpopulations of equal size, with no effect of the variant allele in either sex. In the first scenario, one subpopulation has a minor allele frequency of 0.3, a disease risk of 0.02 in males, and 0.02 in females. The second subpopulation has a minor allele frequency of 0.2, a risk of 0.01 in males, and of 0.02 in females. A second scenario is similar except in the first subpopulation the disease risk is 0.03 in females and the second subpopulation has a disease risk of 0.02 in males. For computational convenience we assume HWE within each subpopulation. The expected counts were calculated for 1000 families with affected offspring. Non-centrality parameters were estimated for tests of (1) BR is 1.5, and R2G1 = RG2 = 2. In the non-carriers, the disease risk in boys is twice that in girls. We calculate power  as a function of minor allele frequencies. We choose an alpha level of 5 × 10−6 as this approximates the alpha 0.05 Bonferroni-corrected value needed for the X chromosome. We modify X-LRT to account for a log-additive dose effect in girls. Therefore, the X-LRT test for a fetal effect involves two degrees-of-freedom.We compare PIX-LRT to X-LRT for a scenario where both are valid. We consider a setting in which there are 1000 triads, We also compare power of the PIX-LRT to the SSX-LRT and XTDT, under a homogeneous population, for computational simplicity. To calculate the NCP for the XTDT we use the method proposed by Deng and Chen . We do nR2G1 = RG2, and a minor allele frequency of either 0.3 or 0.1. We plot the non-centrality parameters as a function of the relative risk (RG1 for girls), and include the corresponding power for a one-degree-of-freedom LRT at alpha level 5 × 10−6.For our power analysis we consider settings in which sex-specific tests are of interest to highlight similarities and differences between the two sexes. We consider the following 500-triad scenarios: affected male offspring and a minor allele frequency of either 0.3 or 0.1; affected female offspring, BR to 2, and RG1 to 2. We plot the non-centrality parameter  as a function of the proportion of missing fathers, missing mothers, or a combination. For the combination scenarios, only one parent is missing, and twice as many fathers as mothers are assumed missing.To study the EM algorithm in PIX-LRT and SSX-LRT, we use the same scenarios and set p-value is 3.74 × 10−6.We applied PIX-LRT with the EM to the X chromosome data from the International Consortium to Identify Genes and Interactions Controlling Oral Clefts. The data were downloaded from dbGaP . We analyzed 1105 European families and 1286 Asian families. The clefting phenotype is divided into two categories: one is cleft palate only (denoted CPO) and the other is cleft lip with or without cleft palate (denoted CL/P). This phenotype split is based on genetic and embryological findings suggesting they are distinct Murray, . The gen10 to look for violations in exchangeability. This allows an overall assessment of exchangeability, but we recognize that SNPs that are truly associated with oral cleft may tend to violate exchangeability.We first test to see if any SNPs violate parental allelic exchangeability with Equation 1, using all pairs of parents. We use a QQ plot of –log10 against the marker position along the X chromosome (as determined by Build 37) can identify regions of interest.We run PIX-LRT with the EM on Asian and Caucasian families together and separately, allowing for different mating type parameters for each ethnic category. When the analysis is on the individual populations, only SNPs with a MAF greater than 0.02 in each population are studied . We test markers separately for cleft palate only (CPO) and cleft lip with or without palate (CL/P). The combined test statistic (1 df) is used to combine information from families with affected sons and daughters. For female triads, we applied a log-additive risk model (1 df). Plots of −logFor CL/P, we compared our top five SNPs using PIX-LRT with the EM to the top five identified in Patel et al. . For theUnder a null scenario, with an admixed population, where the relative risks are 1, the NCPs calculated for PIX-LRT and SSX-LRT (Equations 4 and 7) and XTDT are all zero, which ensures the nominal Type I error rate. Table −6 with a range of minor allele frequencies. The one degree-of-freedom combined PIX-LRT analysis outperforms the two degree-of-freedom X-LRT analysis. Figure −6 with varying disease relative risks. For complete triads, PIX-LRT has higher NCPs (and corresponding power) than both the SSX-LRT and the XTDT. The SSX-LRT and XTDT perform similarly (see Discussion). For instance, for 500 triads with affected sons and a SNP with a minor allele frequency of 0.3 and relative risk of 2, the PIX-LRT has an estimated NCP of 37.22 (power = 0.94), the SSX-LRT has an estimated NCP of 27.45 (power = 0.75) and the X-TDT has an estimated NCP of 26.92 (power = 0.73). For this scenario, the expected number of informative triads used in PIX-LRT is 347.31 compared to 242.31 in SSX-LRT and XTDT. These estimates decrease if the minor allele frequency is 0.1.Figure RG1 = 2 and a MAF of 0.3, the estimated NCP is 36.57 (power = 0.93). If instead, the disease relative risk in sons equals the disease relative risk in daughters with two copies of the variant allele, (RB1 = RG2 = R2G1), then for The NCP plots for 500 triads with affected daughters are similar to those of affected sons  are extreme outliers, less than 1 × 10−16. No father was found to carry any of these SNPs, despite some missing fathers having evidently transmitted the allele to their daughter. We consequently had reason to doubt the quality of the genotyping for those SNPs and omitted them from further analysis. [Patel et al. . The PIX-LRT estimated disease relative risk within the combined Asian and Caucasian populations was 0.48 for male offspring carrying the variant allele, and 0.56 for female offspring carrying one copy of the variant allele (0.32 for two copies), showing good concordance. Similar relative risks are estimated in separate analyses of the Asian and Caucasian populations  for CL/P within our analysis using PIX-LRT with EM and the top 5 SNPs based on the Patel et al. . The SNPs rs17269319, rs5906541, and rs12558269 were excluded for quality control reasons, as discussed above . Transmission-based tests may also be biased if the violation is due to genotyping error or because the SNP is associated with fetal survival. If a SNP affects risk through a maternal effect  and the X-chromosome-transposed region (XTR). These regions have homologous regions on the Y chromosome, so that a male can have two copies of a SNP.The NCP estimates obtained from SSX-LRT and the X-TDT are similar because these two tests are, respectively, the likelihood and score test for the same model. Schaid and Sommer  showed tWe applied PIX-LRT to an international consortium of genotyped families affected by the birth defect oral cleft. In a previous analysis of the data, some of the most significant SNPs identified as by Patel et al.  were notp-value signal. The rs5981162 SNP is located between genes EFNB1 and PJA1, and is downstream of these two genes. EFNB1 is known to play a role in facial development: mutations on EFNB1 are responsible for the majority of cases of craniofrontonasal syndrome (CFNS) (Twigg et al., EFNB1 gene and functional studies could be illuminating.With PIX-LRT, we identified rs5981162 as having a strong and protective effect on cleft lip with or with palate. This SNP was ranked fairly high in the previous analysis of the data by Patel et al. , but PIXThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


During the past decade, findings of genome-wide association studies (GWAS) improved our knowledge and understanding of disease genetics. To date, thousands of SNPs have been associated with diseases and other complex traits. Statistical analysis typically looks for association between a phenotype and a SNP taken individually via single-locus tests. However, geneticists admit this is an oversimplified approach to tackle the complexity of underlying biological mechanisms. Interaction between SNPs, namely epistasis, must be considered. Unfortunately, epistasis detection gives rise to analytic challenges since analyzing every SNP combination is at present impractical at a genome-wide scale. In this review, we will present the main strategies recently proposed to detect epistatic interactions, along with their operating principle. Some of these methods are exhaustive, such as multifactor dimensionality reduction, likelihood ratio-based tests or receiver operating characteristic curve analysis; some are non-exhaustive, such as machine learning techniques  or combinatorial optimization approaches . Genome-wide association studies (GWAS) have generated huge datasets in the past 8 years in order to find association between genetic polymorphisms and phenotypes. Individual risk prediction based on those discoveries was promising. Nevertheless, genetic architecture of complex diseases, such as type II diabetes, is still largely misunderstood , are not manageable at a genome-wide scale, we will next turn our attention to filtering strategies which aim at reducing the size of the dataset, thereby decreasing the size of the search space. A final section will deal with machine learning and data mining techniques. This review does not intend to provide an exhaustive list of all software programs designed to find epistatic interactions, but rather to give an overview of the main categories of strategies put forward in the last 5 years.During the past decade GWAS have played a central role in the discovery of genotype-phenotype associations. In GWAS analyses, geneticists rely on DNA polymorphism markers to detect these associations. One of the most popular classes of genetic markers, Single Nucleotide Polymorphism (SNP), allows comparison of allelic frequencies between a sample of cases ascertained for a disease and a sample of controls. In the standard approach, SNPs are tested one by one for statistical association with the disease  and a binary trait, the disease phenotype . The probability x) is an estimate of the odds ratio between the outcome and predictor variable x when values of other predictor variables are fixed. This is interesting because interpretation of odds ratios is intuitive. An odds is a measure related to probabilities. If an event has some non-null probability to occur in a particular experiment, odds for this event can be viewed has the ratio of the number of events to the number of non-events if the experiment were repeated multiple times. Thus, high odds correspond to high probability for this event, and vice versa. Given a probability p of occurrence for this event, an odds is defined as follows: Odds ratios are highly related to logistic regression models. Indeed, exp(βAn odds ratio (OR) is then simply the ratio of two odds. It evaluates association between disease occurrence and predictor variables. As such, this measure is closely related to statistical independence: if two variables  are statistically independent, their OR reduces to 1. Note that an OR not equal to 1 does not necessarily imply a statistically significant association.Based on Table Sasieni, .Thus, epistasis detection has become an important field of research in human genetics: more complex models are studied nowadays, where combinations of genetic variants are examined for association with a trait. From a biological point of view, it seems unlikely that some phenotypes are only driven by genetic variants acting independently. For instance, large and complex networks of gene-gene and protein-protein interactions are well known in systems biology for their high connectivity, density and resistance to variation  from statistical epistasis Cordell, . The terOn the other hand, statistical epistasis refers to the departure from additive effects of genetic variants at different loci with regard to their global contribution to the phenotype  are subject to false positive inflation when multiple tests are performed. For example, at a traditional 5% threshold set for statistical significance, there is a 5% chance to falsely reject the null hypothesis. Hence, if this test is performed 100 times when the null hypothesis is in fact true, and 5 tests are found to be statistically significant, then all 5 represent false positive associations. In this case, it is said that the risk is high and uncontrolled. This issue is known as the problem of multiple tests.Answer - Bonferroni correction is applied to properly adjust the type I error rate. It consists in dividing the significance threshold by the total number of tests performed. For instance, if a study involves testing for 100 000 hypotheses at a desired global 5%significance level, the corrected significance level for each test is set at Shortcoming - This method tends to reject non-null hypotheses due to its conservativeness. This conservative feature is also a shortcoming. It becomes inaccurate because it only favors strongly significant associations. As a result, many true positive associations will be missed , thereby leading to a loss in statistical power.We will introduce the Boolean operation-based testing and screening (BOOST) software program to exemplify this section. Designed to be fast, BOOST runs an exhaustive analysis of all potential pairwise SNP-SNP interactions  and the model that does consider them (full model).Once contingency tables are constructed, the program is ready to test for pairwise interactions. The way to detect epistasis complies with Fisher's epistasis definition  since authors look for a difference between the independent effect model  and the model which includes both marginal and interaction effects. In other words, for each SNP pair, BOOST tests for a departure from the linear additive model. Under the assumption of equivalence between a logistic regression model and its corresponding log-linear model Agresti, , this de2 test is statistically valid. But when contingency tables are sparse, this requirement is not met, thus leading to failure of epistatic interactions detection. Despite the fact that nearly all true positives are detected , BOOST is sensitive to type I errors  and shows comparative power of detection. A year later, an even faster version that relies on graphic processing units (GPU) instead of central processing units (CPU) was developed. However, an important shortcoming arises because BOOST heavily relies on contingency table construction: low minor allele frequencies (MAF) generate sparse contingency tables, which hampers the detection power of BOOST. Indeed, in each cell of the contingency table, a minimal number of individuals is required so that the χdifference in sensitivity and specificity (DSS). The goal is to quantify the gain in sensitivity and specificity of a ROC curve over another one  model-free approach in 2013 with the purpose of pairwise epistasis detection  is now a reference in the epistasis detection field. No parameters are estimated  and no assumptions are made on the genetic model  under this supervised classification approach. This strategy could detect interactions even when independent main effects are inexistent  is used to build the model and the remaining tenth (testing set) is used to evaluate this model. The model is built following the steps presented in Figure n Figure . This wan Figure . The clan Figure . The topAs the main feature of MDR is to reduce the data dimension, it can easily be combined with other classification methods  based on single-SNP associations significance, before testing for interactions between the selected markers , the procedure determines the nearest individuals  sharing the same phenotype (set noted S for same), and also the nearest individuals that show up the opposite phenotype (set noted O for opposite). If I and S show different values for a marker, then this variant discriminates individuals having the same phenotype, thus decreasing its importance. On the contrary, if I and O show different values for a marker, this variant discriminates individuals having different phenotypes, thereby its importance is increased. These steps are then repeated over a predefined number of individuals. Moore and coworkers showed in 2007 that ReliefF algorithm is scalable  is usually fixed at 10. Using such a predefined number may be considered as a selection bias since the information coded in the data is not fully exploited. To tackle this issue, SURF  proposes to take into account all neighbors within a given distance rather than a fixed number of neighbors  based on expert knowledge, and computational approaches solely driven by GWAS data (neither immune to bias from a statistician point of view). Similarly to computational exhaustive methods, this combined approach is taking advantage of artificial intelligence methods, which we discuss in the next section.Although data-integration techniques yield meaningful and biologically relevant results, exploiting external information sources like pathways or protein-protein interaction networks is controversial. Online databases are incomplete and so is our understanding of biological pathways. Thus, making use of them to build filters would in most cases results in a flawed analysis. Moore and Hill recently recommended  and browse through this space to find the more relevant combinations. Heuristics are commonly used in these algorithms, especially when dealing with genome-wide datasets in search of higher order genetic interactions. Identification of classification variables and interactions between them which allows outcome prediction is a well-known hurdle addressed by the machine learning and data mining fields of artificial intelligence Cordell, . In suchBox 3The aim of machine learning is to explain a system by learning a model with a training dataset. But dataset's particularities result in an overly tuned model adjusted for very specific features  in order to apply an ensemble procedure. An ensemble procedure aggregates the predictions of all trees to produce a powerful and robust prediction tool Breiman, . The SNPi. The tree is then grown up to its largest extent. These previous steps are repeated until a forest is built  . Then for each individual, all likelihood ratios are assembled into a unique one by averaging the total number of trees. Finally, a U-statistic is constructed with comparisons between assembled likelihood ratios of cases vs. controls in order to evaluate the joint association of the selected SNPs with the phenotype  = P(X|Y), then X is conditionally independent of Z, given Y (noted X ⊥ Z|Y). When applied to genetic data, variables are typically SNPs and phenotypic values. Bayesian networks offer an appealing and intuitive way to capture relationships existing between genetic markers and disease status. The structure learning of a Bayesian network amounts to a model selection problem. Because this learning is an NP-hard problem —variables are represented by nodes and dependencies between them are represented by directed edges. The probabilistic component of a Bayesian network associates a probability distribution with each node of the DAG, thus accounting for uncertainty. A Bayesian network encodes the Markov property: each variable is independent of its non-descendants, given its parents in the DAG. The governing theorem of a Bayesian network is the following. Let 2 test of association between a phenotype and a set of SNPs. A detailed explanation of its computation would require a much deeper presentation of BEAM, which is not the aim of this section. The interested reader is referred to Zhang and Liu  . In practice, this stage consists in finding the SNP X which is the most associated with the phenotype, given canMB : ¬(X Phenotype | canMB) ⇒ add X in canMB. This operation is repeated until canMB no longer changes from one iteration to the other. The second phase, called “backward phase,” aims at removing false positives that were included in the previous step. To achieve it, each SNP of the candidate Markov blanket is checked. A SNP Y is detected as a false positive if it is independent of the phenotype given a SNP subset of canMB. Three implementations of this approach were recently developed: DASSO-MB  showed that a Markov blanket-based approach could make the whole SNP set independent of the phenotype when conditioned on three other SNPs identified in the Markov blanket  is an original strategy based on natural selection and Darwinian evolution. The goal is to grow a computer program from several basic building blocks, similar to a DNA strand emerging from a composition of the four basic nucleotides. This program tries to reproduce the natural evolution process underlying complex real biological systems. The first question is what the building blocks are, whenever one wants to build such a computer program. The answer is non-trivial and is decisive in epistasis analysis when trying to avoid dependence to marginal effects. In a recent application of CES  which excludes SNPs with low predictive power, prior to performing epistasis detection, could be extended to other strategies like random forests, thereby improving detection of epistasis.a priori knowledge   instead of traditional central processing units (CPU).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


For almost all complex traits studied in humans, the identified genetic variants discovered to date have accounted for only a small portion of the estimated trait heritability. Consequently, several methods have been developed to identify rare single-nucleotide variants associated with complex traits for population-based designs. Because rare disease variants tend to be enriched in families containing multiple affected individuals, family-based designs can play an important role in the identification of rare causal variants. In this study, we utilize Genetic Analysis Workshop 18 simulated data to examine the performance of some existing rare variant identification methods for unrelated individuals, including our recent method (rPLS). The simulated data is used to investigate whether there is an advantage to using family data compared to case-control data. The results indicate that population-based methods suffer from power loss, especially when the sample size is small. The family-based method employed in this paper results in higher power but fails to control type I error. Our study also highlights the importance of the phenotype choice, which can affect the power of detecting causal genes substantially. With rapid advances in genotyping technologies, it has becoming increasingly feasible to efficiently sequence large number of individuals, which allows us to assess the role of rare variants in influencing complex traits. However, because each rare variant is present in only a small number of individuals, standard association tests designed for common variants have low power to identify rare variants associated with the trait. This fact has led to the development of new statistical tests specifically targeting rare variants.One may classify existing rare variant association methods into 2 categories: burden and nonburden tests. Burden tests, such as SUM  and combRecently, we proposed a 2-step method rare variant Partial Least Squares (rPLS)  to reveaAn important question that has not yet been addressed fully is the relative power of designs based on families and designs using unrelated individuals for identifying rare disease variants. All of the aforementioned methods that have been evaluated extensively are applicable to unrelated samples only. Utilizing the opportunity provided by Genetic Analysis Workshop 18 (GAW18), we compare the power of a family-based method, the modified family-based association test (FBAT)-v , for detThe GAW18 data contain genotypes for odd-numbered chromosomes from a real human whole genome sequencing study with phenotypes at 4 time points and 200 replicates of the simulated longitudinal phenotype data. In this study, we consider only genotypes on chromosome 3. We analyzed 1389 individuals in 20 pedigrees, ranging from 27 to 107 individuals, for the family design. One hundred and forty-two unrelated individuals having observed genotypes were extracted from these pedigrees and used for population-based analysis. Systolic blood pressure (SBP) and diastolic blood pressure (DBP) measurements at the first time point were taken as quantitative traits. An individual with SBP ≥140 mm Hg or DBP ≥90 mm Hg, or who was on antihypertensive medications at that examination was classified as a case. The resulting binary trait corresponding to hypertension (HTN) disease status was included in the analysis. Because age and sex are known to influence blood pressure, we also included them as covariates in the analyses.p SNVs (common and rare) in a gene or a genomic region are available with ij x= 0, 1, or 2 for i = 1,2,...,n and j = 1,2,...,p coding for the number for minor alleles at locus j for individual i. The goal is to test whether the variants within candidate gene are associated with trait y. In this section, the approach proposed for population data (rPLS) and other existing methodologies employed in the paper is briefly described.Suppose that genotypes for The 2-step procedure rPLS  has beeni = E(yi), g is a known link function such as the identity link for continuous and logit link for binary trait; β0 is the intercept; i x=  is the vector of p variants from individual i and β is the corresponding p × 1 unknown coefficient vector; i z=  is the vector of q non-SNV covariates for individual i; and γ is the corresponding q × 1 unknown coefficient vector.where μβ is obtained to determine a subset of SNVs with nonzero coefficient estimates. The corresponding n × k matrix of genotypes is denoted by where k (≤p) is the number of SNVs selected by EN.In the first step of rPLS, the elastic net (EN) estimator of the t, as an optimal linear combination of the variants in using partial least squares (PLS) , where the number of noncausal genes is 1030, 1036, and 1027 for the traits DBP, SBP, and PC1, respectively. These calculations were done using the nominal α = 0.001 threshold. Table MAP4 in any of the replicates. The SUM test provided higher power compared to SKAT and SKAT-O, with a slight increases in type I errors. On the other hand, rPLS had the highest power to detect MAP4 for all 3 quantitative traits, while type I errors were slightly elevated.The top causal variants for the simulated phenotypes DBP and SBP on chromosome 3 are in the gene SCAP, are causal for all traits, which is associated only with SBP. SEMA3F is a notable gene that could not be detected by any of the methods for the trait DBP but was detected 68 times with rPLS when PC1 was used. Four causal SNVs within SEMA3F have moderate and similar effect sizes for DBP and SBP. Therefore, combining information in DBP and SBP using the first PC seems to strengthen the signal and lead to higher power for detecting the association. Overall, Table Table MAP4 was detected, the ranking of the loadings indicated that causal SNV 3_48040284 had the largest value.Another important feature of the rPLS is its ability to identify the most important SNVs within a genomic region, a unique feature not available in the other methods. This can be done by simply ranking the weights (components of the first PLS loading vector) employed to find optimum linear combination. For instance, when we considered the SBP trait for replicate 5 in which For the family-based study, only 2 traits  and the fifth replicate were considered because of the computational burden. In addition to the causal genes, 50 noncausal genes were randomly selected to gauge type I error and accuracy rates that were calculated at α = 0.1%. Here, the type I error is equal to the number of significant unassociated genes divided by 50, while the power to detect association with SBP (HTN) is equal to the number of significantly associated genes divided by 21 (30). Accuracy is defined as the proportion of true results (both true positives and true negatives).MAP4) for SBP, so the highest accuracy was achieved by rPLS. Although 2 versions of FBAT-v give larger powers, they had inflated type I errors.As Table MAP4, SEMA3F, and SCAP genes to be associated with the traits for at least 10 replicates when rPLS is employed. It has been shown that the choice of the trait can affect the power of the test regardless of the methodology used. rPLS was the most powerful among the population-based tests without considerably elevated type I error. In general, the initial variant screening step in rPLS can lead to an elevated type I error, but as shown by Turkmen and Lin [Our analyses based on unrelated individuals have found  and Lin , the incFBAT-v yielded higher powers compared to results based on unrelated individuals but failed to control type I error rate. This is most likely a result of the existence of a large number of noncausal rare variants within the region. As mentioned in the original paper , linkageIn conclusion, although family-based methods can be more powerful because they can make fuller use of available data, further research is needed to find ways to control the type I error rate. Absent a more appropriate family-based method, rPLS emerges as a viable alternative for analyzing population-based data.The authors declare that they have no competing interests.AST and SL conceived the project, designed the algorithm and wrote the manuscript. AST implemented the algorithm and analyzed the data. SL supervised the research and polished the manuscript. Both authors read and approved the final manuscript.


As for many crops, new high-quality grapevine varieties requiring less pesticide and adapted to climate change are needed. In perennial species, breeding is a long process which can be speeded up by gaining knowledge about quantitative trait loci linked to agronomic traits variation. However, due to the long juvenile period of these species, establishing numerous highly recombinant populations for high resolution mapping is both costly and time-consuming. Genome wide association studies in germplasm panels is an alternative method of choice, since it allows identifying the main quantitative trait loci with high resolution by exploiting past recombination events between cultivars. Such studies require adequate panel design to represent most of the available genetic and phenotypic diversity. Assessing linkage disequilibrium extent and panel power is also needed to determine the marker density required for association studies.vs wine) and geographical origin (East vs West), and including the major founders of modern cultivars. With 20 simple sequence repeat markers and five quantitative traits, we showed that our panel adequately captured most of the genetic and phenotypic diversity existing within the entire Vassal collection. To assess linkage disequilibrium extent and panel power, we genotyped single nucleotide polymorphisms: 372 over four genomic regions and 129 distributed over the whole genome. Linkage disequilibrium, measured by correlation corrected for kinship, reached 0.2 for a physical distance between 9 and 458 Kb depending on genetic pool and genomic region, with varying size of linkage disequilibrium blocks. This panel achieved reasonable power to detect associations between traits with high broad-sense heritability (> 0.7) and causal loci with intermediate allelic frequency and strong effect .Starting from the largest grapevine collection worldwide maintained in Vassal (France), we designed a diversity panel of 279 cultivars with limited relatedness, reflecting the low structuration in three genetic pools resulting from different uses  contains supplementary material, which is available to authorized users. Vitis vinifera) is a crop of major economic importance. Worldwide, 73.7 million tonnes of grapes were produced on 7.5 million ha in 2014, and wine trade represented a gross value of 25.6 billion euros . Most datasets supporting the conclusions of this article are included within the article and its additional files, in the SNiPlay repository [http://sniplay.southgreen.fr/cgi-bin/SNPqueries_v3.cgi], in Lacombe et al. [Vitis database [http://www.eu-vitis.de/index.php]. The SNiPlay repository harbors sequence and variation data for several southern and Mediterranean plant species. Although the remaining SSR and phenotypic data will not be widely released before complete analysis, these data can be provided upon request.All plant material is available from the Vassal public repository, and accession information, including ID and passport data, is available on its website [e et al. , in the


Sus scrofa chromosome 7  accounted for ~40 % of the genetic variance for S/P. Objectives of this study were to estimate genetic parameters for PRRS S/P in gilts during acclimation, identify regions associated with S/P, and evaluate the accuracy of genomic prediction of S/P across populations with different prevalences of PRRS and using different single nucleotide polymorphism (SNP) sets.Our recent research showed that antibody response to porcine reproductive and respiratory syndrome (PRRS), measured as sample-to-positive (S/P) ratio, is highly heritable and has a high genetic correlation with reproductive performance during a PRRS outbreak. Two major quantitative trait loci (QTL) on All), SNPs in one (SNPMHC and SNP130) or both (SNPSSC7) QTL, or SNPs outside the QTL (SNPRest).Phenotypes and high-density SNP genotypes of female pigs from two datasets were used. The outbreak dataset included 607 animals from one multiplier herd, whereas the gilt acclimation (GA) dataset included data on 2364 replacement gilts from seven breeding companies placed on health-challenged farms. Genomic prediction was evaluated using GA for training and validation, and using GA for training and outbreak for validation. Predictions were based on SNPs across the genome . Genomic prediction accuracies ranged from low to moderate. Average accuracies were highest when using only the 269 SNPs in both QTL regions  contains supplementary material, which is available to authorized users. Porcine reproductive and respiratory syndrome (PRRS) is a major viral disease that impacts pork production worldwide  and resuReplacement gilts sourced from multiplier herds are usually introduced into commercial herds following acclimation and vaccination procedures that aim at exposing these naïve animals to pathogens (or antigens) that are common to the herd, such as the strains of PRRSV that are circulating in the herd. Due to the impact of PRRS on the swine industry, gilt replacement strategies have been developed with the objective of reducing the chances of introduction of new diseases in the herd or of infection of the replacement gilts . These sRecent studies on host responses to PRRSV indicate that selection for improved performance following PRRSV infection may be feasible for both sow reproduction , 3, 8 anSus scrofa (SSC) 2 (between 32 and 25 Mb) that accounted for 11 % of the total genetic variance for all markers across the genome (TGVM). They also reported two major QTL on SSC7 for S/P, which accounted for 40 % of the TGVM. One of these QTL was located in the major histocompatibility complex (MHC) region, between 24 and 31 Mb, and accounted for ~25 % of the TGVM. The other QTL on SSC7 was located between 128 and 129 Mb and accounted for ~15 % of the TGVM. These two QTL for S/P on SSC7 were recently validated on an independent commercial dataset  by ELISA  at GREMIP  and for genotyping with the Illumina PorcineSNP BeadChip  at Delta Genomics . S/P was measured at four time points: at entry , ranging from 0 to 0.07. These estimates were usually combined with large standard errors and sometimes could not be estimated due to very low genetic variance. Therefore, only analysis of S/PPost-acclimation will be described in the remainder of this paper, which hereafter will be referred to simply as S/P.Preliminary analyses revealed that S/P0%, S/P25%, S/P50%, S/P75%, and S/P100% datasets, respectively. Only CG with at least 10 animals were used for these calculations and further analyses (two CG were excluded). The numbers of animals, CG, commercial herds, and multipliers, as well as the percentage of PRRSV-seropositive animals across S/P datasets are in Table 0%, were equal to 2346, 95, 23, and 17, respectively, and for S/P100% to 1361, 56, 20, and 14, respectively. Data from all seven genetic suppliers were included in each S/P dataset.Five S/P ratio GA datasets were created based on the percentage of animals with a positive (S/P ≥ 0.4) PRRSV ELISA test within a CG, with the objective of assessing its impact on heritability estimates and genomic prediction accuracies. Thresholds used to create the datasets were: ≥0, ≥25, ≥50, ≥75, and 100 % positive gilts within a CG, which will hereafter be referred to as the S/PA total of 3615 animals were genotyped using the Illumina PorcineSNP BeadChip and 48, 1710, and 1857 of these animals were genotyped using versions 60 K v.2, 60 K v.2B, and 80 K, respectively . These versions include 62,163, 61,565, and 68,528 SNPs, respectively. A total of 42,145 SNPs that were common to all three versions were used for subsequent analyses.Before analyses, the genotypes of the GA dataset were evaluated for quality. First, genotypes with a GenCall score lower than 0.5 were set to missing (5.25 %). Second, SNPs that had less than 80 % of genotypes called across all individuals (3954 SNPs) were excluded from the dataset. The final dataset included 38,191 SNPs for 3615 individuals and had a genotype call rate of 99.48 %. The genotype data of the outbreak dataset were filtered in order to include the same 38,191 SNPs.Missing genotypes were replaced with the mean coded  of the SNP genotype within a multiplier to avoid problems with the statistical methods used (see below). For SNPs that were completely missing within a multiplier, the mean genotype was calculated using all individuals provided by the genetic supplier for that multiplier. No SNP was completely missing within genetic supplier.Post-acclimation) on 503 gilts, exclusion of another nine gilts based on the number of animals within CG and of another nine due to missing genotype data, final analyses were performed using 2346 gilts with phenotypes and genotypes.Of the 3615 genotyped animals, 2947 were gilts and 668 were parents of the gilts. Although we had neither the phenotypes on the parents, nor pedigree information on the gilts to identify their parents, we kept the parental genotypes in the dataset to make use of their genomic relationships. Visual inspection of the genomic relationships showed inconsistent relationships of some animals with others from the same multiplier and/or genetic supplier. For instance, 80 animals showed genomic relationship coefficients lower than 0.03 with more than half of the animals from the same multiplier herd, and thus, were excluded, which resulted in 2867 gilts with genotype data. However, due to missing phenotypic data for S/P (S/PA genomic relationship matrix (GRM) was estimated for the GA dataset as proposed by VanRaden , using 3yij is the observed phenotype of individual j at the ith level of CGi, CGi is the ith level of the fixed-effect of contemporary group, uij is the breeding value, and eij is the random error. Vectors of breeding values and residual effects were assumed to be normally distributed as: Using the GRM, the following genomic model was used to estimate variances and genetic parameters with ASReml 4.0 :\documeno et al. .π [π = 0.987) and Bayes-B with this estimate of π was used for the GWAS, consistent with the original analysis of Serão et al. [Bayesian genomic prediction methods were used to perform a genome-wide association study (GWAS) for S/P, using GenSel version 4.4  ratio. Iπ  was usedo et al. .π [π) for each training dataset. Three genomic prediction methods were used for training, with two methods based on the estimated π (Bayes-B and Bayes-C) and one using π = 0 . Estimates of π were similar across training datasets, ranging from 0.987 to 0.991.Bayesian genomic prediction methods were used to estimate the effects of SNPs in the training dataset, using the same models as used for GWAS in GenSel version 4.4 . Bayesiaπ  was usedAll).All SNPs across the genome (SNPMHC region (SNPMHC).SNPs in the QTL130 region (SNP130).SNPs in the QTLMHC and QTL130 regions (SNPSSC7).The combination of SNPs in the QTLMHC and QTL130 regions (SNPRest).All SNPs across the genome excluding those in the QTLEstimates of SNP effects for S/P were obtained by including all SNPs in the training analyses. Based on the initial findings of Serão et al. , five seMHC and QTL130 were located within the regions between 24 and 30 Mb and between 128 and 129 Mb on SSC7, respectively, the QTL intervals that were used herein were obtained from the GWAS of each of the five S/P datasets. The QTL intervals were defined using the two outermost 1-Mb SNP windows that explained at least 1 % of TGVM. Within the outermost 1-Mb windows, the SNP that had the highest posterior probability of inclusion (PPI) [0% analyses   was idenon (PPI)  and to rTo assess the accuracy of S/P predictions, two training and validation scenarios were used.The GA dataset was used for training and the outbreak dataset was used for validation. Genotypes of 425 individuals that were from the same genetic supplier as the outbreak dataset were excluded from the training (GA) dataset for this analysis, which will hereafter be referred to as the reduced-GA dataset and included 1939 animals from six genetic suppliers. Independence of the outbreak and reduced-GA datasets was assessed by principal component analysis of the genotype data.100% dataset were used in order to allow comparison to accuracies obtained in scenario 1, since all animals in the outbreak dataset were also tested positive. Preliminary analyses showed that using S/P100% for validation yielded slightly better and more consistent results across SNP sets than other S/P datasets.Data from six of the seven genetic suppliers were used as the training dataset and data from the other genetic supplier was used as the validation dataset. This was repeated until all seven genetic suppliers were used as the validation dataset. For validation, only CG included in the S/PThe numbers of individuals used for training and validation are in Table Population structure of the GA dataset was evaluated by constructing a neighbor joining  phylogenGEBV) with phenotypes from the outbreak dataset adjusted for estimates of fixed-effects  , and h2 ni are the correlation of GEBV with ith genetic supplier validation dataset. Phenotypes were adjusted for estimates of the fixed effect of CG obtained from the validation dataset only, using a model that included only CG as fixed effect. The marker-based heritability (h2) used in this step was from the whole S/P100% GA dataset  was slightly higher than that for the GA dataset with 100 % PRRSV-seropositive animals, primarily because of a lower residual variance estimate.Estimates of genetic parameters for S/P are in Table 0%  were similar to those for S/P0%.Results from GWAS using the GA dataset and the original analysis of the outbreak dataset of Serão et al.  are in F0% Fig. b and S/P0%, are in Table MHC and QTL130 accounted for 20.1 and 6.7 % of the TGVM, respectively, for S/P0%  and e (SNPRest) demonstrate that the reduced-GA and outbreak datasets were genetically independent, with the two groups clustering in different areas of the plot. When using the other SNP sets  and reduced-GA (training) datasets Fig. . The firAll  than those based on QTL SNPs, i.e. 0.008, 0.007, and 0.008 for SNPMHC, SNP130, and SNPSSC7, respectively.Since the GA dataset included data from seven genetic suppliers, we assessed differences in genetic background between genetic suppliers based on their genetic distances for each of the five SNP sets Fig. . ResultsAll Fig. a and SNPest Fig. e were thest Fig. b–d diffeSSC7 resulted in the highest accuracy, followed by SNPMHC, SNPAll, SNP130, and SNPRest, with overall average accuracies across methods and S/P datasets of 0.39, 0.34, 0.26, 0.21, and 0.05, respectively. For the GA validation dataset, SNPSSC7 resulted in the highest accuracy, followed by SNPAll, SNPMHC, SNP130, and SNPRest, with overall average accuracies of 0.31, 0.28, 0.25, 0.22, and 0.12, respectively. In general, Bayesian model selection methods (Bayes-B and Bayes-C) showed higher accuracies than GBLUP. This was always the case when the outbreak dataset was used for validation, but GBLUP showed higher accuracies than Bayes-B and Bayes-C with the GA validation dataset for SNPMHC .Genomic prediction accuracies for the outbreak Fig. a and GA 0% to S/P75%. However, this decrease in accuracy was greater when using SNPAll than when using QTL SNPs. In contrast, when performing cross-validation with the GA dataset, there was an increase in genomic prediction accuracies from S/P0% to S/P75%.Increasing the percentage of PRRSV-seropositive animals in the GA dataset used for training had opposite effects on accuracies of prediction in the outbreak and GA datasets. When the outbreak dataset was used for validation, there was a steady decrease in accuracy as the percentage of PRRSV-seropositive animals increased from S/PThis study analyzed data from commercial herds to (1) identify and validate genomic regions associated with PRRSV ELISA antibody response, measured as S/P ratio; (2) evaluate the use of different SNP sets, with or without QTL SNPs, for genomic prediction of S/P in commercial gilts and sows; and (3) assess the impact of the proportion of PRRSV-seropositive animals on heritability estimates and accuracy of genomic prediction.MHC), which harbors genes associated with immune response to infectious diseases and vaccines [130, explained ~15 % of the TGVM [MHC. Serão et al. [tumor necrosis factor receptor-associated factor 3 gene (TRAF3), which has an important role in immune response activation [Serão et al.  performevaccines , and expvaccines . Associavaccines , 25, PRRvaccines , and witvaccines . The othtivation . Due to MHC and QTL130. In both the GA and outbreak datasets, S/P ratio was measured, on average, around peak PRRS antibody response (40 to 60 days after exposure), although the time of measurement varied greatly in the GA data (from 26 to 103 days) following introduction into the herd. Additional studies are necessary to evaluate the impact of the time of S/P ratio measurement and of method of exposure on genomic prediction accuracies.The PRRSV antibody response data used in this study were collected on commercial animals sourced from different genetic suppliers and reared under standard production settings in commercial herds. The use of field data has several advantages, such as working with a large sample size, use of animals from different genetic backgrounds (genetic suppliers and multipliers) that represent current commercial crossbred genetics, and the use of different environments under a range of disease pressures and current industry production practices. However, the main disadvantages of using field data are the variability in management and data collection procedures between farms, such as the use and timing of vaccination, inability to account for multiple unidentified sources of variation, and limitations in obtaining additional information that could improve the analyses, such as age of the animals and complete pedigree. However, in spite of the heterogeneity of the GA dataset, we obtained several promising results, including moderate to high heritabilities of PRRSV antibody response of replacement gilts, measured as S/P after the acclimation period, and low to moderate-high accuracies of genomic prediction of antibody response following a reproductive PRRS outbreak based on S/P following acclimation, especially when using SNPs located within QTLAnother point that requires attention is the fact that none of the animals used in this study were experimentally infected with PRRSV. In the outbreak dataset, all animals were naturally infected with PRRSV and infection likely occurred within a limited amount of time. In contrast, in the GA dataset, pigs within a CG were exposed using different methods, including vaccination with a modified live PRRSV, natural exposure, or deliberate exposure using other acclimation methods, but the specific method used for each CG was uncertain. In addition, the timing of the outbreak or vaccination was variable and often unknown. Nevertheless, it is known and expected that natural PRRSV infection and response to modified live PRRSV vaccination result in similar antibody responses . NeverthEstimated heritability of S/P was numerically lower in the GA datasets (0.28 to 0.47) than in the outbreak dataset (0.54). This is likely due to the greater uniformity of the data in the outbreak herd. For example, all animals in the outbreak dataset were from the same genetic source and farm. In addition, the outbreak dataset was composed of animals that underwent a PRRS outbreak during the same period of time. These more homogeneous environmental conditions were reflected in the lower residual variance for the outbreak dataset (from 0.07 vs. 0.10 to 0.16 for the GA datasets). However, the marker-based heritability (0.54) reported here for the outbreak dataset was greater than the pedigree-based estimate (0.45) reported by Serão et al.  for the In general, the estimate of residual variance for S/P decreased and the estimate of genetic variance increased as the percentage of positive animals for the PRRSV ELISA test within CG increased, thereby increasing heritability estimates Table . The impMHC and QTL130 were positioned between 22.9 and 33.5 Mb and between 127.9 and 132.5 Mb on SSC7, respectively, compared to between 24.0 and 30.9 Mb and between 128.0 and 129.9 Mb in the previous study of Serão et al. [The locations of the QTL identified in this study encompassed the two regions that were originally reported by Serão et al. , using t0% to S/P75%. QTLMHC had similar %TGVM in the GA dataset (~20 %) as in the outbreak data (~25 % [130 were lower in the GA dataset (S/P0% to S/P75%) than in the outbreak dataset, with ~7 and ~15 % of the TGVM, respectively. For S/P100%, the %TGVM explained by these QTL was slightly lower (15.2 % for QTLMHC and 4.7 % for QTL130) than for S/P0% to S/P75%. These differences could be due to the big drop in sample size from S/P75% (n = 1849) to S/P100% (n = 1361). Nevertheless, these results are promising, considering that the outbreak data included data from only one herd and genetic line, while the GA data included data from multiple genetic suppliers, multipliers and commercial herds.Overall, the GWAS results were consistent across S/Pa (~25 % ). ResultAll  showed considerable relationships across populations, suggesting that these sets of SNPs should indeed result in higher across-population genomic prediction accuracies.Thus, both methods used to assess within- and across-population diversity showed that SNPReports on genomic prediction of antibody response are scarce in the literature. In poultry, Liu et al.  evaluateRest) to moderate-high , which suggested that the rest of the genome had little predictive ability and that only SNPs within the two QTL (QTLMHC and QTL130) were needed to obtain sizeable genomic prediction accuracies across genetically different populations. Although accuracies differed between folds (i.e. genetic suppliers), S/P datasets, and SNP sets when using the GA dataset , the differences in accuracies when validation was done with the GA versus the outbreak dataset were interesting; while there was a clear increase in genomic prediction accuracies as the percentage of PRRSV-seropositive animals in the training dataset increased (S/P0% versus S/P100%) when validation was done with the GA dataset, accuracies decreased from S/P0% to S/P100% when using the outbreak data for validation. Based on the increase in heritability with increasing % of positive animals in the GA training dataset, one would expect accuracies to increase with % of positive animals. However, the increase in % of positive animals in the GA training data was confounded with a decrease in the size of the training data, which is expected to decrease accuracies. In order to assess the effect of sample size on genomic prediction accuracies using the outbreak validation dataset, we randomly selected CG from the reduced-GA training dataset to have a similar number of animals as in the S/P100% dataset (n = 1233) and a similar percentage of PRRSV-seropositive animals in S/P0% (81 %). We performed five replicates and results yielded similar accuracies (e.g. average accuracy of 0.323 using Bayes-B) as obtained when using S/P100% for training and validating with the outbreak data. Thus, the drop in accuracies with the outbreak dataset from training on S/P0% to S/P100% was due to the smaller number of animals used for training, and not due to differences in the % of positive animals.Overall, the accuracies of genomic prediction for PRRS S/P ratio that we obtained in this study ranged from low  was needed to achieve the highest accuracy, while with the GA dataset, the largest training population size  resulted in lower accuracies.However this does not explain the increase in accuracy with % of positive animals that was observed for the GA validation data. There are several differences between the GA and outbreak validation datasets that may have contributed to these opposite trends in accuracies. For example, although “noisy”, the data from different herds within the GA dataset are expected to be more similar to each other than to the outbreak dataset, since the GA dataset included data from several commercial production herds, while the outbreak dataset was composed of data from a more controlled environment . In addition, the impact of sample size and % of PRRSV-seropositive animals on the accuracy of genomic prediction could also be a factor explaining the differences in results between validation datasets. When validation was done with the outbreak dataset, a larger training population size , the accuracy based on SNPSSC7 based on additivity is expected to be SSC7 (0.31) across all methods and S/P datasets. This was also observed for the outbreak dataset: SSC7. These results also showed that selection based on only 269 SNPs (i.e. SNPSSC7) would result in greater response to selection for PRRS S/P, compared to using the whole genome .Genomic prediction accuracies obtained across all methods and validation and S/P datasets suggest that the effects of the two major QTL on SSC7 for S/P are additive and, thus, orthogonal to each other; accuracies using SNPHowever, it should be noted that there is general concern about losing genetic variability in the MHC region . Due to MHC and QTL130) were validated as being associated with S/P in all datasets. In addition, results from this study indicate that the magnitude of the PRRSV IgG response by S/P ratio can be predicted across populations and from S/P measured during acclimations and PPRSV vaccination to S/P measured in a natural reproductive PRRS outbreak with low to moderate accuracies using SNP genotypes. Moderate genomic prediction accuracies were obtained by using only the SNPs within the two major QTL regions, with overall accuracies across all scenarios of 0.39 and 0.31 for the outbreak and gilt acclimation datasets, respectively. SNPs in the QTLMHC region showed overall greater predictive ability (0.34 for the outbreak and 0.25 for the gilt acclimation datasets) than SNPs in the QTL130 region (0.21 for the outbreak and 0.22 for the gilt acclimation datasets). In addition, genomic prediction accuracies using the rest of the genome (SNPRest) indicated that SNPs not located within the two major QTL had little to no predictive ability for S/P. Overall, variable selection methods (Bayes-B and Bayes-C) resulted in greater genomic prediction accuracies than Bayesian GBLUP.Results from this study using field data show that PRRSV antibody response, measured as sample-to-positive ratio, had moderate to high heritabilities, with estimates increasing as the proportion of PRRSV-seropositive animals increased in the dataset. The two major QTL for S/P that were previously found on SSC7 (QTLOur findings suggest that PRRSV antibody response (S/P ratio) in replacement gilts following standard acclimation procedures or in reproductive sows at approximately 45 days post-natural PRRSV infection can be predicted with high accuracy by using the SNPs that are included in just two QTL. Combined with our previous result, i.e. that S/P ratio is genetically correlated with reproductive performance during PRRS outbreak, this suggests that reproductive performance during PRRS infection can be selected for using PRRS S/P ratio or genomic predictions for S/P ratio, although further research is needed to validate these results. Due to the nature of the data, we were not able to assess the impact of using crossbred versus purebred animals for training or validation, or the impact of vaccination, or of the environment (production versus multiplier), or of the age of animals (gilts versus sows). Therefore, additional studies are needed to address these issues and better understand the role of these factors on the host genetics of antibody response to PRRSV.