The contributions of the proposed approach are three-fold: 1) We consider all possible genotype models for each locus, thereby enabling identification of combinatorial relationships between multiple loci. 2) We develop a framework for the integration of PPI and eQTL into a heterogenous network model, enabling efficient identification of functionally related variants that are associated with the disease. 3) We develop a novel method to integrate the genotypes of multiple loci in a PoCo into a representative genotype to be used in risk assessment. We test the proposed framework in the context of risk assessment for seven complex diseases, type 1 diabetes (T1D), type 2 diabetes (T2D), psoriasis (PS), bipolar disorder (BD), coronary artery disease (CAD), hypertension (HT), and multiple sclerosis (MS). Our results show that the proposed method significantly outperforms individual variant based risk assessment models as well as the state-of-the-art polygenic score. We also show that incorporation of eQTL data improves the performance of identified POCOs in risk assessment. We also assess the biological relevance of PoCos for three diseases that have similar biological mechanisms and identify novel candidate genes. The resulting software is publicly available at http://compbio.case.edu/pocos/.Susceptibility loci identified by GWAS generally account for a limited fraction of heritability. Predictive models based on identified loci also have modest success in risk assessment and therefore are of limited practical use. Many methods have been developed to overcome these limitations by incorporating prior biological knowledge. However, most of the information utilized by these methods is at the level of genes, limiting analyses to variants that are in or proximate to coding regions. We propose a new method that integrates protein protein interaction (PPI) as well as expression quantitative trait loci (eQTL) data to identify sets of functionally related loci that are collectively associated with a trait of interest. We call such sets of loci “population covering locus sets” . Earlier studies only focus on individual genetic variants. However, studies on disease mechanisms suggest the aggregation of genomic variants may contribute to diseases. For this reason, researchers commonly use prior biological knowledge to identify genetic variants that are functionally related. However, these approaches are often limited to variants that are in the coding regions of genes. However, several risk variants are in the regulatory region. Here, we incorporate known regulatory and functional interactions to find sets of genetic variants which are informative features for risk assessment. Our result on seven complex diseases show that our method outperforms individual variant based risk assessment models, as well as other methods that integrate multiple genetic variants. RecentlAn important problem with GWAS is that the identified variants account for little heritability , 9. HoweThe Polygenic score is a commonly used method to identify the joint association of a large mass of the loci to predict disease risk . The firet al. propose a method to discover sets of genomic loci that are associated with a phenotype while being connected in an underlying biological network [Since detection of epistasis and higher order interactions is computationally expensive, many methods first assess the disease association of individual loci and then use functional knowledge to integrate these associations –26. The  network . They us network . Several network .oCos) [oCo is a set of loci that harbor at least one susceptibility allele in samples with the phenotype of interest. Here, we extend the notion of PoCos to enable adaptive identification of “susceptibility genotype”  for each locus. We also develop a method for aggregating the genotypes of multiple loci in a PoCo to compute representative genotypes for use in risk assessment. Finally, in order to capture the functional relationship between genomic loci, we integrate GWAS data with human protein-protein interaction (PPI) network and regulatory interactions identified via expression quantitative trait loci (eQTL).In this paper, we propose a new algorithm for the identification of multiple functionally related genomic variants that are collectively associated with a phenotype. The proposed method builds on the concept of “Population Covering Locus Sets” (PoCos) , 34. A PoCos identified by the proposed framework to construct features that can be used in risk assessment. We evaluate the performance of PoCos in risk assessment via cross-validation on seven GWAS case-control data sets obtained from the Wellcome Trust Case-Control Consortium (WTCCC). We compare the risk assessment performance of models built using PoCos to that of models built using individual loci and polygenic score. Our experimental results show that PoCos significantly outperform individual loci and polygenic score in risk assessment. Furthermore, we assess the information added by the incorporation of PPI and eQTL and observe that inclusion of these data leads to more parsimonious models for risk assessment.We use the PoCos. Then we describe how we use PoCos to develop a model for risk assessment. Subsequently, we present comprehensive experimental results on GWAS data sets for Type 2 Diabetes (T2D), Psoriasis (PS), Type 1 Diabetes (T1D), Hypertension (HT), Bipolar Disorder (BD), Multiple Sclerosis (MS) and Coronary Artery Disease (CAD). Our results show that the proposed method significantly outperforms individual variant based risk assessment model as well as the state-of-the-art polygenic score. We also observe that integrating prior biological information leads to more parsimonious models for risk assessment.In the next section, we describe the proposed procedure for modeling the genotypes and identifying PoCos) and describe the algorithm we use to identify PoCos. Finally, we describe our feature selection framework for the selection of PoCos to be used for risk assessment. The workflow of the proposed method is presented in In this section, we first present the set-up for genome-wide association studies. We then define “Population Covering Locus Sets” , where C denotes the set of genomic loci that harbor the genetic variants  that are assayed, S denotes the set of samples, g denotes the genotype of locus c ∈ C in sample s ∈ S, and f(s) denotes the phenotype of sample s ∈ S. Here, we assume that the phenotype variable is dichotomous, i.e., f(s) can take only two values: if sample s is associated with the phenotype of interest , s is called a “case” sample (f(s) = 1), otherwise , s is called a “control” sample (f(s) = 0). We denote the set of case samples with S1 and the set of control samples with S0, where S1 ∪ S0 = S. While we focus on qualitative traits here for brevity, the proposed methodology can also be extended to quantitative traits  is a continuous phenotype variable).The input to the problem is a genome-wide association (GWA) dataset The minor allele for a locus is usually defined as the allele that is less frequent in the population. While it is common to focus on the minor allele as the risk allele, specific genotypes can also be associated with a phenotype –37. Diffmi).5. Presence of Major Allele: The locus is considered to harbor a genotype of interest if at least one copy contains the major allele. This is the complement of m(1).m4 and m5 are complements of other models, we consider them separately. This is because, as we discuss in the next section, the 1s and 0s in the binary genotype profiles are considered asymmetrically while integrating the genotypes of multiple loci. Also note that “homozygous minor allele or homozygous major allele” is not considered since it is not associated with a specific risk allele.Note that, although models To select a genotype model for each locus, we separately assess the association of the resulting five genotype profiles with the phenotype of interest. Subsequently, we choose the model that leads to greatest discrimination between cases and controls, and use the respective binary genotype profile as the representative genotype of that locus. This process is illustrated in c, binarization according to the five different genotype models produces five |S|-dimensional binary genotype profiles mi)((c), i ∈ {1, … 5}. For each binary genotype profile mi)((c), we compute the difference in the fraction of case and control samples that harbor the genotype of interest as follows:1 denotes a vector of all 1’s and <.> denotes the inner product of two vectors. We then determine the binary genotype model for each locus as the model that maximizes the difference of relative coverage between case samples and control samples, i.e.:For each locus oCos). In previous work, we define and use PoCos in the context of prioritizing locus pairs for testing epistasis [oCo to utilize five different models for determining the genotypes of interest, as described in the previous subsection.Once we compute the binary genotype profiles for all loci, we identify Population Covering Locus Sets | = |S1| while minimizing |T(P)|. Note that, since we are interested in finding all sets of loci with potential relationship in their association with phenotype, we do not define an optimization problem that aims to find a single PoCo with minimum |T(P)|. We rather develop an algorithm to heuristically identify all non-overlapping PoCos with minimal |T(P)|.A PoCos, we use a greedy algorithm that progressively grows a set of loci to maximize the difference of the fraction of case and control samples covered by the loci that are recruited in a PoCo. In another words, we initialize P to ∅ and at each step, add to P the locus that maximizesS′ = S\(E(P) ∪ T(P)). The algorithm stops when all case samples are covered. We then record P, remove the loci in P from the dataset, and identify another PoCo. This process continues until it is not possible to find a set of loci that covers all case samples.To identify all non-overlapping PoCos. The first type of PoCos (named “network-free PoCos”) are identifed using the greedy algorithm described above, without the use of any prior biological information. The second type of PoCos are NetPocos, which are identified by restricting the search space to connected subgraphs of a network of potential functional relationships among genomic loci. As we describe below, this network is constructed by integrating established locus-gene associations from eQTL studies and protein-protein interaction (PPI) data that contains functional relationships among genes.We develop two methods to identify two different types of PoCos, the search space for the problem contains all the loci that are genotyped and no restriction is applied on the search space. We use δ(.) to guide the search for PoCos, and require the search to proceed until all case samples are covered.For network-free PoCos. This approach is inspired by the NetCover algorithm that is used to identify dysregulated subnetworks in the context of cancer [etPocos, in addition to GWAS data, we utilize a heterogeneous networkG =  that represents the functional relationships among genomic loci. The network contains two types of nodes: genomic loci and genes/proteins. More precisely, the set U ⊆ C contains all genomic loci that are genotyped in the GWAS and are located in the gene region of interest or are expression quantitative trait loci. The set V contains all human genes/proteins.Since our aim is to find sets of variants that are related to each other in their association with a phenotype, interaction data can provide a useful functional context for Pf cancer . To idenThe interactions and associations between these nodes are represented by three different sets of edges:F contains an edge between locus c ∈ U and gene v ∈ V if c is in the region of interest  of v. We call these edges RoI edges.Q contains an edge between locus c ∈ U and gene v ∈ V if c is found to be significantly associated with the expression of v in an expression quantitative trait loci (eQTL) screen. We refer to these as eQTL edges.E contains an edge between two genes u and v if u and v code for interacting proteins. We refer to these as PPI edges.et al. [Note that Azencott et al.  also proetPocos is illustrated in oCos. However, while growing PoCos, the set of loci that can be added to a growing PoCoP is constrained by the network. Namely, at any step of the algorithm, only loci that are at most 3 hops away from at least one locus in P are considered as candidates for addition into P. This ensures that the loci in a NetPoco are functionally related to each other. In other words, reachability within three hops captures all functional association patterns between a pair of loci in this heterogeneous network:The algorithm for identifying NROI-ROI association: Two loci that are in the RoI of the same gene are within 2 hops of each other.ROI-eQTL association: A locus that is in the RoI of a gene u is 2 hops away from loci that are associated with u’s expression.ROI-PPI-ROI association: Two loci that are in the RoI of the genes coding for two interacting proteins are within 3 hops of each other.ROI-PPI-eQTL association: A locus that is in the RoI of a gene u is 3 hops away from a locus that is associated with the expression of gene v such that the products of u and v interact with each other.Π of all discovered PoCos. As we discuss in the next section, each identified PoCo contains multiple loci and most of the loci in the dataset are not assigned to any of the PoCos in practice. For this reason, we usually have |Π| < < |C|.When the algorithm terminates, it returns the set oCos is risk assessment. By construction, PoCos (NetPocos) contain  loci that exhibit improved power in distinguishing cases from control. Consequently, as compared to individual variants, they may provide more robust and reproducible features to be used in predictive models. To investigate the utility of these multi-locus features in risk assessment, we use PoCos to build a model for risk assessment using L1 regularized logistic regression classifier.One potential utility of the PoCos for risk assessment, we compute a representative genotype for each PoCo. For this purpose, we use the fraction of the loci in the PoCo that harbor a genotype of interest in the respective sample. To be more precise, for each PoCoP ∈ Π, we compute the profile of P ass ∈ S. The set of features utilized by the classifier is comprised of h for all P ∈ Π. Next, we perform feature selection to identify a parsimonious set of PoCos to be used in risk assessment.To facilitate the use of PoCos to be used for risk assessment, we use a two-step feature selection method. The first step implements filtering-based feature selection, and the second step incorporates feature selection into model building by using a L1-regularized logistic regression classifier that enforces sparsity. Note that feature selection is applied within a cross-validation framework, so that test samples are not used in the identification and selection of the PoCos that are used in the model.High dimensionality is always an important problem in GWAS . The large number of features makes feature selection quite challenging. In particular, the models can be easily over-fit if too many features are entered into the model. For this reason, many researchers suggest filtering algorithms for dimension reduction and feature selection –42. Furtp-value representing the significance of the association of each PoCo with the disease. For this purpose, we use two different methods:For filtering-based feature selection, we compute a Logistic regression: We compute a logistic regression model by including all identified PoCos in the model. The p-value of the coefficient of each PoCo in this model represents the significance of the PoCo in predicting phenotype at the presence of all other PoCos.KS-statistic: We assess the significance of the Kolmogorov-Smirnov (KS) statistic comparing the distribution of h in case samples against that in control samples. The p-value of the KS-statistic quantifies the significance of the difference between the two sample classes in terms of the distribution of the values of the feature representing that PoCo.p-values to reduce the number of PoCos that are used in model building. Namely, for a given threshold α, we filter out all PoCos with p-value greater than α and retain all other PoCos to be entered into model building. This is done separately for each of the filtering methods.We then apply a threshold on these H be the matrix in which rows represent samples and columns represent PoCos that pass the filtering stage, such that H = h. As before, f denotes the vector composed of the phenotypes of samples. Then the L1-regularized logistic regression classifier computes a vector β to solve the following optimization problem:Let q denotes number of PoCos that are entered into the model and λ is a non-negative regularization parameter. The second term in the objective function is a penalty function that enforces sparsity of the model and the parameter λ controls the number of PoCos selected in the model . For larger λ, the model is expected to be more sparse.Here, oCos in risk assessment, we use nested K-fold cross validation. Namely, we divide the set of samples into K subsets {T1, …, TK}, while keeping the proportion of case and control samples fixed across all subsets. For the kth subset of samples, we reserve the samples in this subset as test samples. We divide the training group further into K groups and use this partitioning to perform genotype identification, PoCo identification, feature selection, filtering-based feature selection and model building using the L1-regularized logistic regression classifier. Once the model is optimized in the inner fold, we use the resulting model to predict the class of each sample in the kth subset, and evaluate prediction performance on this outer fold. This process is iterated for k = 1, 2, …, K and the performance of classification is evaluated based on the predictions across all samples. The typical choices of K are 5 or 10 and here we use 5-fold cross validation in our experiments. We also repeat the randomization of folds five times and report the averages of performance figures across these randomizations.To evaluate the performance of PRisk assessment models produce quantitative predictions of susceptibility to the disease of interest. To evaluate the predictive ability of these risk assessment models, we apply different thresholds on the predicted risk to obtain a binary prediction for each test sample. Using these binary predictions, we obtain the counts of true positives , false positives , and false negatives , and compute the precision  and recall  figures based on these counts. We assess the performance of each risk assessment model based on the area under the ROC curve (AUC), which characterizes the ability of the model in trading off precision and recall for varying thresholds on the quantitative prediction.p-value of the association of each loci with the phenotype is calculated. For a given parameter α, L is defined as the set of loci with p-value less than α. Subsequently, the polygenic score for a sample s is the defined as follows:γ(c) denotes the effect size of locus c which can be estimated using an appropriate regression model(i.e. logistic for a binary phenotype or linear for a continuous phenotype).We compare the performance of PoCo-based risk assessment models against models based on individual loci, as well as Polygenic score. Polygenic score is a commonly used method for risk assessment in GWAS. It is based on the assumption that the joint effect of multiple loci on the phenotype is additive . Based ooCos in producing informative multi-locus features, we evaluate their utility in the context of risk assessment. For this purpose, we use GWAS data from the Welcome Trust Case-Control Consortium (WTCCC), which includes data from studies for seven complex diseases, namely type 1 diabetes (T1D), type 2 diabetes (T2D), psoriasis (PS), bipolar disorder (BD), coronary artery disease (CAD), hypertension (HT), and multiple sclerosis (MS). On each dataset, we first identify PoCos, select features to build a model for risk assessment, and then evaluate the performance of the resulting model. To control for overfitting and to ensure that the performance figures are not biased, we use cross validation.To assess the ability of PetPocos against Polygenic Score, which is a commonly used method for risk assessment. Subsequently, to gain insights into the information provided by network data and specifically eQTL-based regulatory interactions, we also compare the performance of NetPocos, network-free PoCos, and eQTL-free PoCos. Moreover, we investigate the effect of λ in the L1 regularized logistic regression classifier, i.e. the parameter that controls the parsimony of the model. We also assess the biological relevance of some of the selected PoCos using enrichment analysis and a literature-driven list of genes and processes that have been reported to be associated with diseases. Finally, we compare the most frequently recruited genes in PoCos in different diseases to gain insights into shared genetic bases of different diseases. This analysis also suggests novel potential susceptibility genes for these diseases.We first compare the risk assessment performance of the multi-locus features against the standard approach of using individual significant loci. To facilitate fair comparisons, we use the classification and feature selection methods described in the “performance evaluation for risk assessment” section identically for all types of multi-locus and individual-locus based features. We also compare the performance of NoCos, in order to avoid marginal effect of individual loci and reduce the risk of artifacts, we filter the loci with nominal p-value of individual association less than ≤ 10−7 . Since we utilize the PPI networks and eQTL data to identify NetPocos, we include in our analyses the SNPs that are either within 50kb upstream and downstream of coding regions or are identified by eQTL to be associated with the expression of a gene. The number of loci and the the number of samples for each dataset are shown in We use genome wide association data for all seven diseases obtained from the Wellcome Trust Case-Control Consortium (WTCCC) –45. For We use a human PPI network downloaded from BioGRID  database. The BioGRID PPI network contains 194639 interactions among 18719 proteins.We use an eQTL dataset obtained from RegulomeDB which aims to annotate noncoding common variants from association studies . This daoCos, we do not use gene information. To facilitate the identification of NetPocos, we map SNPs to genes by defining the region of interest (RoI) for a gene as the genomic region that extends from 50kb upstream to 50kb downstream of the coding region for that gene.To identify network-free PWe identify individually significant loci using PLINK , a well-etPocos on the remaining four groups. Then, we use these four groups for feature selection and model building. Finally, we test the performance on the group reserved for testing. All of the reported performance figures are averages across five different cross-validation runs. The number of PoCos identified on each dataset and the size of these PoCos are presented in oCos does not have a significant effect on the performance  as the filtering criterion. Similarly, we filter individual loci based on the statistical significance of their association with the disease (after correction for multiple hypothesis testing). Polygenic risk score, which is commonly used in risk assessment, is a sum of the scores of associated loci, weighted by effect sizes, which are estimated using the training set. For polygenic score, the features are also selected using the p-value threshold in training samples and they are used to score the individuals in test samples.To investigate the benefits of using Nα). Namely, for each α ∈ {5E − 8, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3}, we build the risk assessment model using the NetPocos or loci with p-value less than α. Note that we use p-values to rank and select individual loci or PoCos to be entered into the model as features. As discussed in Methods, the p-values for PoCos reflect the significance of logistic regression coefficients or KS-test, whereas for individual loci, the p-value reflect the significance of case/control association analysis as computed by PLINK. Since p-value are used for ranking, correction for multiple hypotheses does not influence the behavior of the methods. Nevertheless, the p-value thresholds shown in the figure are based on Bonferroni-corrected p-value. For model building, we use the L1 regularized logistic regression classifier described in the Methods section, for both NetPocos and individual locus based features. L1 regularized logistic regression provides a second layer of feature selection through the regularization term in the associated objective function. Polygenic score has its own classification algorithm by definition.To comprehensively understand the effect of filtering, we test all methods using different thresholds on p-value for filtering  are shown in The results of cross-validation for using individual loci (using L1 regularized logistic regression), polygenic score, and NetPocos based on regression p-value provides favorable prediction performance when a strict threshold is used for statistical significance . However, as the threshold increases , the performance of regression based filtering declines. On the other hand, the prediction performance of NetPocos filtered based on KS p-value is improved with increasing threshold on significance. This observation suggests that, while regression p-value tends to rank the most informative NetPocos at the top, KS-statistic based ranking provides a more reliable set of NetPocos for L1 regularized logistic regression to choose from when more NetPocos are entered into the model , but the performance of the classifier that uses individual locus based features remains below the performance of the classifier that uses NetPoco-based features. These results suggest that NetPocos are useful in “feature construction” for risk assessment, i.e., they bring together robust sets of loci to be used together in risk prediction , type II diabetes (T2D), and coronary-artery disease (CAD). The results of these analyses are shown in oCos have been identified using all genotyped loci and the search space is not limited to the loci that can be mapped to gene regions. Therefore, network-free PoCos can include some loci that are out of gene regions as well, providing them with an advantage over NetPocos. However, as seen in the figure, NetPocos outperform the network-free PoCos for T2D. In contrast, the results for BD and CAD suggest that constraining the search space by functional interactions based on PPIs and eQTL may slightly reduce the predictive power of PoCos. However, importantly, when we consider model size, we observe that NetPocos provide more parsimonious final models for all three diseases.Many computational methods are developed to integrate the GWAS data with other biological datasets that provide information on the functional relationships between individual biological entities . In this study, we integrate PPI data and eQTL data in the identification of NoCos in MATLAB. We assess the runtime of this procedure using Intel(R) Xeon(R) CPU E5-4620 with a 2.2 GHz processor with 50 GB RAM. The results of this analysis are shown in oCos by providing more parsimonious models. Furthermore, using prior knowledge makes the problem computationally feasible since it drastically reduces the running time.We implement the procedure for the identification of PetPocos. To assess the benefits of including eQTL-based interactions, we also identify PPI-based PoCos using a network that does not contain eQTL edges, and compare the risk assessment performance of these PoCos against that of NetPocos (which are identified using PPI and eQTL data). Note that removal of eQTL edges causes the removal of loci that are connected to the network just by eQTL edges. Such loci are usually those that are not in close proximity of coding regions.An important limitation of network-based analyses of GWAS data stems from the constraints posed by the lack of regulatory interactions in network models. If the functional relationships that are used to drive the search are limited to protein-protein interactions (PPIs), the search is limited to loci that are in close proximity to coding regions and regulatory interactions that involve non-coding loci are not considered . One impoCos and eQTL+PPI-based NetPocos is similar for all three diseases. However, for BD and CAD, the predictive models provided by the incorporation of eQTL data are significantly more parsimonious than the models provided by PPI-only NetPocos. For T2D, the incorporation of eQTL edges leads to more complex models, but the prediction performance is enhanced with the inclusion of eQTL edges. These observations suggest that incorporation of eQTL data indeed provides biologically relevant information in the discovery of NetPocos.The results of this analysis are presented in λ in λ forces the model to be more parsimonious. Therefore, as λ grows, the learning task becomes more difficult, in that L1 regularized logistic regression tries to simplify the model by compromising model fit. For this reason, if the features that are input into the classifier are “high-quality” features, the classifier can be expected to be more robust to this parameter. Based on this premise, we assess the “quality” of the features constructed from NetPocos by comparing the models based on NetPocos and individual loci in terms of their performance as a function of λ. For this purpose, we fix the p-value threshold (0.05) for both NetPocos and individual SNPs and compute the AUC in cross-validation for a range of different values of λ. The results of this analysis are shown in etPocos, but NetPocos can tolerate larger lambdas.In L1 regularized logistic regression, the parameter λ = 0.001 which provides a reasonable balance between the complexity and predictive performance of the model.In all other results reported in this section, we use etPocos using pathway analysis, Gene Ontology enrichment analysis, and literature-driven list of genes and processes that are reported to be associated with disease. For this analysis, we focus on three diseases  which are shown to have similar molecular mechanisms [We assess the biological relevance of the predictive Nchanisms , 50 and chanisms .Type II Diabetes (T2D). We focus on NetPocos that have highest coefficient in the model constructed by L1-regularized logistic regression classifier. Top two NetPocos are shown in etPoco shown in etPoco. Interestingly, some of the genes in this NetPoco are previously reported to be associated with T2D [et al. [etPoco that is used in risk assessment for T2D suggests that this gene can be a potential novel candidate for association with T2D as well. We also use ontologizer for Gene Ontology enrichment analysis [oCo is enriched in isocitrate metabolic process  and also NADH metabolic process, which both contribute to the amplification of insulin secretion [with T2D , while s [et al.  show thaanalysis . The Genecretion .oCo shown in STC1 and LOXL2 are genes that are previously reported to be associated with T2D [TINAGL1 is involved in Glucose/Energy metabolism pathway and CHRNA9 is involved in Postsynaptic nicotinic acetylcholine receptors pathway with other genes such as CHRNA2, CHRNA4 and CHRNA6 that are previously reported to be associated with T2D [TINAGL1 and CHRNA9 can be potential candidate genes for T2D. Additionally, it is known that acetylcholine can enhance glucose-stimulated insulin secretion from pancreatic beta-cells [oCo is also enriched in calcium ion homeostasis  which is one of the T2D associated pathways.The Pwith T2D . It is nwith T2D . This obta-cells . This PoNote that, for T2D, non-genetic risk factors including age, sex, and body-mass index (BMI) play an important role in risk. These factors can be also combined with genetic factors to obtain better performance in risk assessment . JanipalCoronery-Artery Disease (CAD). Two NetPocos that have highest coefficient in L1 regularized logistic regression for CAD are shown in etPoco in p-value = 0.0003), positive regulation of cardiac muscle cell proliferation , cardiac muscle tissue regeneration , and activation of MAPKK activity . These pathways are previously reported to be associated with susceptibility to CAD [ERBB4 is not previously reported to be associated with CAD, it plays a role in MAPK pathway, which is one of the top pathways for CAD [ERBB4 can be a potential candidate gene for CAD as well. The NetPoco in p-value = 3.3E-6), prostate glanduar acinus development , and muscle cell differentiation. This NetPoco is also enriched in positive regulation of calcieneurin-NFAT signaling pathway  and positive regulation of insulin-like growth factor receptor signaling pathway. IGF1 and RXRA are both involved in a pathway named “Pathways in cancer” which is known to be related to CAD. More than 20 genes in this pathway are known to be associated with CAD [RXRA may be a novel CAD risk factor.y to CAD . Althoug for CAD . Therefowith CAD . This obBipolar Disorder (BD). Two NetPocos with highest coefficient in L1 regularized logistic regression in the risk prediction model for bipolar disorder are shown in etPoco in p-value = 8.67e-6), which plays a central role in bipolar disorder [etPoco in p-value = 0.0007), cell migration involved in coronary angiogenesis , and insulin receptor signaling pathway.disorder . The NetShared molecular bases among diseases. Identifying the links between the molecular etiologies of different diseases can provide an insights on the underlying mechanisms of these diseases. Elucidation of such relationships can also help to detect the novel candidate genes for diseases. For example, patients with bipolar disease frequently have coexisting medical conditions such as obesity, cardiovascular disease, and diabetes mellitus [et al. [etPocos can capture the relationship between diseases. For example, the NetPoco in mellitus . Torkama [et al.  also shoetPocos selected by L1 regularized logistic regression in the risk assessment models for these diseases. For each disease, we identify the top 10 most frequent genes. We then assess whether they are previously reported to be associated with T2D [etPocos identified in CAD dataset. Among these genes, WWOX and CD36 are previously reported candidates for CAD. They are also known to be associated with BD. This result suggests that, for example, GRID1 can also be a potential susceptibility gene for CAD. This hypothesis is also supported by the observation that GRID1 plays a role with 14 other known CAD genes in neuroactive legand-receptor interaction. WWOX also can be a good candidate for T2D, considering that it plays a role in apoptosis and autophagy pathway, which is the main form of beta-cell death in T2D [To gain further insights into the shared molecular bases of T2D, CAD, and BD, we examine the genes that appear most frequently in the Nwith T2D , CAD [59with T2D , 62 as wh in T2D .etPocos do not overlap at the SNP-level, however, they may overlap at the gene-level since multiple SNPs can be mapped to the same gene. This shows the power of NetPocos in identifying molecular bases of diseases, since multiple NetPocos can arise from similar functional contexts, providing stronger statistical evidence for the involvement of genes that are associated with these NetPocos.Note that NoCos) and investigate the utility of these multiple-loci features in risk assessment. We also perform extensive experiments to evaluate the effect of using network information to drive the search for multi-locus features on risk assessment. We also investigate the effect of the variants that have regulatory effects (i.e. eQTL data) on performance for risk assessment. Moreover, we compare the proposed method with the polygenic score which has been shown to be successful in different studies. Our result show that our method is significantly more powerful in risk assessment.In this paper, we propose a novel criterion to assess the collective disease-association of multiple genomic loci  data leads to more parsimonious models for risk assessment. However, inclusion of functional data does not yield significant improvement in prediction performance. This may be indicative of the limitations of genomic data in risk assessment. Furthermore, since PoCos contain loci that are related to each other in the context of a phenotype, PoCos that are discovered without the inclusion of functional information also likely contain functionally related loci. However, utilization of functional information reduces the search space to render the problem computationally feasible, and brings forward PoCos that are more functionally relevant and robust, thereby leading to more parsimonious models.Based on the success of multi-locus genomic features in risk assessment, we conclude that combining these features with non-genetic risk factors and other biological data may lead to further improvements in risk assessment.http://compbio.case.edu/pocos/) as open source software.The proposed method is implemented in MATLAB and provided in the public domain Click here for additional data file.S2 FigThe x-axis shows the p-value threshold used in filtering based feature selection and the y-axis shows the area under the ROC curve (AUC) for performance in risk assessment. The curve shows the average AUC score and error bars show the standard deviation of AUC score across 5 folds in 5 different runs.(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.


Attention deficits may present dysfunctions in any one or two components of attention ). However, these various forms of attention deficits generally have abnormal microstructure integrity of inferior fronto-occipital fasciculus (IFOF). In this work, we aim to deeply explore: (1) associations between microstructure integrities of IFOF  and attention by means of structural equation models and multiple regression analyses; (2) genetic/environmental effects on IFOF, attention, and their correlations using bivariate genetic analysis. EC function was attributed to the fractional anisotropy (FA) of left  and right IFOF , especially to left frontal part and right occipital part (correlation was driven by genetic factors). Alerting was associated with FA in parietal and insular parts of left IFOF. No significant correlation was found between orienting and IFOF. This study revealed the advantages of lobar-segmental analysis in structure-function correlation study and provided the anatomical basis for kinds of attention deficits. The common genetic/environmental factors implicated in the certain correlations suggested the common physiological mechanisms for two traits, which should promote the discovery of single-nucleotide polymorphisms affecting IFOF and attention. The inferior fronto-occipital fasciculus (IFOF) connects various parts of the occipital cortex, temporo-basal area, and the superior parietal lobule to the frontal lobe through the external/extreme capsule complex134et al. proposed that the parieto-frontal connections of IFOF were not involved in the orientation of attentionAlthough direct fronto-parietal connection is crucial for attention7According to previous disease studies, abnormal microstructural integrity of IFOF had been linked with attention deficit hyperactivity disorder (ADHD)et al. suggested that the heritability of IFOF was 7–35% in early puberty (9 and 12 year olds) and the genetic factors on the variation of FA increased with age20Identification of genetic factors affecting white matter integrity and cognitive functions is vital important in neuroscience. However, little is known about the heritability of IFOF or attention. Brouwer in vivoQuantitative tractography has the advantages of mapping the direction of white matter fibers and provides a unique opportunity to study white matter architecture Our research aims to calculate the white matter integrities FA and mean diffusivity (MD) of the IFOF, as well as the five specific segments, using the quantitative tractography method, and to correlate these attributes with the three subnetworks of attention. Furthermore, based on the advantages of twin study design, we have a chance to clarify the genetic and environmental impact on the correlations between the two traits. With the evidence that EC alternation is an important neuropsychological endophenotype in schizophreniaThe accuracy of ANT performance was 80.1 ~ 99.5% (averaged = 96.6%) and no one was excluded from the study, indicating that the participants understood the behavioral task and could make a reliable determination on the direction of the central arrow.The correlations between the ratio scores of alerting, orienting and EC are shown in −3), respectively. Using quantitative tractography, high intra-rater reliability of 0.96 was obtained for the left IFOF. Mean FA and MD of the right IFOF was 0.4497 ± 0.0185 and 0.8201 ± 0.0293 (*10−3), respectively. The intra-rater reliability for the right IFOF was 0.97 in our study.The main courses of the left and right IFOF, as well as their lobar segments, were shown in According to the p values of the path coefficients in structural models, we found the significant effects of FA in the left insular and parietal parts on alerting  and the The correlations between different parts of the tract were low and no significant multicollinearity was found. The results of multiple regression models for FA of IFOF were shown in Heritability results were shown in ph = 0.208) and the right occipital part (rph = −0.266); genetic factors were implicated in these correlations  and the extent of phenotypic correlation due to gene was 0.452 and −0.168, respectively. The phenotypic and environmental correlations were found between EC and the right  and left IFOF ; the extent of phenotypic correlation due to environmental factors was −0.228 and −0.244, respectively. None of the other phenotypic correlations were found to be driven by significant genetic or environmental factors.The results of the bivariate genetic analysis were shown in The FA value may reflect the fiber density, axonal diameter, and myelination in white matteret al. revealed the clear structural connectivity between the insular cortex and cingulate cortexThe alerting component during ANT task, which was defined as phasic or exogenous alertness, represented the ability to activate the required cognitive systems to make the person ready to respond to a task3031et al. found the significant structure–function correlations between alerting and the left posterior limb of the internal capsuleOur findings revealed the importance of left hemisphere in alerting, which is consistent with some prior studies, while opposite to others. By means of DTI and region of interest (ROI) analysis, Niogi et al.’s report of a neglect study that proposed the inefficiency of IFOF in the orientation of attentionThe orienting system had been reported to be associated with frontal eye fields, superior and inferior parietal lobes, the superior colliculus, and reticular nuclei313638Executive control is involved in the resolution of incongruent stimuli impacting decision planning and making. This network includes the white matter tracts that connect the frontal lobe with other regions3236et al. found that the association between FA values within a ROI in anterior corona radiata (ACR) and EC was significant in the left hemisphere and appeared a non-significant trend in the right oneBesides, DTI studies have addressed the importance of left frontal white matter tracts in attention. Niogi Different from earlier developing structures that are under higher genetic control, tract-level heritability was not modulated by age and the earlier developing white matter tracts did not show a higher degree of genetic contributionIn addition, determining the extent of genetic or environmental influence on structure-function correlations enhances our knowledge about brain morphology eventually contributing to human behavior. Previous studies have demonstrated the genetic correlations between microstructural properties of white matter tracts and intelligenceAlthough these findings are robust, some limitations still need to be addressed. First, estimates of the eigenvector directions, and hence the local tract directions, are sensitive to thermal noise, physiologic fluctuations, and image artifacts. Algorithms based on the major eigenvector are unable to resolve regions of crossing white matter pathwaysWhite matter tract segmentation provided a new sight into the brain structure-function correlations. In this study, we were able to identify the role of lobar-segmented IFOF in attention. Our segmental analysis suggested the phenotypic contribution of IFOF in the left frontal lobe and right occipital lobe to EC function and that of IFOF in the left insular and parietal lobes to alerting, which provided anatomical basis for alerting and EC deficits. Moreover, due to the small sample size, genetic factors were only implicated in the right occipital part and EC association. Future studies with much more subjects and multi-model methods should be applied to investigate the underlying explanation for the associations between lobar segments of IFOF and three subnetworks of attention.60 healthy subjects  with 15–20 years of age (mean age: 16.9 ± 1.53 years old) were recruited for the study. All were Chinese native speakers with normal or corrected-to-normal vision. Inclusion criteria were: (1) right-handed measured with Edinburgh InventoryThe ANT task was adopted as a cognitive task in our studyThe reaction time (RT) and total accuracy of each subject were calculated. The participant with low accuracy (<80%) should be excluded from our study. Trials with incorrect responses or RTs shorter than 200 ms or longer than 1,500 ms were also excluded to avoid the influence of the abnormal values. Responses following erroneous ones were removed to avoid post-error slowing effect. In this study, we used ratio scores of alerting, orienting, and EC to define the efficiency of three components of attention. The formulas were as follows:2; matrix, 96 × 96; slice thickness, 2.6 mm with no gap; slice number, 56. 30 non-colinear diffusion gradients directions  and 3 non-diffusion-weighted images (b = 0 s/mm2) were included in the DTI scans. Array spatial sensitivity encoding technique (ASSET) was used with an acceleration factor of 2. The sequence was repeated twice to increase signal-to-noise.MR imaging was performed on a 3.0 T GE Signa scanner . The spin-echo, single shot echo planar imaging sequence was used to acquire the diffusion MR image with the following parameters: TR, 14,000 ms; TE, 75.1 ms; field of view (FOV), 250 × 250 mm2; matrix, 256 × 256; flip angle, 15°; slice thickness, 1.0 mm with no gap; slice number, 174. Both the diffusion MR and structural images collections were the same to our prior studyAfter the DTI scans, the structural images were collected using a three-dimensional spoiled gradient-echo (SPGR) pulse sequence: TR, 6.5 ms; TE, 2.0 ms; FOV, 256 × 256 mmhttp://pipeline.loni.usc.edu; version 6.0). First the DTI data were preprocessed using the FSL toolboxhttp://www.trackvis.org). To ensure reliability, we adopted a multi-ROIs approach to extract the IFOF manually. The first ROI delineated the occipital lobe on a coronal slice, which was identified at the middle point between the posterior edge of the parieto-occipital sulcus and the posterior edge of the cingulum. The second ROI was also selected on a coronal slice, which located at the anterior edge of the genu of corpus callosum and delineated the entire hemisphereDTI data processing was performed using the Laboratory of Neuro Imaging (LONI) Pipeline Workflow Environment http://www.smartpls.de) was preliminary used to assess the effect of FA in manifest variables (segments of IFOF) on alerting, orienting, and EC, respectively. Structural model assesses the relationships through evaluating the path coefficients  of the model. The path coefficient has to be tested for its significant level by t-value test (two-tailed), which is achieved by bootstrapping technique. The same procedure was repeated for MD of segmented IFOF.Advanced multivariate statistical software of Structural Equation Modelling (SmartPLS v3.0) , version 20.0 . As a matter of fact, one variable in a multiple regression model can be linearly predicted from the others with some certain degree of accuracy and the coefficient estimates of the multiple regressions may be changeful due to small changes in the model or the data, multicollinearity was used to test whether two or more variables were highly correlated. Subsequently, ten blocks of independent variables were applied in a step-wise fashion. Likewise, multiple regression analyses were performed to test the specificity of the whole IFOF to the three attention subnetworks. A Bonferroni correction was applies for multiple comparisons and the alpha level was set to 0.05 divided by the times of repetitions for each attention component.http://openmx.psyc.virginia.edu) in the R statistical computing environment (http://www.r-project.org). Phenotypic variance in the twin genetic model was estimated by the contribution of three factors: additive genetic factors (A), common environment factors (C) and specific environment factors (E), which could be called ACE model. A full ACE model was compared with an AE-model, a CE-model, or an E-model. The goodness of fit of different models was evaluated by Chi-square differences and the Akaike’s Information Criterion (AIC)Heritability calculation was performed using the OpenMx package (ph) between attention and the IFOF, which can result from genes or environmental factors. The extent of the overlap is reflected by the genetic and environmental correlation rg and re, respectively. In addition, combining the genetic and environmental correlations with the heritability of each trait, we also established the genetic (rph-a) and environmental (rph-e) contributions to the phenotypic correlation between the two traitsThe bivariate genetic analysis yielded an estimate of the phenotypic correlations .


Avian influenza (AI) is a devastating poultry disease that currently can be controlled only by liquidation of affected flocks. In spite of typically very high mortality rates, a group of survivors was identified and genotyped on a 600K single nucleotide polymorphism (SNP) chip to identify genetic differences between survivors, and age- and genetics-matched controls from unaffected flocks.In a previous analysis of this dataset, a heritable component was identified and several regions that are associated with outcome of the infection were localized but none with a large effect. For complex traits that are determined by many genes, genomic prediction models using all SNPs across the genome simultaneously are expected to optimally exploit genomic information. In this study, we evaluated the diagnostic value of genomic estimated breeding values for predicting AI infection outcome within and across two highly pathogenic avian influenza viral strains and two genetic lines of layer chickens using receiver operating curves. We show that genomic prediction based on the 600K SNP chip has the potential to predict disease outcome especially within the same strain of virus (area under receiver operating curve above 0.7), but did not predict well across genetic varieties (area under receiver operating curve of 0.43). Avian influenza (AI) is a devastating disease and the current approach that is used to control it is based on isolation and extermination of affected flocks in order to stop the spread of the virus. Alternative approaches, including the use of vaccines, have been only 60% effective in chickens , 2 due tAn alternative to searching for causal mutations, is to use high-density SNP genotypes for genetic improvement of disease resistance by using all genetic markers across the genome to predict breeding values of selection candidates through the concept of genomic prediction and selection . GenomicIn clinical epidemiology, the receiver operating characteristic (ROC) curve is often used to evaluate diagnostic methods in terms of their ability to distinguish between healthy and sick subjects. This method has several advantages, including independence of prevalence of disease or choice of the decision criterion . In thisThree sets of samples were used for this study (see  for a moThe phenotype of survivor/control (0/1) was analysed using the BayesB method by fitting all SNPs simultaneously, in GenSel , separatTo verify the potential of genomic prediction for genetic improvement of AI resistance, random fivefold cross-validation was performed within Hy-Line US and Mexico commercial samples, as well as prediction of the Hy-Line US commercial samples from the Hy-Line Mexico commercial samples, to represent prediction across different virus strains, and prediction of non-Hy-Line US commercial samples from Hy-Line US commercial samples, to represent prediction across different genetic varieties of layer chickens. The usefulness of the genomic estimated breeding values (GEBV) for predicting disease outcome was summarized by ROC curves. Sensitivity (true positive rate) and specificity (true negative rate) were calculated across the whole range of thresholds to classify birds as survivors versus controls based on their GEBV, i.e., for a given GEBV threshold, sensitivity is the proportion of survivors among birds with GEBV above this threshold and specificity is the proportion of controls among birds with GEBV below the threshold. Sensitivity was plotted against (1-specifity)  to create the ROC curves, together with a 45° line that represents random assignment of survivors and controls. Summary statistics of area under the curve (AUC) and significance test for AUC = 0.5  were performed using the program easyROC .Windows explaining more than 1% of the genetic variance within each dataset are included in Table The ROC curves are in Fig. P = 0.02). These results show that genomic predictions based on the 600K SNP chip have potential to predict disease outcome, especially within the same strain of virus, but do not predict well across genetic varieties. Methods to implement this type of crossbred performance for pure line selection using genomic data was discussed by Ibánẽz-Escriche et al. [The ROC curves show significant improvement Table  in accure et al. .Poor performance of genomic prediction across layer lines for egg production was previously reported by Calus et al.  using geGenomic predictions based on the 600K SNP chip have potential to predict avian influenza infection outcomes, especially within the same strain of virus but do not predict well across genetic varieties.


Piscirickettsia salmonis is a major disease affecting the Chilean salmon industry. Genomic selection (GS) is a method wherein genome-wide markers and phenotype information of full-sibs are used to predict genomic EBV (GEBV) of selection candidates and is expected to have increased accuracy and response to selection over traditional pedigree based Best Linear Unbiased Prediction (PBLUP). Widely used GS methods such as genomic BLUP (GBLUP), SNPBLUP, Bayes C and Bayesian Lasso may perform differently with respect to accuracy of GEBV prediction. Our aim was to compare the accuracy, in terms of reliability of genome-enabled prediction, from different GS methods with PBLUP for resistance to SRS in an Atlantic salmon breeding program. Number of days to death (DAYS), binary survival status (STATUS) phenotypes, and 50 K SNP array genotypes were obtained from 2601 smolts challenged with P. salmonis. The reliability of different GS methods at different SNP densities with and without pedigree were compared to PBLUP using a five-fold cross validation scheme.Salmon Rickettsial Syndrome (SRS) caused by Heritability estimated from GS methods was significantly higher than PBLUP. Pearson’s correlation between predicted GEBV from PBLUP and GS models ranged from 0.79 to 0.91 and 0.79–0.95 for DAYS and STATUS, respectively. The relative increase in reliability from different GS methods for DAYS and STATUS with 50 K SNP ranged from 8 to 25% and 27–30%, respectively. All GS methods outperformed PBLUP at all marker densities. DAYS and STATUS showed superior reliability over PBLUP even at the lowest marker density of 3 K and 500 SNP, respectively. 20 K SNP showed close to maximal reliability for both traits with little improvement using higher densities.These results indicate that genomic predictions can accelerate genetic progress for SRS resistance in Atlantic salmon and implementation of this approach will contribute to the control of SRS in Chile. We recommend GBLUP for routine GS evaluation because this method is computationally faster and the results are very similar with other GS methods. The use of lower density SNP or the combination of low density SNP and an imputation strategy may help to reduce genotyping costs without compromising gain in reliability.The online version of this article (doi:10.1186/s12864-017-3487-y) contains supplementary material, which is available to authorized users. Piscirickettsia salmonis is considered one of the major diseases of the salmonid aquaculture industry in Chile [Salmo salar) industry, P. salmonis is responsible for up to 74% of infection-related mortality and economic losses of up to US$100 million. Antibiotic treatments may inhibit the growth of the pathogen, but have been unsuccessful in stopping disease outbreaks and pose serious health issues for fish and humans [P. salmonis they have not proven to be consistently effective under field conditions [Salmon Rickettsial Syndrome (SRS) caused by an intracellular bacterium in Chile . SRS outin Chile , 2. It hd humans , 4. Althnditions .P. salmonis, indicating the potential for selective breeding for P. salmonis resistance [Selective breeding for resistance against infectious diseases represents a realistic and sustainable approach to control disease outbreaks in livestock and aquaculture species , 7. Tradsistance , 11.P.salmonis in Atlantic salmon is under moderate polygenic control. The same study identified five SNP significantly associated with P.salmonis resistance traits in chromosomes Ssa01 and Ssa17. However, due to the small amount of phenotypic variance explained by each marker, it was suggested that resistance to P.salmonis can be more efficiently improved with genetic evaluations incorporating dense SNP genotype information compared to MAS alone [Genetic markers associated with quantitative trait loci (QTL) alleles for disease resistance can be used in Marker Assisted Selection (MAS) of breeding candidates with genotypes, even in the absence of phenotypes, to accelerate genetic progress . The carAS alone . GenomicAS alone –21. In GAS alone . In aquaAS alone –25 and rAS alone , 26 haveSeveral GS methodologies varying with respect to assumptions about marker effects have been proposed for the genome-enabled prediction of EBV , 28. TheP. salmonis resistance traits in Atlantic salmon and ii) to evaluate the effect of different marker densities on the reliability of genomic predictions for different genomic prediction models and pedigree based BLUP for P. salmonis resistance traits in Atlantic salmon.The objectives of this study were i) to compare the reliability of commonly used genomic prediction methods for genomic selection under various underlying genetic models and pedigree based BLUP for th Region, Chile. After a 29 day acclimation period in salt water (31 ppt) a total of 2601 fish, an average of 22 (ranging between 9 and 24) fish per family, weighing on average 274.8 g (SD = 90.6 g) were experimentally challenged with P.salmonis as described previously [Renibacterium salmoninarum by RT-PCR and negative for Flavobacterium spp. culture. To induce infection, fish were injected with 0.2 ml of a LD50 inoculum of P.salmonis through intra-peritoneal (IP) injection. Post IP injection, infected fish were distributed equally by family into three different tanks with salt water (31 ppt) such that each of the 118 full-sib families were represented in all three tanks. The challenge test continued for 40 days and mortalities were recorded daily. The Kaplan-Meier curves of the survival function was plotted for the test period to show the cumulative mortality across the challenge .The breeding program for Atlantic salmon was started by the company AquaChile  in the year 1997 with the aim of improving economically important traits. The base population of the breeding nucleus originated from the Irish strain Fanad-Mowi  , 33 and eviously , 18. In p < 1 × 10−10), Minor Allele Frequency (>0.001) and the call rate for SNPs and samples (>0.95). The quality control step resulted in a total of 2392 individuals and 49,684 SNPs distributed across the genome for further analysis.Genomic DNA was isolated from the stored fin clip samples of all 2601 challenge tested fish using a commercial kit , following manufacturer’s protocol. Genotyping was performed using a 50 K Affymetrix® Axiom® myDesign™ SNP Genotyping array designed by the joint collaboration of AquaInnovo SA and the University of Chile. The 50 K SNP array used in this study was derived from a previously developed and validated custom made 200 K SNP array  based onP. salmonis was considered to be challenge survival, defined as the time to death measured in days (DAYS) with values ranging from 1 to 40 depending on the day the fish died; and as binary survival status (STATUS), scored as 1 if the fish died during the 40-day challenge and 2 if the fish survived until the end of the challenge. Thus, the fish with higher DAYS and a STATUS of 2, were assumed to be more resistant animals. Test tank designation and final body weight on the day of death or at the end of the challenge for survivors were recorded.Resistance to The two resistance traits DAYS and STATUS were analyzed separately as a linear trait and threshold trait, respectively in univariate models. The EBV were estimated using polygenic pedigree based BLUP (PBLUP) . The SNPThe conventional pedigree-based variance components and EBV were estimated using PBLUP:X and T are the incidence matrices, th sample were saved.where β is a vector of fixed overall mean and age of fish at challenge (AGE) as co-variate, p matrix  and \docprograms . Brieflyprograms . For BayM1) described above. However, in GBLUP, M1).The SNP based variance components and GEBV were estimated using GBLUP, similar to the PBLUP model . It was assumed that a priori a normal distribution The SNP based BLUP method used to estimate marker effects and to predict GEBV was similar to GBLUP, where e normal , 42. The effects , 42. The effects  with kno effects . The tra effects . For bot−12 (1d-12) and correction every 100 iterations. For MCMCBLUP, a single chain with a length of 150 000 iterations was run. The burn-in period and the thinning interval used was 50 000 and 100 iterations, respectively.All model parameters are as described above. The BLUP was run for 10 000 iterations with convergence criteria of 10M2) and SNPBLUP (M3), hereafter referred to as PBAYESC and BAYESC, respectively. All model parameters are defined as above, except the elements of vector ith marker, i, and ith marker has an effect or not. In turn, variables The Bayes C method is a mixture model for SNP effects with an assumption that there is a large group of SNPs with zero or near zero effects and a second smaller group of SNPs with larger effect , 44. TheM2) and SNPBLUP (M3) as proposed by Legarra et al. [a priori distributions of individual SNP effects  were estimated using the Gibbs sampling algorithm implemented in GS3 software . A singlThe total additive genetic variance In contrast, for Bayesian models, the total additive genetic variance  or just SNP effects, depending on whether pedigree and SNP information or only SNP information was used.y), and a “common” heritability  were assessed through a five-fold cross validation (CV) scheme. All the fish with both phenotypes and genotypes were randomly sampled into five validation sets. The GEBV of the validation data sets were predicted one at a time where the phenotype of the validation fish (20% of the population) was masked (set to missing) and all remaining fish with phenotype and genotype (80% of the population) were used as training data. To reduce the stochastic effects, the CV analysis was replicated 10 times. Predictive ability was presented as reliability, which was estimated as:The Pearson’s correlation coefficients between the (G)EBV obtained by the different models was used to measure the degree of similarity between the rankings of fish. Also, for all models, the slope of regression of actual phenotype (either DAYS or STATUS) on (G)EBV were calculated and used as a measure to indicate the bias of the (G)EBV . A slopeIn addition, the effect of marker densities on the estimated reliabilities in different GS models was tested. For this, a random sample of 500, 1 K, 3 K and 20 K SNPs was used separately to predict GEBV for all GS models under the CV scheme described above. Using the lowest possible SNP density with higher or similar reliability of the 50 K SNP could help reduce genotyping costs.h2 = 0.185±0.038 and 0.260±0.037 for DAYS and STATUS, respectively). When comparing the PBLUP model  and GS models with only markers (BAYESC and BLASSO) are presented for DAYS and STATUS in Table mentclass2pt{minimThe mean correlations between the predicted breeding values estimated from PBLUP (EBV) and all seven GS models (GEBV) based on five-fold cross validation are shown in Table Based on the five-fold cross validation, the reliability of the PBLUP model was higher for DAYS 0.342±0.080) than for STATUS 0.201±0.038) (Table 42±0.080 ±0.038 (TThe bias of predicted EBV for PBLUP for DAYS (0.960±0.146) was lower than for STATUS 0.304±0.042)  also reported a similar heritability estimate (0.16±0.04) for SRS resistance trait DAYS [The genetic variance and heritabilities estimated for this population with the PBLUP linear model for DAYS 0.185±0.038) and threshold model for STATUS (0.260±0.037)  lead to slightly higher heritability estimates possibly because the pedigree information was useful in capturing unmarked loci that are also involved in the genetic control of this trait. In contrast, the heritability estimates were slightly lower from PBAYESC and PBLASSO for STATUS which was probably due to the scaling parameters in the model as well as the binary nature of the trait.There is always debate about the minimum number of SNP markers required and whether causative SNPs are needed to obtain robust estimates of heritability. The low proportion of phenotypic variance in the population used in this study was previously explained to be the result of primarily polygenic control of SRS resistance with few QTLs . In humaThe GEBV predicted from the genomic relationship based GBLUP and marker-effect based GS models  for both SRS resistance traits were moderately correlated (0.76 to 0.81) with the predicted EBV Table . These rreported . The preentclass1pt{minimareported . These hThe accuracy of breeding values estimated in terms of reliability for DAYS 0.342±0.080) was similar to the previously reported reliabilities for fillet color (0.36) and lice resistance (0.34) in Atlantic salmon using the PBLUP model . However42±0.080 All GS models outperformed the PBLUP model with respect to estimated reliabilities for both the traits Table . In otheIt was interesting to note that reliability of GEBV estimated from combined pedigree and marker effect based GS models  were lower than the models with only marker-effects for the trait DAYS  Table . The GEBThe reliabilities of predicted GEBV from different GS models were very close and the differences between GS models were negligible for both traits Table . On the There is always a debate around the effect of marker density on GS prediction accuracy. The use of a low marker density panel may represent a cost-effective approach for GS prediction especially for aquaculture where thousands of potential breeders need to be genotyped. However, high density marker panels are expected to be more accurate and whole genome sequencing data or targeted causative variants genotyping are expected to give higher accuracies . The choIn our study, a marker density less than 3 K gave considerably lower reliability of GEBV, which was likely due to insufficient LD between the markers caused by the large distance between the randomly selected markers Fig. . In addiThe choice of exact marker density for genotyping a large number of potential breeders would largely depend on the added cost of genotyping and the economic benefit obtained by the extra gain in accuracy of the trait under selection. The cost-benefit is also likely to be most favorable for traits that cannot be measured on potential breeders  and traits with high economic value . Also, the marker density of 20 K gave a reliability close to that of highest marker density (50 K) showing that the LD between markers at 20 K and 50 K are similar and no additional gain would be obtained using a marker density beyond 20 K  or the combination of low SNP density  and an imputation strategy may help reduce genotyping cost without compromising the gain in reliability. We are currently working on an imputation strategy to explore the possibility of reducing the genotyping cost. The BLUP model which uses genomic relationship calculated from pedigree as well as SNP information (GBLUP) performed similar to the SNP based BLUP GS models and Bayesian variable selection GS models (Bayes C and Bayesian Lasso). The relative advantage of using SNP data to improve disease resistance depends on the cost of the disease challenge test to collect SRS phenotypes, genotyping thousands of training candidates (candidates with phenotype) and validation  which are expensive. The added economic impact of the extra improvement in SRS resistance needs to be evaluated carefully.


Male pattern baldness (MPB) or androgenetic alopecia is one of the most common conditions affecting men, reaching a prevalence of ~50% by the age of 50; however, the known genes explain little of the heritability. Here, we present the results of a genome-wide association study including more than 70,000 men, identifying 71 independently replicated loci, of which 30 are novel. These loci explain 38% of the risk, suggesting that MPB is less genetically complex than other complex traits. We show that many of these loci contain genes that are relevant to the pathology and highlight pathways and functions underlying baldness. Finally, despite only showing genome-wide genetic correlation with height, pathway-specific genetic correlations are significant for traits including lifespan and cancer. Our study not only greatly increases the number of MPB loci, illuminating the genetic architecture, but also provides a new approach to disentangling the shared biological pathways underlying complex diseases. Male pattern baldness (MBP) is a complex trait that has genetic associations. Here, Pirastu and colleagues perform a genome-wide association study to show 71 susceptibility loci associated with MBP — 30 of which are novel — and that these loci can explain 38% of heritability. Male pattern baldness (MPB) is a common multifactorial condition characterised by a progressive thinning of scalp hair with a very specific pattern. First, the hairline recedes at the temples (widow’s peak) and then a bald patch develops on the crown, progressing such that eventually only a horseshoe of hair is left on the sides and back of the head (the Hippocratic wreath).1 and prostate cancer2, suggesting a common underlying biology, and has negative impacts on body image and social perceptions3.MPB co-exists with numerous other important pathologies such as cardio-metabolic diseasesWnt and TGF-beta, come into play. Despite MPB’s high heritability (~80%), after the first identification of the AR/EDA2R locus on the X chromosome5 it took several years to identify additional loci, bringing the overall number to 128. Recently, a larger study including 20,000 people has greatly increased the number of loci although independent replication was not demonstrated9. Studies investigating the genetic correlations of MBP with other traits/diseases have been inconclusive. Despite the identification of several loci associated with MBP, a number of questions remain unanswered. It is unclear if multiple SNPs at the same locus substantially contribute to MBP risk; moreover, although many predisposing loci have been identified, which genes are actually causal to MPB and which common pathways they share is not always clear; finally, despite numerous described co-morbidities with MPB, the biology responsible for these correlations remains largely unknown.The development of MBP is clearly linked to the response to androgens although many other pathways, such as In order to shed light on these issues, we performed a large-scale genome-wide association (GWA) analysis to uncover the genetic architecture of baldness. We find 71 significantly associated loci, 30 of which were previously undescribed. These loci account for 38% of the heritability of MPB, suggesting a relatively low level of complexity in the genetic architecture. Further, we show that the identified loci contain genes which are enriched in pathways known to be important for hair follicle development and growth. Finally, we reveal that although MBP shows overall genetic correlation only with height, this changes once the correlations are estimated only over the enriched pathways, helping to understand the observed epidemiological results.10, who self-identified as British and were also considered genomically British by UKB. All imputed SNPs on the autosomes and genotyped SNPs on chromosome X were used, for a total of 27,512,692. Discovery GWA identified 12,192 SNPs significantly (p < 5 × 10−8) associated with MBP. Replication was sought for significant SNPs using several independent cohorts: UKB participants of non-British origin, two prospective cohorts of European Americans (ARIC11 and HPFS12) and 23andMe Inc.13  from UK Biobank (UKB)14. Fig. .Table 1S15. The 71 loci contain 107 distinct SNPs  but also foreskin keratinocyte and melanocyte primary cells . All SNPs with p < 1 × 10−5 in the 71 replicated loci were subject to tissue- and gene-set enrichment with DEPICT 1.121. Tissue enrichment analysis did not yield any results , and three distinct signals. SRD5A2 encodes a protein that converts testosterone to dihydrotestosterone (DHT), with five distinct hits near the gene. Additionally, our SNP rs5934505, located on chromosome X close to FAM9B, has also been associated with testosterone levels24.Androgen receptor signalling , genes involved in apoptosis  and a third more heterogeneous group including the androgen receptor and TGF-beta pathways . Supplementary Fig. 25, our results suggest that in addition to the androgen receptor pathway, for which we confirm a prominent function, the Wnt and apoptosis pathways play central roles. MPB is characterised by a shorter growth (anagen) phase, which has been associated with increased apoptosis25 of the hair follicle cells. These results suggest that the anagen phase becomes shorter because of differences in the genes regulating apoptosis. The Wnt pathway has been implicated in the transition from the resting (telogen) phase to the anagen phase26, and also in the determination of the fate of the stem cells in the hair bulge27, which are both dysregulated in balding tissue.Three main groups were found: genes linked to 28 to build an interaction network between the prioritised genes. Thirty-three of the selected genes were connected in a large network which included 8 of the 13 genes differentially expressed in balding dermal papilla cells under DHT stimulation29. Overlaying the GO term-based communities with the interaction pathways shows that the genes in the signalling community  revealed that 14 loci show strong correlation with previously published GWAS loci including various diseases and quantitative traits  or at the genome-wide level (genetic correlation), however it is plausible that any genetic overlap is limited to specific pathways and that this correlation is lost in the overall score. We thus tested each of the enriched pathways and the three pathway-based communities. Each PGRS was tested against numerous traits on the genomically British UKB cohort (see “Methods” for details). Table Wnt signalling, whereas this genetic predisposition is shared with increased risk of any cancer, when considering only variants in the apoptosis pathway or community. Although in both examples, one of the loci in the pathway is significant by itself, the pathway score was stronger, suggesting the other genes in the pathway also contribute, with the same direction of effect. Finally, baldness risk loci in the WNT ligand biogenesis and trafficking and Class B/2 (Secretin family receptors) pathways were also associated with height, despite none of the individual loci in these pathways being significant: this suggests a “pathway-wide” effect. Therefore, baldness shows pathway-specific genetic correlations, which provide a potential biological basis to observed epidemiological correlations. Pathway-specific genetic correlations hold promise in disentangling the shared biological pathways underpinning complex diseases.Pleiotropy analysis conducted with GENOSCORES , however we must consider that in the first case a different method of converting the explained phenotypic variance from the observed scale to the liability one was used instead of the one implemented in GCTA while in the other rather dubious baldness cases were included , which may explain the difference.We have observed an hIn conclusion, we show baldness to be one of the most heritable complex traits, for which we are able to explain nearly two fifths of the heritability with only 71 loci. Recurring themes in complex trait genetics are highlighted, including multiple distinct signals in many loci, aggregation of genetic effects in pathways important to the trait and widespread pleiotropy with other traits and diseases; but we also emphasise pathway-specific genetic correlations as a new approach to dissect the genetics and biology of complex diseases.All subjects gave written informed consent. UK Biobank has approval from the North West Multi-centre Research Ethics Committee (MREC), In Scotland, UK Biobank has approval from the Community Health Index Advisory Group (CHIAG). ARIC has approval from the ARIC Publications Committee and the ARIC Coordinating Center. The HPFS was approved by the IRB of the Harvard School of Public Health.35 scale, the third to a IIIv–IV grade and the fourth to a V+ grade. To be certain of using people actually affected by MPB, we used as cases people who self-identified themselves as being in the third or fourth group while as controls people in the first category. Given that people in UK Biobank have been selected to be of ages between 40 and 69, by when baldness is fully developed, no age filter was applied. Genotypes both measured and imputed were obtained from UK Biobank and no further QC was applied. Details can be found at http://www.ukbiobank.ac.uk/wp-content/uploads/2014/04/UKBiobank_genotyping_QC_documentation-web.pdf and http://www.ukbiobank.ac.uk/wp-content/uploads/2014/04/imputation_documentation_May2015.pdf.In UK Biobank samples, the degree of baldness was defined as part of a self-administered questionnaire. Each male participant was asked to recognise his hair/balding pattern comparing with four different pictures. The first would correspond to no sign of baldness, the second to a II–IIIa grade on the Norwood–Hamilton36. Participants were asked to select their hair pattern at age 45 from five images  modified from the Hamilton–Norwood scale35 Cases were defined as experiencing frontal and (any) vertex baldness at age 45, which corresponds to at least a IV grade on the Hamilton–Norwood scale. Controls were defined as those experiencing no baldness at age 45.Health Professionals Follow-up Study (HPFS) is an on-going prospective analysis of male US health professionals, information on hair pattern at age 45 was collected by self-administered questionnaires during the 1992 follow-up11. Baseline examinations took place from 1987 to 1989. During the fourth visit (1996–1998), baldness pattern was classified according to the Hamilton baldness scale, as modified by Norwood35. A trained technician in each clinic observed the participant’s head from two angles (side and top), compared the natural hair pattern with a series of 12 figures, and chose the best matching figure. These figures corresponded to categories on the Hamilton baldness scale . A score of 13 was recorded for complete baldness. More details about these measurements have been previously described37. Cases were defined as individual with grade III or higher, whereas controls were defined as individuals with grade I. Given that the participants of the ARIC study were all between 53 and 74 years old, no age filter was applied. We restricted our analysis to European-American men.The Atherosclerosis Risk in Communities Study (ARIC) is a prospective population-based cohort study of individuals from four US communities9 who provided informed consent and participated in research online, under a protocol approved by the external AAHRPP-accredited IRB, Ethical & Independent Review Services. Participants provided responses to the “Hair Loss in Men and Women” survey. Only responses from male research participants were included. Survey questions included the following: “Please choose the image that best captures your hair’s pattern and density. If your head is shaved, please answer for how your hair looks when grown out. If none of these images are similar to your hair’s pattern and density, choose none of the above.” ; “Have you experienced hair loss or thinning?” ; “How old were you when you first started to notice hair loss?”  Cases reported having experienced hair loss or thinning, with onset before age 40, and current hair loss of Hamilton grade III or higher. Controls are at least 30 years old, and report not having experienced hair loss or thinning, and at most Hamilton grade I, or if age 50 or older, Hamilton grade II.23andMe data were obtained from research participants of 23andMe, Inc.38 on all 27,512,692 imputed SNPs, which had a minor allele count of at least 100 using the following model:Case–control association analysis on UK Biobank genomically British samples was conducted in two steps. First genome-wide association using linear regression  was conducted using RegScanp < 1 × 10−5 were extracted from the original bgen files using bgenix (http://www.well.ox.ac.uk/~gav/bgen_format/) and analysed using logistic regression using the same covariates as in the first step. For this step, SNPtest v2.5.239 was used. The two-step approach was used in order to make the analysis time tractable since available software would have taken months to run the logistic regression analysis even on a large computing cluster.For chromosome X, given the unavailability of imputed SNPs, genotypes were used. All SNPs with p value inflation was checked using genomic control and LD regression: λGC 1.15, LD regression intercept 1.0451. The difference in value indicates that the inflation measured by genomic control is due to the GWA and not to stratification.Potential 13 was obtained from 23andMe. The association analyses in the replication cohorts were limited to only the 12,192 SNPs significant at the discovery step. After association analysis in each cohort, results were meta-analysed using the inverse variance approach as implemented in METAL40. Given the large sample size, no filter on MAF or imputation quality was applied. For UK Biobank non-genomically British samples, case–control association analysis was performed using SNPtest v2.5.239. Logistic regression was performed assuming an additive model for the allelic effect using the model:Replication association analysis was performed using four different cohorts: samples self-defining as British but genomically non-British from UK Biobank, HPFS and ARIC. Additionally, data from the recent MBP GWASGC 1.02, LD regression intercept 1.0021). Finally, in order to verify possible heterogeneity of effect between the two UK Biobank cohorts, we compared effect sizes for the 107 detected distinct SNPs. Figure In order to verify if PCs were able to correct for the population structure, we used two different methods applied to the association GWA analysis: genomic control and LD regression. Both methods showed no evidence of test statistic inflation  to transform the results from the observed to the liability scale. In order to verify how much variance was explained by the identified SNPs, we added the estimated polygenic risk score as a fixed effect in the GREML and measured the decrease in the proportion of variance due to the relationship matrices.Heritability was estimated on 20,000 unrelated samples from the discovery cohort using GCTA. Two separate kinship matrices were estimated from SNP array genotype data: one for the autosomes and the other one for chromosome X. We then calculated the heritability explained by each of these matrices using the GCTA-GREML22 enrichment software. Nine genes in different loci were annotated as being associated with hair follicle development (GO:0001942) and hair cycle processes (GO:0022405). As a third criterion, we verified if any of the genes in our loci showed significantly different expression patterns between balding and non-balding dermal papilla cell lines at baseline and after stimulation with DHT (the active form of testosterone)29 (Supplementary Data http://129.125.135.180:8080/GeneNetwork/) to assess if any of the candidate genes were predicted to be associated with hair cycle or growth. Sixteen additional genes not previously selected were predicted to be related to hair cycle. Fifth, we evaluated the presence of eQTL, which could be explained by the selected SNPs or those in strong LD with them using various approaches: HaploReg v4.120, the GENOSCORES platform (see below) and eQTL analysis in peripheral blood. For this last analysis, we used cis-eQTL data from a total of 2360 unrelated individuals obtained from three data sets with gene expression data measured from whole peripheral blood  cosmopolitan reference panel45 and imputation dosage values were used for analysis. A more detailed overview of the quality control has been published elsewhere18. To detect cis-eQTLs, we assessed only those combinations of SNPs and probes where the distance between SNP and the midpoint of the probe was smaller than 1 megabase (Mb). Individual data sets were meta-analysed using a Z-score method, weighted for the sample size of each data set. The sample labels were permuted (repeated 100 times) in order to obtain the p value distribution used to control the FDR at 5%. Since SNPs can be highly correlated due to LD, cis-eQTL effects are often caused by SNPs in high LD with the disease-associated query SNP. In order to determine whether our disease-associated SNPs have independent cis-eQTL effects with respect to other SNPs in their locus, we performed conditional analysis. Using the procedure described above, we first determined which SNPs show the strongest cis-eQTL (eSNP) effect for each of the probes associated with the 107 disease-associated SNPs (gSNP). Then, we adjusted the gene expression data for these effects using linear regression, and repeated the cis-eQTL analysis on the disease-associated SNPs (and vice versa). This analysis allowed us to identify disease-associated variants that were also the best cis-eQTL SNPs. For the remaining loci, genes were assigned based on the DEPICT gene prioritisation only for those with FDR < 0.05. Supplementary Data 23.Given the particular nature of our phenotype, in order to prioritise the genes present in the 71 identified loci, we created a set of custom criteria. Given the importance of the androgens in MBP, the first criterion was to belong to any of the androgen-related pathways, six genes fulfilled this criterion. The second criterion was if any gene could be linked to hair cycle or growth. We ran the whole gene list through the ConsensusPathDB-humanhttps://pm2.phs.ed.ac.uk/genoscores/). Briefly, summary results of the GWAS were used to compute genotypic scores for each hit region in the 2432 individuals comprising the UK10K reference panel. These genotypic scores were merged with a table of genotypic scores computed on the same reference panel using a comprehensive database of publicly available GWAS summary statistics for diseases and quantitative traits including gene transcript levels. SNPs were filtered at a p value of 1 × 10−6. Each genotypic score was computed as a sum of genotypes  weighted by the effect size estimate . For all traits except gene transcript levels, genotypic scores were computed separately for each trait-associated region. For each trait, trait-associated regions were assigned for each genomic region containing at least one SNP with p value <1 × 10−7. The boundaries of this region were defined by the positions at which there was a gap of at least one megabase from any other SNPs with p value <1 × 10−6. This procedure yielded 74 regional genotypic scores for baldness, of which 15 were correlated (squared correlation at least 0.5) with at least one other score for another trait. For each block of traits correlated with one of the regional genotypic scores for baldness, the correlations were plotted in a heat map. Results from this analysis were kept only for the 71 significant replicated loci.Pleiotropy with previous GWAS was estimated using the GENOSCORES platform . The characteristic that described each community was determined by visually examining how the genes in each community related to the enriched known pathway. We used the same approach using as input the 303-enriched GO terms and then using the Louvain method to identify communities of genes highly interconnected with each other. Given the complexity of the resulting network, it was impossible to assign a significance to each group through visual inspection of the gene-term graph. We thus ran enrichment analysis on each set of genes separately for each identified community. The interaction network resulting from the prioritised genes was created using STRING28, allowing only for direct interactions.Enrichment analysis was conducted limited to the selected genes using ConsensusPathDB-humanWe created two sets of polygenic risk scores plus an overall PGRS comprising all 107 SNPs. Before creating the scores, the betas for each SNP were re-estimated running logistic regression on all SNPs at the same time using as covariates age and 10 PCs. Genotypes for each SNP were weighted by their beta (dosage × beta). The score at each locus was defined as the sum of all the weighted “distinct” SNPs belonging to the locus: in this way, we obtained 71 locus scores. The overall PGRS was obtained by summing all the locus scores. We then estimated a PGRS for each of the enriched pathways by adding all the locus scores for the loci, which contained the genes in the pathway. “Apoptosis” was merged with “apoptotic signalling pathway”, “Wnt signalling pathway” was merged with “Wnt signalling pathway and pluripotency” and “WNT ligand biogenesis and trafficking” with “Wnt signalling in kidney disease” since in all cases the scores were composed of the same loci and were thus identical. We thus obtained 25 further pathway PGRS. Table q values were used for assessing significance considering multiple testing. Binary traits of participants were tested using logistic regression. The traits tested were smoker, ever smoked and attended college. Disease traits in participants were tested using logistic regression. The traits tested were cancer diagnosis, suffered stroke, suffered depression, diabetic, female reproductive problems, suffered bone fracture, heart disease, multiple sclerosis, peripheral artery disease, psoriasis, renal problems and respiratory problems. Disease traits in parents were tested using logistic regression. The traits tested were Alzheimer’s disease, bowel cancer, breast cancer, chronic obstructive pulmonary disease, diabetic, heart disease, hypertension, lung cancer, Parkinson’s disease, stroke and prostate cancer. Survival traits of parents were tested using a Cox model with age as the time of survival and alive/dead as status. The trait tested was age.Each polygenic risk score was tested for association with trait using a regression model, with age, sex, genotyping array batch, Townsend deprivation index (a measure of socio-economic status) and the first 15 principal components of the genomic relationship matrix as covariates. Where parental traits were tested, maternal and paternal traits were considered separately. In total, 96 traits were selected for testing for a total of 4320 tests. Storey’s Quantitative traits in participants were tested using linear regression. The traits tested were educational attainment, height, weight, BMI, body fat %, age at menarche and age at menopause.All data that support the findings of this study are available from the corresponding author on reasonable request with the exception of results from 23andMe. To request access to the 23andMe summary statistics, please email apply.research@23andme.com.Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Supplementary Data 15Supplementary Data 16Supplementary Data 17Supplementary Data 18Supplementary Data 19Supplementary Data 20Supplementary Data 21