Most quantitative measures of phenotypic traits represent macroscopic contributions of large numbers of cells. Yet, cells of a tissue do not behave similarly, and molecular studies on several organisms have shown that regulations can be highly stochastic, sometimes generating diversified cellular phenotypes within tissues. Phenotypic noise, defined here as trait variability among isogenic cells of the same type and sharing a common environment, has therefore received a lot of attention. Given the potential fitness advantage provided by phenotypic noise in fluctuating environments, the possibility that it is directly subjected to evolutionary selection is being considered. For selection to act, phenotypic noise must differ between contemporary genotypes. Whether this is the case or not remains, however, unclear because phenotypic noise has very rarely been quantified in natural populations.S. cerevisiae morphology at single-cell resolution. We profiled hundreds of quantitative traits in more than 1,000 cells of 37 natural strains, which represent various geographical and ecological origins of the species. We observed abundant trait variation between strains, with no correlation with their ecological origin or population history. Phenotypic noise strongly depended on the strain background. Noise variation was largely trait-specific (specific strains showing elevated noise for subset of traits) but also global (a few strains displaying elevated noise for many unrelated traits).Using automated image analysis, we describe here the phenotypic diversity of Our results demonstrate that phenotypic noise does differ quantitatively between natural populations. This supports the possibility that, if noise is adaptive, microevolution may tune it in the wild. This tuning may happen on specific traits or by varying the degree of global phenotypic buffering. Modern biology is quantitative and scientists now pursue the exciting goal to link quantitative phenotypic variations to mechanistic molecular regulations. A frequent limitation in these investigations is the ability to accurately quantify the phenotype of interest. Tracking molecules and their abundance is sometimes not an issue, but defining and acquiring phenotypic traits precisely can be very demanding. In particular, most phenotypic measurements are made on macroscopic quantities reflecting the contribution of many cells. This is the case when describing tissue morphologies, growth rates of microorganisms, virulence of pathogens, yields of plants or the clinical outcome of a patient. However, rare cells, or heterogeneities among cells, may have important macroscopic consequences. Traits such as cancer, developmental defects, escape from drug treatment, or latency of infections can rely on one or few cells that did not follow the average behavior of a tissue. In these cases, quantifying biological traits at single-cell resolution is invaluable because it offers the possibility to link molecular variations to the microscopic sources of phenotypic variation. For example, an increased penetrance of a macroscopic trait may be associated to increased noise or to the presence of a stochastic switch, but finding this association requires to track the underlying mechanism in numerous individual cells ,2. BioloS. cerevisiae, with appropriate amino acid and base supplements. The final concentration of each amino acid supplement was 20 μg/ml for adenine, uracil, histidine, methionine and 30 μg/ml for leucine. Cells were cultured in the 20 ml liquid SD medium at 30°C to logarithmic-phase. Cell fixation, staining and image acquisition were performed as described previously . At leaseviously .http://www.r-project.org). A Kruskal-Wallis rank sum test was performed for every trait against the null hypothesis of no strain effect. The dataset contained, for each trait, 5 independent values per strain, across 37 strains. We compared the observed values of the K statistics with an empirical null distribution obtained by running the test 1,000 times on permuted datasets. At each permutation, all 185 traits values were re-attributed to strains, so that each strain was associated with 5 randomly picked values. On average across these permutations, only 4.15 traits showed K > 56, whereas this threshold was reached for 440 traits when using the actual dataset. We therefore used this list of 440 significant traits corresponding to FDR = 0.01.All statistical analyses were done using R , we concluded that no significant association could be claimed.For each trait, a possible association to the ecological or geographical origin of the strains was tested as follows. For each strain, the trait values across the 5 replicates were averaged. We then applied a Kruskal-Wallis rank sum test on the factor of interest (ecology or geography). The lowest pvclust1/2, where n = 37 is the sample size, significantly deviated from the t-distribution with n - 2 degrees of freedom. We applied a Bonferroni correction to retain only those with nominal p-value lower than 0.05/532, which are listed in Additional file We considered only the 76 noise traits that were significantly affected by the strain background. We first transformed the dataset of 185 × 76 noise trait values into sums of ranks: for each noise trait, every strain was assigned the sum of its 5 ranks as previously described . This rehttp://sunlight.k.u-tokyo.ac.jp/wild37noise/index.html.Raw images and datasets are freely available at The authors declare that they have no competing interests.GY: Conceived and designed the study, analyzed the data, interpreted the results, developed analysis codes, wrote the paper. SO: Analyzed the data, interpreted the results, developed analysis codes and made figures of the paper. SN: Managed experiments. YI: Performed the experiments. SF: Interpreted the results. JS: Contributed strains and interpreted the results. YO: Conceived and designed the study, directed experiments and analyses, interpreted the results. All authors read and approved the final manuscript.List of strains used in this study.Click here for fileList of 440 traits with significant inter-strain variation at FDR 1%.Click here for fileFigure S2. Principal component analysis of S. cerevisiae morphological variation. Dots represent strains by their coordinates along principal components pPC3 and pPC4, from the same PCA analysis as in Figure Figure S3. Heatmap of the rank-sum values of the parameters contributing to discriminate strain classes I, II and III by LDA. The dendrogram and strain labels at the top are the same as in Figure Figure S4. Strains distribution along the parameters representing the morphological features of each class. Pink, greenyellow, lightorange and black circles indicate strains of classes I, II, III and others, respectively. Red frames indicate scatter plots of the distribution of the 37 strains on the representative parameters for each class. A) Parameters representative of Class I. B) Parameters representative of Class II. C) Parameters representative of Class III. Figure S5. Principal component analysis of S. cerevisiae genetic variation. A boolean matrix of the single nucleotide polymorphisms  was used for principal component analysis. A) Strains are represented by their coordinates along the first two principal components, using the same colors as in Figure B) Cumulative proportion of variance. Grey bars indicate the proportion of variance (left axis) in the gPCs. Red circles indicate the cumulative proportion of variance (right axis) in the gPCs. Horizontal broken red line indicates 0.45 of the cumulative proportion of variance.Cumulative proportion of variance of the principal component analysis for the phenotypes. Black and grey bars indicate the proportion of variance (left axis) explained by the pPCs without randomization and after randomization, respectively. Red circles and rectangles indicate the cumulative proportion of variance (right axis) explained by the pPCs without randomization and after randomization, respectively. The horizontal dashed red line indicates 97% of the cumulative proportion of variance. r et al. 9) was usClick here for fileParameters contributing to the first four phenotypic principal components.Click here for fileParameters contributing to phenotypic classes I, II and III, as determined by Linear Discriminant Analysis.Click here for fileList of 76 noise traits with significant inter-strain variation.Click here for fileNoise traits contributing to the first six noise principal components.Click here for file


MSI2 gene on chromosome (SSC) 14 was very strongly associated with NVD. Thirty-six SNPs were located in genome regions where QTLs have previously been reported for behavior and/or feed intake traits in pigs. The regions: 64–65 Mb on SSC 1, 124–130 Mb on SSC 8, 63–68 Mb on SSC 11, 32–39 Mb and 59–60 Mb on SSC 12 harbored several signifcant SNPs. Synapse genes , dephosphorylation genes  and positive regulation of peptide secretion genes  were highly significantly associated with feeding behavior traits. This is the first GWAS to identify genetic variants and biological mechanisms for eating behavior in pigs and these results are important for genetic improvement of pig feed efficiency. We have also conducted pig-human comparative gene mapping to reveal key genomic regions and/or genes on the human genome that may influence eating behavior in human beings and consequently affect the development of obesity and metabolic syndrome. This is the first translational genomics study of its kind to report potential candidate genes for eating behavior in humans.This study was aimed at identifying genomic regions controlling feeding behavior in Danish Duroc boars and its potential implications for eating behavior in humans. Data regarding individual daily feed intake (DFI), total daily time spent in feeder (TPD), number of daily visits to feeder (NVD), average duration of each visit (TPV), mean feed intake per visit (FPV) and mean feed intake rate (FR) were available for 1130 boars. All boars were genotyped using the Illumina Porcine SNP60 BeadChip. The association analyses were performed using the GenABEL package in the R program. Sixteen SNPs were found to have moderate genome-wide significance (p<5E-05) and 76 SNPs had suggestive (p<5E-04) association with feeding behavior traits.  However, QTLs are often mapped by linkage analysis to a large interval of 20 centimorgans (cM) or more that may contain several hundreds of genetic variants, not ideal for accurate mapping of potential causal variants Feed represents a large proportion of the variable costs of breeding. Therefore, selection for reducing feed intake is a very important goal in breeding programs, at least in Danish pig breeds. Genetic improvement in feed efficiency was historically achieved as a correlated genetic change resulting from selection for growth rate and carcass lean content for animals tested in groups, where individual feed intake was too expensive to be measured on a large number of pigs. In recent years, the study of feed intake and behavior in pigs has been greatly facilitated by development of computerized systems that record the feed intake and related measures of individual animals within a group each time they enter the feeder. Several studies have shown low to moderate and positive genetic correlation between feeding behavior traits and daily feed intake. For instance, DFI had a positive genetic correlation with NVD (r = 0.27) The obesity epidemic has become one of the most important public health problems et al. ad libitum from 30 kg to approximately 100 kg live weight with the same feed composition. The time, duration and feed consumption was recorded for each individual visit. Average daily feed intake (DFI) was derived from the total amount of recorded feed intake divided by the number of corresponding days at the feeder. The following feeding behavior traits were defined and calculated for each boar: DFI: total daily feed intake (kg/d), TPD: total time spent at feeder per day (minute), NVD: number of visits to the feeder per day, TPV: average duration of each visit ( =  TPD/NVD), FPV: mean feed intake per visit (kg) and FR: mean feed intake rate (g/minute) ( = DFI/TPD) A total of 7388 Duroc pigs had phenotypic records from the period of 2008–2011 and 1909 boars had 60 k SNP genotype records. The selection of boars to be genotyped and sent to the test station (i.e. phenotyping) was primarily based on their aggregate breeding value, but feeding behavior is not directly part of the breeding goal of Danish pig breeds and some genotyped boars have no recorded phenotype. For GWAS, anmials had to have both phenotypic and genotypic information; 1130 boars that had both genotypic and phenotypic records for feeding behavior traits were used in the study. Summary statistics of phenotypes are shown in et al. et al. et al. The estimated breeding values (EBVs) for DFI and feeding behaviors were calculated by single-trait animal model with fixed effect of herd-year-season, random effect of pen and a random additive genetic effect, as in Duy The details of the genotyping method have been described previously ibs function of GenABEL which uses identity by state (IBS) genotype sharing to determine the realised pairwise kinship coefficient. Then a genome-wide association analysis was performed using a score test, a family-based association test, implemented in the mmscore function of R/GenABELy  =  Xb + Wp + Za + e (1) is implemented in two steps in GenABEL. In the equation (1), y is the vector deregressed EBVs for a given trait, X is an incidence matrix for fixed non-genetic effects b (herd–week section and pen), W is a vector with genotypic indicators  associating records to the marker effect, p is a scalar of the associated additive effect of the SNP, Z is an incidence matrix relating phenotypes to the corresponding random polygenic effect, a is a vector of the random polygenic effect with the normal distribution a ∼ N is fitted only once and all fixed, polygenic and residual components are estimated using the REML approach. In the second step, with the estimated heritability estimate and kinship coefficients for each pair of relatives, the correlation between phenotypic records of relatives are adjusted and approximate IID  phenotypes with normality are obtained.The relationship matrix used by the “polygenic” linear mixed effects model was generated by the mmscore test for family-based association is then conducted on the adjusted phenotype from the second step which takes into account pedigree structure and allows unbiased estimations of SNP allelic effect when relatedness is present between examinees This http://animalgenome.org/cgi-bin/QTLdb/indextag (significant and suggestive) SNPs with human genomic map using RH map and comparative maps provided by Mayer et al., tag SNPs was obtained using Ensembl annotation of Sscrofa10.2 genome version (http:// ensembl.org/Sus_scrofa/Info/Index). The positional candidate genes within 1 Mb bin size on either side of top SNPs peak were scanned using the function GetNeighGenes in the NCBI2R package at http://cran.r-project.org/web/packages/NCBI2R/index.html using the R program http://david.abcc.ncifcrf.gov/SNP positions were updated according to the newest release from Ensembl (Sscrofa10.2 genome version). Comparative mapping was performed by annotating significant SNP position to previously mapped QTL in pigs using the pig QTL database: Following quality control of SNP data, 23795 markers were excluded as having a low (<5%) minor allele frequency, 1836 markers were excluded because of low (<95%) call rate and 3463 markers were excluded because they were not in HWE (p<0.001). A final set of 33945 SNPs and 1130 pigs was retained for GWAS. The number of markers on each chromosome and average distances between two markers after quality control are given in Among 92 significant SNPs, 16 were found to have moderate genome-wide significance  and 76 wA total of 652 gene identities (Entrez ID) was located in 1Mb window size from SNP positions . HoweverA total of 36 SNPs were located in the genomic region where QTLs have previously been mapped for behavior and/or feed intake traits in pigs . Eight lWe indentified the five most significant QTL (contained more than 5 significant SNPs) for eating behavior traits including regions of 64–65 Mb on SSC 1 influencing DFI, 124–130 Mb on SSC 8 influencing both FR and TPD, 63–68 Mb on SSC 11 influencing TPD, 32–39 Mb and 59–60 Mb influencing NVD and TPV on SSC 12, respectively. The QTL region for DFI on SSC 1 located on p2.1 cytogenetic band  which isSince no GWAS study for feeding behavior in pigs has been previously published, we have made an attempt to overlap our association signals with those of previously reported QTLs. However, direct comparison between data obtained in this study and those from previous QTL studies is hindered by the fact that locations given in centimorgan on different genome assemblies do not necessarily reflect the same physical location on the genome et al. et al, On SSC 1, we found that eight SNPs associated with DFI are in previously mapped QTL which spanned 49–73 (cM) for feed intake in a Pietrain/Meishan F2 family 2 = 0.56 between adjacent markers) GABRR2 and SRSF12); hence, it could be interesting to further investigate the functional involvement of these two genes in relation to DFI. Adjacent to GABRR2 is the GABRR1 gene which encodes the GABA receptor γ1 subunit  gene. GABRR2 encodes for a receptor of Gamma-aminobutyric acid (GABA) which is the most important inhibitory neurotransmitter in the vertebrate central nervous system (CNS) and is involved in manifold physiological and pathological processes GABRR1 gene, which is in the same transcriptional orientation, suggesting a similar expression and regulatory pattern as GABRR2. The GABA and these receptors have a known function in controlling feed intake, as shown in different species such as rats GABRR2 was significantly changed after fasting and refeeding in the hypothalamus in mice et al. SRSF12, ANKRD6, RRAGD, PM20D2, RNGGT, MDN1, and UBE2J1 might be interesting to investigate, since these functions are related to regulation of gene expression or signaling pathway  was found to be significantly associated with DFI in the current study and it is located in the intron region of the Gamma-aminobutyric acid receptor subunit rho-2  as a key fuel sensor in hypothalamic neurons DDIT4L may involve feeding behavior via nutritional impacts.The significant loci MARC0085057 was closest to LX1 gene , whose frotensin . NeuroteMIS2) is the known gene located closest to them. This gene encodes an RNA-binding protein and play central roles in posttranscriptional gene regulation in mammals MSI2 gene and GABA receptor genes are connected in controlling feeding behavior. Moreover, we found two mutations in the TCF7L2 gene suggestively associated with NVD  was close to significant SNPs associated with TPV (GATA3 is a transcription factor of the Gata Zn-finger family which performs important functions during organogenesis The ElaC homolog 2 (with TPV . This gewith TPV . GATA3 iACO1 gene was close to significant SNPs associated with FPV (DLGAP2 gene (DLGAP2 variants were found significantly associated with autism spectrum disorders CLN8) plays a role in cell proliferation during neuronal differentiation DLGAP2 and CLN8 were located on SSC15  is the most interesting gene for FR  plays an important role in linking the actin cytoskeleton to the plasma membrane at the synaptic junction CADPS2 gene encodes a member of the calcium-dependent activator of secretion (CAPS) protein family, which are calcium-binding proteins that regulate the exocytosis of synaptic and dense-core vesicles in neurons PTPN4, PTPN18 and PTPRZ1 genes are members of the protein tyrosine phosphatase (PTP) family. A recent review described PTPs as central regulators of metabolism, specifically highlighting their interactions with the neuronal leptin and insulin signaling pathways PPM1E was located in the nucleus of the cell and it encodes a member of the PPM family of serine/threonine-protein phosphatases. The encoded protein dephosphorylates and inactivates multiple substrates such as 5′-AMP-activated protein kinase (AMPK) which is well documented to play key roles in controlling energy balance PPM1E gene on feeding behavior may be mediated by AMPK. Another significant biological process involves the nearby genes  having a positive regulation of peptide secretion  also plays a very important role in energy homeostasis by balancing food intake MMTP) gene located in HSA q24 were found as a candidate gene for obesity MTTP gene in feed intake may be due to its involvement in the gut leptin-melanocortin pathway Our pig-human comparative mapping approaches revealed key genomic regions and/or genes on the human genome that may influence eating behavior in human beings and consequently lead to obesity and metabolic syndrome. For instance, the QTL for DFI on SSC 1 was homologous with HSA 6q23–24 region  which haFeeding or eating behavior are important traits in pig production, as they are directly related to feed efficiency and hence cost of pig production, but their genetic mechanisms have not been extensively studied. This is the first GWAS study pinpointing a number of significant SNPs associated with feeding or eating behavior in pigs. This study presented a comprehensive approach by combining GWAS and post-GWAS bioinformatics as well as comparative mapping approaches to elucidate genomic regions and candidate genes associated with eating behavioral traits in pigs. Post-GWAS analyses highlighted potential candidate genes for feeding behavior. Several nearby genes have been mentioned directly or indirectly as being involved in the genetic control of eating or feeding behavior traits in either pigs or other species. Pigs are a well-known animal model for studying human obesity. We have conducted pig-human comparative gene mapping to reveal key genomic regions and/or genes on the human genome that may influence eating behavior in human beings and consequently affect the development of obesity and metabolic syndrome, both of which are key societal and public health problems. This is the first study to report results on genes that may affect human eating behavior via such translational genomics approaches.Figure S1Multidimensional scaling plot of identity by state distances. The principal component analysis fitted the genetic distances along the two components. The results showed that no population stratification in the data. Each point on the plot corresponds to a pig, and the 2D distances between points were fitted to be as close as possible to those presented in the original identity by state matrix. You can see that study subjects clearly cluster in a group.(TIF)Click here for additional data file.Figure S2A quantile-quantile plot of observed and expected p-values for feeding behavior traits. The inset shows a quantile-quantile (qq) plot with the observed plotted against the expected p-values for total daily feed intake (DFI), total time spent at feeder per day (TPD), number of visits to the feeder per day (NVD), time spent to eat per visit (TPV), mean feed intake per visit (FPV), and mean feed intake rate (FR) from top to bottom, respectively.(TIF)Click here for additional data file.Figure S3Comparative mapping between QTL on pig chromosome 8 and humanchromosome 4. (a) Cytogenetic band, approximate positions of QTL for mean of feed intake rate FR) and total time spent at feeder per day (TPD) shown in both cM and Mb, (b) linkage map, radiation hybrid mapping and human map of selected regions based on QTL database (release19). The read band indicated QTL presence.(TIF)Click here for additional data file.Figure S4Comparative mapping between QTL on pig chromosome 11 and humanchromosome 13. (a) Cytogenetic band, approximate positions of QTL for total time spent at feeder per day (TPD) shown in both cM and Mb, (b) linkage map, radiation hybrid mapping and human map of selected regions based on QTL database (release19). The red band indicates QTL presence.(TIF)Click here for additional data file.Table S1Distribution of SNPs after quality control and average distances on each chromosome.(DOC)Click here for additional data file.Table S2Suggestive SNPs associated to studied eating behavioral traits, their positions and nearest genes for feeding behavior traits.(DOC)Click here for additional data file.Table S3List of nearby genes in 1 Mb region flanking the associated SNPs.(DOC)Click here for additional data file.Table S4Haplotypes and their frequencies in the candidate region for number of visits to feeder per day on chromosome 12.(DOC)Click here for additional data file.


These developments are geared toward explaining a part of the missing heritability, and when combined with individual genomic profiling, such systems medicine approaches may also provide a principled means for tailoring personalized treatment strategies in the future.A central challenge in systems biology and medical genetics is to understand how interactions among genetic loci contribute to complex phenotypic traits and human diseases. While most studies have so far relied on statistical modeling and association testing procedures, machine learning and predictive modeling approaches are increasingly being applied to mining genotype-phenotype relationships, also among those associations that do not necessarily meet statistical significance at the level of individual variants, yet still contributing to the combined predictive power at the level of variant panels. Network-based analysis of genetic variants and their interaction partners is another emerging trend by which to explore how sub-network level features contribute to complex disease processes and related phenotypes. In this review, we describe the basic concepts and algorithms behind machine learning-based genetic feature selection approaches, their potential benefits and limitations in genome-wide setting, and how physical or genetic interaction networks could be used as  A major challenge of medical genetics is to determine a set of genetic markers, which when combined together with conventional risk factors could be used in predicting an individual's susceptibility to developing various complex disorders. The recent advances and wide availability of genetic technologies, such as those based on genome-wide association (GWA) and next-generation sequencing (NGS), have allowed for the in-depth analysis of the variation contained in the human genome. In particular, these technologies are enabling the investigation of the genetic architecture of complex diseases, with the aim of constructing more accurate disease risk prediction models that would eventually facilitate effective approaches to personalized prevention and treatment alternatives for many diseases ,2. Whiletability’. Suggesttability’,9. The repistatic interactions, as one of the major factors contributing to the missing heritability [gray zone’ of genetic information is likely to result in models that are missing an important proportion of the quantitative variation in heritability. Therefore, it may be that most of the heritability is hidden rather than missing, but has not previously been detected because the individual effects are too small to pass the stringent significance filters used in many studies, yet still having significant contribution to the predictive power at the level of variant or subject subsets, or when combined with non-genetic risk factors.Given the multi-factorial nature of complex diseases, many authors have reiterated the concept of interactions among genetic loci, so-called tability ,10. Epistability -14. Thertability ,16. Althtability ,18. Ignop < 10-8), machine learning algorithms place special emphasis on maximizing the predictive accuracy at the level of individual subjects. The goal of feature selection is to identify such a panel of genetic and other risk factors, which result in a model that optimally predicts the phenotypic response variables, either the class labels in case-control classification , or quantitative phenotypes in regression problems (e.g. height prediction). While epistatic genetic interactions may easily end up being averaged out in statistical association models, machine learning-based predictive modeling can also take into account those individual effects that are dependent on interactions with other variants or environmental exposures, making these models convenient for developing predictive strategies for multi-factorial diseases. Indeed, it has been shown that single-locus p-value-based selection strategies for constructing prediction models may lead to sub-optimal prediction accuracies [p-values, which does not take into account any gene-gene interactions.Here, we discuss how computational machine learning approaches can utilize hidden interactions among panels of the genetic and other risk factors, predictive of the individual disease risk by means of implementing genetic feature selection procedures and network-guided predictive models. In contrast to the conventional population-level association testing, which often detect only a few variants with statistical support beyond the genome-wide significance level , comparp-values for disease risk association, are perhaps not the most appropriate means for evaluating the predictive or clinical value of the genetic profiles [Filter methods for genetic feature selection are the most common in GWA studies due to the simplicity of their implementation, low computational complexity, and the human interpretability of the results. In their simplest form, filter methods calculate a univariate test statistic separately for each genetic feature, and the features are then ranked based on the observed statistic values. The highest ranked features form the final set of selected features, on which a predictive model may be subsequently trained. The number of features to be selected is either decided in advance or determined by a pre-defined significance threshold for the test statistic. Several well-known statistical tests have been used in GWA studies, including the Fisher’s exact test and Armitage trend test -28, and profiles .n), testing all the feature subsets (2n) is computationally infeasible . Therefore, one must resort in practice to local search methods that do not guarantee finding the optimal subset but, nevertheless, usually lead to good local optima. For example, the greedy forward selection adds one feature at a time to the set of selected features after checking which of the remaining features would improve the value of the scoring function the most. Thus, the whole data set is traversed through once for each selected feature. To avoid getting trapped in poor local optima during the search in the complex and high-dimensional genetic landscapes, modified local search strategies can be utilized, including the backtracking option or several variations of evolutionary algorithms. The most popular scoring functions used with wrapper methods are the prediction error on the training set, a separate validation set, or cross-validation error. The feature selection can be in principle wrapped around any learning method, but it is beneficial if the method can be efficiently trained or if the already learned model can be efficiently updated. Indeed, for some learning methods, such as regularized least-squares (RLS), the search process can be considerably accelerated with computational short-cuts for scoring function evaluation [Wrapper methods consist of three components: a search algorithm for systematically traversing through the space of all possible feature subsets, a scoring function for evaluating the predictive accuracy of the feature subsets, and the learning algorithm around which the feature selection procedure is wrapped . Since taluation . These iEmbedded methods have the feature selection mechanism built into the training algorithm itself , that ismodel overfitting. Therefore, the models learned from genetic data should always be tested on independent data not used for training the model. In case the number of labeled data is small, one must resort to cross-validation techniques that repeatedly split the data into training and test sets, and the predictive accuracy is reported as an average over the test folds. In many applications of genomic predictors, there are a number of examples of the so-called selection bias[nested cross-validation[One of the main challenges in feature selection is the accurate estimation of the prediction performance of the machine learning models on new samples unseen at the training phase, especially in settings in which the data is high-dimensional and the number of labeled training data is relatively small. Given the massive dimensionality of modern GWAS and NGS studies, it is in fact not very hard to find genetic features that can almost perfectly fit to a small training set but fail to generalize to unseen data, a phenomenon known as tion bias, meaningtion bias-43. Thisalidation,44. An eThe evaluation of the predictive power is important also when considering predictive models constructed on the basis on statistical significant variants. For instance, there are numerous observations showing that the increases in the proportion of variance explained by significant variants does not go hand in hand with improved genetic prediction of disease risk. For instance, when using statistical modeling on the single training sample only, a panel of thousands of non-significant variants collectively could capture over one-third of the heritability for schizophrenia, but the same panel only explained a few percent of disease susceptibility in another replication cohort . Similarp-value based filters, may seem quite modest , are systematically characterizing the structural basis of cancer, by identifying the genomic mutations associated with each cancer type. These efforts have revealed tremendous inter-individual mutational and phenotypic heterogeneity, which renders it difficult to translate the genetic information into clinically actionable individualized treatment strategies -108. TheThe authors declare that they have no competing interests.SO contributed to the drafting of the manuscript and conducting experiments for the illustrations. TP contributed to the drafting of the manuscript. TA conceived the study, participated in the design of the experiments and contributed to the drafting of the manuscript. All authors read and approved the final manuscript.


Although many methods are available to test sequence variants for association with complex diseases and traits, methods that specifically seek to identify causal variants are less developed. Here we develop and evaluate a Bayesian hierarchical regression method that incorporates prior information on the likelihood of variant causality through weighting of variant effects. By simulation studies using both simulated and real sequence variants, we compared a standard single variant test for analyzing variant-disease association with the proposed method using different weighting schemes. We found that by leveraging linkage disequilibrium of variants with known GWAS signals and sequence conservation (phastCons), the proposed method provides a powerful approach for detecting causal variants while controlling false positives. The decline in DNA sequencing cost permits the interrogation of potentially all variants across the entire allele frequency spectrum for their associations with complex human diseases and traits. However, the identification of causal variants remains challenging. Existing single variant tests do not distinguish between causal association and association induced by linkage disequilibrium and tend to be underpowered for rare or low-frequency variants, whereas variant grouping methods do not identify individual causal variants. We propose a novel Bayesian hierarchical regression approach that estimates effects of multiple variants on a disease trait simultaneously and incorporates prior information on the likelihood of causality. By simulation, we show that by combining linkage disequilibrium with known genome wide association signals and functional conservation, the proposed method, the first of its kind, is powerful to correctly detect causal variants. Next-generation DNA sequencing technologies allow discovery of genetic variants across the full spectrum of allele frequencies, thereby enabling exhaustive screens for association between diseases and variants. Numerous statistical methods Here we introduce a Bayesian multi-variant liability regression model that does not involve grouping and tracks directly to individual variants. More generally, this model falls into a broader framework of Bayesian hierarchical modeling, which attempts to estimate all regression coefficients (variant effects) simultaneously by imposing variant-specific shrinkage on the estimated effects. This class of approaches has seen wide and successful applications in predicting quantitative traits, particularly in agricultural species There are two attractive features of the proposed approach. The first is that all variants are jointly analyzed so as to reduce bias of estimated effects by borrowing information from and/or accounting for other variants. The second feature is its ability to quantitatively incorporate prior information to weight individual variants based on their prior likelihoods of causality. Both features are expected to enhance power and reduce false discoveries. The weighting scheme is entirely customizable and can represent multiple sources of information. Here we have explored weighting schemes that incorporate two sources of information: sequence conservation  and an intermediate genotypic relative risk (GRR) of 3 under a dominant model, which is when single variant tests would likely underperform given a realistic sequencing sample size. We evaluated performance by the power of the methods to correctly identify the precise causal variants  and their false positive rates.NOD2 gene that are known to be causal NOD2 locus that is significantly (p = 9.4×10−12) associated with Crohn's disease. For HCV treatment induced anemia, rs6051702 was identified as the most significant signal  in a GWAS scan ITPA gene were also identified as causal. A subsequent biochemical study confirmed that these variants are indeed causal and described biochemically how they protect against treatment induced anemia We then performed the Bayesian analysis on a set of exome sequencing samples, for which we assigned case/control statuses according to well-documented disease causing variants. We considered Crohn's disease and hepatitis C virus (HCV) treatment induced anemia. For Crohn's disease, there are two SNPs  in the −8 and 10−8 respectively. Causal variants were chosen within the central 100 Kb region of the first chromosome. To distinguish between the two chromosomes, the first was termed ‘causal chromosome’ and the second was termed ‘null chromosome’. Under this design, among variants being interrogated approximately a half of them were linked to causal variants to varying degrees and the other half were unlinked to any causal variant.The coalescent-based software GENOME We simulated a three-locus dominant genetic model and a baseline disease risk of 1%. The presence of one or more causal  alleles increased the risk by a factor of GRR = 3. We were interested in the performance of the methods among different scenarios of causal variant MAF. We considered five MAF intervals: 0.2%–1%, 1%–2%, 2%–3%, 3%–4%, and 4%–5%.p<10−8) and a smaller sequencing sample (500 cases and 500 controls) was used to detect causal variants among candidate variants.A diagram of the procedure of analysis is shown in We used a two-stage approach. In the GWAS stage, tests were limited to common SNPs (MAF>5%), since rare variants are typically underrepresented on GWAS arrays. On the other hand, in the sequencing data analysis, we focused on variants of MAF lower than 5% . This type of test cannot distinguish between causal variants and variants that are in LD with causal variants.We considered two types of statistical methods for identification of causal variants. A univariate logistic regression model  between the candidate variant and all GWAS signals. Here, r was calculated using the 3000 GWAS controls . To prevent the r weights that enter the model from getting too small, we set a minimum value at 0.01 so that all r values less than that were forced to be 0.01. Second, we defined a composite ‘phastCons weight’ as the weighted average of phastCons among different lineages  based on the consideration that conservation among a broader lineage scope implies potentially stronger functionality. phastCons scores for causal variants were drawn from the empirical distribution of ‘pathogenic’ SNPs in the dbSNP database; and phastCons scores for non-causal variants were drawn from the empirical distribution of all variants on chromosome 20 in a whole-genome sequence data set (161 samples) in our laboratory. As with r weight, the minimum composite phastCons value was set to be 0.01. Third, besides ‘r weight’ and ‘phastCons weight’ individually, we also calculated the product of the two, ‘r×phastCons weight’. Finally, an uninformative weight  was also considered for comparison. All weights were scaled to be between 0.01 and 1 by dividing by the maximum.The Bayesian regression approach we implemented incorporates information from GWAS signals and sequence conservation  underlies case/control status, and the liability follows a Normal distribution. A case (control) corresponds to a situation when an individual's liability is larger  than a threshold. A formal description is provided below.id and iy denote the disease status and liability, respectively, of individual i ; there is a fixed threshold t such that id = 1 if iy>t and id = 0 otherwise. Moreover, the liability is related to a set of variants by the Normal regression model:p is the total number of variants; μ is the population mean; ijx is the genotype of variant j in individual i, coded as 0, 1 or 2 for aa, Aa or AA, where A is the minor allele of variant j. The genetic effect of variant j is given by jβ, an unknown quantity which we wish to make inference about. Finally, ie is the random error with a Normal distribution t = 0 and the error variance Let id  and genotypes ijx ; the unknown parameters consist of iy , μ and jβ . The central idea of a Bayesian analysis is to combine what is known about parameters before data are observed (represented by a prior probability distribution) with the information coming from the data (represented by a likelihood function) to arrive at a posterior probability distribution. Once the posterior distribution is known, one can make inference on parameters of interest  using an appropriate Markov chain Monte Carlo sampling method.In the above-mentioned liability model, the observed data consists of the binary response variables a priori enters the Bayesian modeling process through the specification of the prior distributions of jβ's. That is, we assume a Normal prior for jβ: N, where jw is the predefined weight of variant j, as noted earlier. According to this distribution, the larger the weight, the more likely that the variant has an effect. To complete the posterior distribution, we also need to write the likelihood function as well as prior distributions for μ and σ2. Following common practice, we choose a flat prior for μ (p(μ)∝1), and a scaled inverted Chi-square distribution for σ2, with both the degrees of freedom (υ) and scale (2S) being equal to 0.1. The final joint posterior distribution  can then be written asth value. Empirical evaluation of several random replicates of our simulated data showed that the posterior estimates of variant effects were robust to different initializations in the Gibbs sampling. For each variant effect, we recorded its posterior mean and standard deviation for significance test as described in the next section. A C++ program was coded for the Bayesian analysis. With a sample size of 1000 (500 cases and 500 controls) and a total number of 1000 variants, a complete run with 100,000 iterations took approximately 1 CPU hour on a 64-bit, 2.5 GHz Linux workstation.Our belief of a variant being causal B times. The second step is to apply a statistical test on each of the B shuffled data sets and obtain a corresponding test statistic. For single variant logistic regression, we chose the minimum model p-value across all variants as the test statistic. For the Bayesian multi-variant regression, we chose the maximum absolute standardized effect size (the posterior mean of an effect divided by its posterior standard deviation) across all variants as the test statistic. The second step yields an empirical distribution of the test statistic under the null hypothesis of no variant-disease association. Finally, we compute a permutation p-value for each variant as (0B+1)/(B+1), where 0B is the number of permutations that yield a test statistic at least as extreme as the one from unshuffled data. We used a significance threshold of p = 0.01 for all analyses throughout. Because of the computational burden with the Bayesian method and the need to replicate the study in different scenarios, we ran B = 500 permutations, which corresponded to a binomial standard error of p values of approximately 0.004 . This method has been theoretically justified in controlling family-wise type I error The entire procedure  was fully and independently repeated 200 times. Power of detecting a causal variant was the proportion of the 200 replicates in which it was declared to be significant. For non-causal variants, we calculated the proportion of them that were incorrectly identified as causal, i.e., the false positive rate (FPR). In each replicate, FPR was calculated separately for non-causal variants on the causal chromosome and those on the null chromosome. It was then averaged over the 200 replicates. Due to LD with causal variants, it may be inappropriate to call a non-causal variant on the causal chromosome a false positive if it was identified as causal. However, we loosely used the term FPR for convenience.NOD2 data included 728 individuals and 100 candidate variants, and the ITPA data included 715 individuals and 338 candidate variants  filtering  were applied to remove SNPs and individuals. After QC, the variants . We nextNOD2 mutations on chromosome 16 for Crohn's disease, we focused on rs2066844 and rs2066845 only, because the third one (rs2066847) is an insertion variation and absent from our exome data. In addition, the GWAS signal in NOD2, rs17221417, was also unavailable in our data. However, we found another SNP, rs2066842, located 5 Kb downstream of rs17221417, is in complete LD with rs17221417  and is present in the data, making it a perfect proxy for rs17221417. Attention was then restricted to 1 Mb region centered around the position of rs17221417. Within this region, variants with MAF≥0.2% were chosen as candidate (proxy SNP rs2066842 was excluded), resulting in a total of 100 variants. While the overall LD pattern showed small linkage disequilibrium among the variants, there were a handful of SNP pairs in high or even complete LD  were dealt with in exactly the same way as the NOD2 variants. A perfect proxy was used in lieu of the original GWAS signal, which was absent from our data. Within 1 Mb region centered around rs6051702, there were 338 variants with MAF≥0.2% and chosen for analysis. Inspection of LD plot (r2 = 1) with causal variant rs1127354 and two SNPs in almost complete LD (r2 = 0.9) with causal variant rs7270101.The two l (liability) = g +e (error), as noted from our previous description of liability model. Assuming a dominance model as above, we set g = 1 when a risk allele  was seen at any of the two causal sites, and g = 0 otherwise. The error was drawn from a Normal distribution with mean zero and variance eV; value of eV was chosen such that heritability, gV/(gV+eV), was equal 10%, where gV was estimated by the empirical variance of g's across samples. To achieve an equal number of cases and controls, we used the median of all samples' liability as a threshold so that a half of samples below the threshold were designated as controls and the other half as cases. Since only a small fraction of individuals carried risk alleles, the entire liability distribution was dominated by that of non-carriers. Also, as we assumed a low heritability (10%), the error variance was therefore large, leading to a wide overlap between liability distribution of carriers and of non-carriers  and the Bayesian multi-variant liability regression model with ‘no weight’, ‘r×phastCons’ weight, achieved an average  power of 0.34 and was able to detect at least one causal variant 67% of the time. When MAF was raised to 4–5%, the average power was 0.4 for single variant test, 0.7 for Bayesian models with r weight and no weight, and 0.9 for Bayesian models with phastCons and r×phastCons weight.As expected, increasing causal MAF led to an increase in the power of all methods . NotablyFPR was overall controlled at a very low level . Across Next we describe in more detail results from the comparison among different methods.Bayesian multi-variant model with r weight consistently improved power over the one without weight. The percentage of increase was especially appreciable in low MAF ranges. For example, the average power under MAF = 1–2% was 0.097 and 0.17 for no weight and r weight, respectively, corresponding to a 75% increase from no weight to r weight (Fisher's exact test p = 0.038). Likewise, under MAF = 2–3%, we found a 41% increase in power from no weight (0.32) to r weight (0.45) (Fisher's exact test p = 0.01). The advantage of using r weight was attributed to its discriminative ability between causal and non-casual variants .r×phastCons weight had higher power than phastCons alone when MAF<2% and similar power when MAF>2%. Comparing phastCons against r×phastCons, it was found that both weights rendered the Bayesian model equivalent average power (about 0.8∼0.9) when causal MAF was greater than 2%. Below 2%, however, the advantage of r×phastCons was remarkable. In particular, when MAF was between 0.2% and 1%, Bayesian with the r×phastCons weight was markedly better powered than that with phastCons . A closer examination of the distribution of effect sizes , where FPR by these two weights were substantially lower than that by other methods.r × phastCons vs. phastCons, and compared their effect estimates at these null variants  beyond −1, and the entire distribution was shifted to the left as compared to phastCons weight. These results indicated that the incorporation of r into variant weighting suppressed false positives effectively, making r×phastCons weight the method of choice when considering both power and FPR.We next examined FPR of non-causal variants on the null chromosome  and the two ITPA variants (rs1127354 and rs7270101) is given in NOD2 data, 28% of non-causal variants had higher composite phastCons scores than the causal variant rs2066844 (0.32), and in the ITPA data 34% of non-causal variants had higher scores than the causal variant rs7270101 (0.17). However, it was rare for non-causal variants to have both high r and high phastCons. This made r×phastCons an attractive weighting scheme because it incorporates both measures to discriminate causal from non-causal variants.We then applied our method to real exome sequence data with simulated phenotypes. Information about the two r×phastCons weight, based on one representative example out of the 100 simulated data sets. We then summarize results from both methods by displaying for each candidate variant the proportion of the 100 simulations where it was detected .In r×phastCons weights had a clear pattern in the NOD2 sequence variants: the two causal variants ranked 4th and 5th among all 100 variants; with a few exceptions, almost all non-causal variants had very small weights. The last panel illustrates by replicating simulations how well each method identified causal vs. non-causal variants. For the relatively common causal variant rs2066844 (MAF = 5%), it was almost always identified by both methods across the 100 simulations. For the low-frequency causal variant rs2066845 (MAF = 1%), however, proportion of detection was about 40% and 20% by the Bayesian model and single variant test, respectively. Considering the low heritability (10%) and modest sample size (∼700), 40% is a substantial improvement over 20% for detecting causal variant at an allele frequency of 1%. In the meantime, false detection among non-causal variants produced by either method was negligible, likely a result of the absence of linkage disequilibrium in this region.As seen in NOD2 region, variants in the ITPA region had a less clear pattern in r×phastCons  by a large margin (80% vs. 30%), for rs7270101 (MAF = 13.85%) the pattern was opposite: the proportion of single variant far exceeded that of the Bayesian model (80% vs. 40%). However, the higher power of single variant test was accompanied by a large number of false positives, as opposed to virtually no false positives by the Bayesian model. This is in fact a strength of our Bayesian model in that it is able to select the correct causal variants out of many SNPs in LD. In addition, the two causal variants were always the top ranked variants in the Bayesian results while they were lower ranked in the single variant test. This makes prioritization much more accurate and efficient by the Bayesian model.Compared with variants in the hastCons : causal ITPA data created great ambiguity in interpreting the results from single variant test, the Bayesian model using r×phastCons to weigh variants was able to effectively discriminate causal from non-causal variants in terms of their effect size estimates.Here we developed and evaluated a Bayesian multi-variant regression approach for detecting causal variants in sequence data. We first tested its performance in simulated data using an intermediate risk (GRR = 3), a moderate and realistic sample size (500 cases and 500 controls), and a range of minor allele frequencies for the causal variants. Compared with the standard single variant test, our method, when coupled with informative prior weights, showed a clear advantage in statistical power. Application of the method to real exome sequence data in order to identify known causal variants implicated through GWAS showed similar results. In particular, while the high LD among variants in the The Bayesian multi-variant regression model entails leveraging informative prior information on variants so as to better distinguish causal variants from non-causal variants. In this study, the uses of different kinds of weights give rise to different prior specifications (shrinkage) of variant effects, which in turn affect posterior estimation of variant effects and their statistical significance. As we have shown in the Results section, power and FPR of the Bayesian regression model were greatly dependent on the choice of prior weighting scheme. A good weighting scheme is data-dependent and often requires combining different pieces of information. In the full simulation study, which served as a proof of concept, we generated data assuming that variant causality is correlated with its conservation as encoded by phastCons. We found that the combination of significant associations from GWAS and variant phastCons rendered the Bayesian model a highly improved performance in power than one without weighting. However, while there is a tendency for causal variants to be evolutionarily more conserved for many diseases, this may not be always true, especially for late on-set diseases that are not subject to natural selection. In such scenarios, some form of prediction for variant effect, such as the PolyPhen scores Using prior biological knowledge in genetic association studies has increasingly been adopted recently. Several studies have proposed using variable significance threshold for variants. For example, the Prioritized Subset Analysis (PSA) As in the common theme of Bayesian shrinkage regression methods, our knowledge on variant effect appears only in its prior variance, since all effects are shrunk toward a single prior mean, which is zero. As such, the weight only indicates magnitude of variant effect but not direction. Indeed, for variants with high phastCons weights, it is unlikely for their minor alleles to have a protective role in disease liability. Thus, it is desirable to assign a positive prior mean for these variants in order to enhance the power of discovery. On the other hand, for variants with near zero weights, we still can use zero mean as prior. These considerations require a different prior specification than presented here as well as more complicated posterior computations An alternative Bayesian approach to identifying variants associated with disease is Bayesian model selection via Bayes factor. A representative example under this framework is the Bayesian risk index method We tested our method on a relative small candidate region (1 Mb) around GWAS signals for convenient demonstration of the method, mainly for computational feasibility as many replicates needed to be run in the simulation study. The method can be extended to a larger candidate region to account for the situation that some causal variants could be far away from GWAS signals. Also, while we focused on low frequency candidate variants in our analyses, the method can readily encompass both common and rare variations. In both cases where the number of variants to be fitted in the model would be increased substantially, sample size needs to be increased accordingly to ensure accurate estimation of variant effects. On the other hand, as computing time grows when a large number of variants are analyzed, it may be useful to prescreen variants based on one or more criteria . In addition, another incentive for prescreening is that, with a limited sample size, adding more non-causal variants to the model would lead to less accurate effect size estimation for causal variants. In fact, the same argument holds for single variant test where prescreening can alleviate the burden of multiple testing.r weight’ improved power substantially. We also performed a small experiment  of the 100 candidate variants in NOD2 region in the exome sequencing data. Lower: LD (r) between each candidate variant and the GWAS signal. Causal variants are marked in red color.Upper: pairwise LD ((PDF)Click here for additional data file.Figure S2ITPA region.Same as (PDF)Click here for additional data file.Figure S3NOD2 data, where 12% of samples were risk allele carriers. (B): ITPA data, where 39% of samples were risk allele carriers.Distributions of the simulated liability values for exome sequencing samples. Dashed line marks median of the distribution of all samples, which was used to classify samples to cases and controls. (A): (PDF)Click here for additional data file.Figure S4Heatmap plots showing the number of non-causal variants that were falsely identified as causal in each of the 200 replicates. Numbers on the right side of each plot are false positive rates averaged across replicates for different methods.(PDF)Click here for additional data file.Figure S5r×phastCons weight. In each scenario (plot), effect estimates of Bayesian with phastCons weight (or r×phastCons) were collected from 200 replicates to form a distribution density.Distributions of standardized variant effect estimates from Bayesian liability model with phastCons weight and with (PDF)Click here for additional data file.Figure S6Same as (PDF)Click here for additional data file.Text S1Gibbs sampling in Bayesian liability regression model.(PDF)Click here for additional data file.Text S2Exome sequencing data processing and quality control.(PDF)Click here for additional data file.Text S3Using simulation to demonstrate effect of clustering variants on power.(PDF)Click here for additional data file.


Many genome-wide association studies focus on associating single loci withtarget phenotypes. However, in the setting of rare variation, accumulatingsufficient samples to assess these associations can be difficult. Moreover,multiple variations in a gene or a set of genes within a pathway may allcontribute to the phenotype, suggesting that the aggregation of variationsfound over the gene or pathway may be useful for improving the power todetect associations.Here, we present a method for aggregating single nucleotide polymorphisms(SNPs) along biologically relevant pathways in order to seek geneticassociations with phenotypes. Our method uses all available genetic variantsand does not remove those in linkage disequilibrium (LD). Instead, it uses anovel SNP weighting scheme to down-weight the contributions of correlatedSNPs. We apply our method to three cohorts of patients taking warfarin: twoEuropean descent cohorts and an African American cohort. Although theclinical covariates and key pharmacogenetic loci for warfarin have beencharacterized, our association metric identifies a significant associationwith mutations distributed throughout the pathway of warfarin metabolism. Weimprove dose prediction after using all known clinical covariates andpharmacogenetic variants in VKORC1 and CYP2C9. In particular, we find thatat least 1% of the missing heritability in warfarin dose may be due to theaggregated effects of variations in the warfarin metabolic pathway, eventhough the SNPs do not individually show a significant association.Our method allows researchers to study aggregative SNP effects in an unbiasedmanner by not preselecting SNPs. It retains all the available information byaccounting for LD-structure through weighting, which eliminates the need forLD pruning. Accurate prediction of clinical phenotypes, such as disease manifestations or drugtherapeutic response, using genotype data is a fundamental challenge intranslational biology. A primary method for establishing phenotype-genotype links isthrough Genome-Wide Association Studies (GWAS), which interrogate the genome inregions of common variability and attempt to statistically associate thisvariability to the phenotype of interest .This phWarfarin, an anticoagulant prescribed to over 30 million patients annually to preventthromboembolic events, is a drug with known pharmacogenetic influences-4. The dThe biological pathways involving warfarin are well characterized, and warfarinmetabolism genes show high genetic variability not only between individuals but alsobetween populations, making it cumbersome to refine the warfarin dosing equationsfor each specific population -16. FurtBiologically-driven methods use information from known pathways to group SNPstogether, with the assumption that the SNPs may have similar effects on phenotypeand thus can be aggregated. Such methods allow for the combination of SNPs that maynot be significant alone, but in aggregate, are associated with pathway dysfunction.Biologically-driven pathway-based methods have been used for analyzing geneexpression data, proteomic data, and are now emerging as a mode of analysis forgenotyping and sequencing data 24]..24].Pathway-based methods group mutations from genes in a biologically relevant pathway. For insThese studies demonstrate the potential value of pathway-based methods and underscorethe importance of aggregated genetic effects. However, they have focused primarilyon gene expression data and can be limited by a SNP selection strategy that relieson individually significant p-values from a single-locus analysis. Here, we usebiologically curated pathways, such as warfarin metabolism, to create a statisticthat can be tested for association with warfarin dose. In particular, we aggregatethe mutational burden of genes in the metabolic pathway of warfarin and demonstratethat this mutational burden explains some of the missing heritability in warfarindose.Several methods exist for aggregating SNPs across genes or pathways. VAAST assignsgene scores using both variant frequency data and amino acid substitution data totest the association of entire genes to cases and controls . The weiWe used three data sets from prior studies: all subjects were on stable doses ofwarfarin with repeated INR measurements between 2-3.1. Genotypes for 188 patients of European descent with a stable warfarin dose andclinical covariates were obtained from Cooper et al . Samples2. We obtained genotypes from 233 venous-thromboembolism patients of Europeandescent on warfarin from the Malmo Thrombophilia Study . These s3. We obtained genotypes from 342 African Americans (the IWPC GWAS) fromdifferent IWPC sites. Subjects were genotyped using the Illumina 610 QuadBeadChip at the RIKEN Center for Genomic Medicine in Yokohama, Japan. SNPs withless than 2% minor allele frequency were excluded except for SNPs in VKORC1 andCYP2C9, because of evidence suggesting their possible involvement in warfarindosing. Data collection and quality control were based on previously describedIWPC protocols -37.For each dataset, PCA was performed on the genotype data using the pca_modulepackage (version 1.1.02) for Python (version 2.7.1).Aggregate Number of Minor Alleles (A#m) sums the number of minor alleles observedin a given gene . Itassigns a point to the gene whenever a SNP is the minor allele, or two if theSNP is homozygous for the minor allele Figure . Majora2as the similarity metric. SNPs were clustered using single linkageclustering (where the shortest distance between any two leaves of a cluster isused as the cluster difference). The resulting clusters were used to create abifurcating tree that relates all loci using LD  for each SNP was calculated for all pathway SNPswithin 1 Mb using plink (version 1.07). Once clustered, we used theGerstein-Sonnhammer-Chothia algorithm to compute the weights of each leaf node(SNP) [To account for LD, we used an algorithm previously developed for protein sequencesimilarity to weight a SNP based on its LD with nearby SNPs . We clusde(SNP) . This alWe mapped SNPs to genes using dbSNP based on build hg19 of the human genome. ForNCBI's hg19, we used the default feature set  of all genes andadded 10,000 bases upstream (5') and 3,000 bases downstream (3') in order tocapture regulatory regions.http://pharmgkb.org[We determined drug metabolic pathway by selecting the metabolic enzymes inPharmGKB's warfarin pharmacokinetic pathway (PA145011113) and the drug targetpathway by using PharmGKB's warfarin pharmacodynamic pathway (PA145011114),available for download at rmgkb.org,39.We performed several tests using our pathway method to assess how variation inwarfarin metabolizing enzymes influenced dose prediction and the effectivenessof our weighted pathway metric. First, we applied our pathway method in a cohortof European descent to test the significance of pathway-level variation inpredicting dose. Next, we dissected the pathway score into two pieces -- CYP2C9and the rest of the pathway and tested how these two separate variablespredicted dose. This helped determine whether or not the pathway was beingdriven by CYP2C9, which is known to contain many important warfarin variants. ThenweWe produced the A#m score for the warfarin metabolic and pharmacodynamic pathwayin a population of 188 patients (182 of European descent and 6 of Hispanicdescent) on warfarin. We used a linear regression to model warfarin dose withthe warfarin metabolic pathway A#m and known clinical and genetic covariates:age, weight, race ,amiodarone, losartan, VKORC1 (rs9923231) and CYP2C9 status . We excluded nineteen subjects who were missing one of theabove covariates. We used an ANOVA to test the difference between the modelsincluding and not including the pathway score. All statistical analyses wereperformed using the R statistical package (version 2.10.1).We removed CYP2C9 scores from the pathway score in the Cooper et al. data. Then,we modeled warfarin dose using a linear regression with the aforementionedclinical and genetic covariates and individually added either the CYP2C9 A#mscore or warfarin metabolic A#m score without CYP2C9 as covariates. Allstatistical analyses were performed using the R statistical package (version2.10.1).We ran 100 permutations of random pathways from a combination of the PharmGKB,Biocarta, and Pathway Interaction Database using MySQL (version 5.1.14). Wecalculated the score for each random pathway using the A#m method previouslydescribed using the Cooper et al. data. We then modeled warfarin dose using alinear model with the previously mentioned genetic and clinical covariates andeach pathway. We used the random pathways to compute a background distributionof correlations. The empirical p-values were then estimated from thisdistribution, and reported in addition to traditional statistical tests.We also applied pathway scores in another cohort of 233 individuals of Europeandescent genotyped through the International Warfarin Consortium (IWPC). For thecovariates, we used age, height, weight, principle component 1, principlecomponent 2, rs1799853 (CYP2C9 *2), rs1057910 (CYP2C9 *3), rs9923231 (VKORC1-1639 G>A), and rs9934438 (VKORC1 1173 C>T). The VKORC1 SNPs were in perfect LD,and thus, only one was used in the regression. We excluded ten subjects becausethey were missing some of the above covariates. Amiodarone and aspirin statuswere not available.We replicated this method in a population of African Americans genotyped by theInternational Warfarin Pharmacogenetic Consortium (IWPC). We used a similar setof covariates as used by the IWPC warfarin pharmacogenetic equation with theaddition of our pathway scoring metric . These cWe calculated the predicted dose of each individual in the IWPC African Americancohort using the IWPC dose equation .We then2 cutoffs from 0.1 to 0.9. Variants werepruned using plink v1.07 with pairwise genotypic correlations using the defaultwindow size of 50 SNPs and a sliding window of 5 SNPs.We LD-pruned the Cooper et. al. pathway SNPs and the IWPC African American GWASpathway SNPs at incremental r2 cutoffs.We used the resulting sets of pruned SNPs to generate A#m scores withoutweighting. We modeled warfarin dose using a linear regression with theaforementioned clinical and genetic covariates with the A#m scores generated atthe different pruning rThe Cooper et al. cohort included 188 patients (182 of European descent and 6 ofHispanic descent) on warfarin doses ranging from 1 mg/day to 15.54 mg/day. Asummary of the patient demographic data of the Cooper et al. cohort is availablein Table 2with the addition of the weighted pathway scores (0.466 to 0.48). The A#mtarget (pharmacodynamic) pathway was not a statistically significant predictorof warfarin dose and was not tested in the subsequent cohorts.The A#m metabolic pathway consisted of 49 SNPs in 7 genes  . This populationconsisted of 342 individuals on doses of warfarin ranging from 1.43 to 17.41mg/day. Patient demographic data is summarized in Table 2 of 1.3 percentage points (0.259 to 0.272)with the addition of the weighted metabolic pathway score.In this cohort, the A#m pathway score was significantly predictive of warfarindose  Table . There wNext, we found that A#m was a statistically significant predictor  of the residual dose unexplained by the current IWPC warfarinpharmacogenetic equation  amongthe various cutoffs. In several cases, choice of LD cutoff influencessignificance due to information loss, whereas the weighted method produces asignificant p-value.We present a comparison of p-values, number of SNPs included, and adjustedrPrevious genetic analyses of warfarin response have used single-locus or single-genebased approaches in order to discover candidate variants influencing dose,40. HereOur method is based on the assumption that aggregate effects of the mutational burdenof the warfarin metabolizing enzymes have a similar effect and direction of effecton the overall sensitivity to warfarin. This strategy assumes that minor allelesgenerally lead to a decrease or loss of function. This assumption is supported by arecent systematic review of loss-of-function variants in the human genome, whichfound loss-of-function variants to consistently occur at lower frequencies. Moreove2 in the Cooper data, theweighted method produced the best adjusted r2 in the African AmericanIWPC GWAS data. LD pruning; however, is biased; one does not know a priori whatcutoff will produce the best results, and thus, it becomes necessary to choose areasonable cutoff based on preference. For instance, the LD cutoff of 0.3, whichproduced the highest adjusted r2 in the Cooper et al. data would haveproduced one of the worst adjusted r2 values in the African American IWPCGWAS data. In fact, any cutoff below 0.5 would not have produced a statisticallysignificant A#m pathway score in the African American IWPC GWAS data due toinformation loss. The weighted method allows one to evaluate the data in an unbiasedmanner without the need for pruning, eliminating the arbitrary step of LD cutoffselection.We avoid the information loss and biases of LD pruning by using a weighting schemebased on LD. This method allows each SNP to contribute independent informationwithout double counting. We found that while LD pruning at a cutoff of 0.3 producedan A#m pathway score with the best adjusted rIn the Cooper et al. data, our A#m pathway score is a statistically significantpredictor of dose even when using all available covariate data (including genotypedata). Since CYP2C9 has such a large influence on warfarin dose in individuals ofEuropean descent, we evaluated whether CYP2C9 was driving the A#m pathway score, suggesting that the pathway score may have an effect on dose predictionin this cohort. The SNPs used in this analysis were different from the SNPs used inthe Cooper analysis, due to the use of different genotyping chips. In order to avoidbias, we used all available SNPs in a pathway, which can affect the pathway score ifsome SNPs do not contribute to the signal and introduce noise. Filtering SNPs basedon prior biological knowledge or findings may lead to a stronger signal, but willmiss effects of rare variants or SNPs that have not been characterized. Moreover, weexpect that the pathway score to be less predictive in populations of Europeandescent compared to populations of African descent because variation along theentire metabolic pathway is lower in populations of European descent .African Americans have greater genetic variation in the cytochrome p450 enzymesmaking pharmacogenetic warfarin dose prediction particularly difficult. Weanticipated that this method would be successful in an African American cohort,where much of the heritability in warfarin dose has not been explained. The additionof the A#m pathway score to the other known covariates for warfarin dosedemonstrated that the A#m pathway was a statistically significant contributor topredicting warfarin dose in African Americans. In both the Cooper et. al. andAfrican American analysis, the coefficient for the A#m pathway was negative --consistent with our assumptions that minor alleles lead to loss of function, sincedecreased enzyme activity leads to reduced clearance, resulting in a lowertherapeutic dose. However, we acknowledge that some alleles may yield a gain offunction, and refining our method to take into account the directionality of eachSNP's effect would improve our future models.To show clinical relevance, we calculated the predicted IWPC dose for the AfricanAmericans -- this including pharmacogenetic factors such as variants in VKORC1 andCYP2C9. We predicted warfarin dose in the IWPC African American GWAS data using theestimated IWPC dose plus our A#m pathway score, and showed that our A#m pathwayscore was a statistically significant covariate for dose prediction beyond what ispredicted by the IWPC pharmacogenomic algorithm. The pathway score was able tocapture 1.4 percentage points of the missing signal in dose prediction,demonstrating that pathway interactions and mutational load may be a contributor tothe missing heritability in warfarin dosing.We used a pathway-based method to show that aggregate effects along biologicallyimportant pathways could influence a phenotype . Wewere able to create an unbiased tool for downweighting SNP contributions based oninformation similarity (LD), thus eliminating the need for LD pruning prior toaggregation. Currently, we treat each SNP the same - SNPs do not get additionalupweighting if functional significance is known. Future methods may assignadditional weights to SNPs or genes with biologically known functional relevancethat may have a stronger influence on the pathway score. Our method may also haveuseful predictive value for other phenotypes influenced by pathway-level changes,such as cancer biology.http://Personalis.com. JKBhas a patent pending for the use of CYP4F2 in warfarin dosing.RBA is a founder and scientific consultant to RD contributed to experimental design, pathway and weighting method implementationand statistics, and drafted the manuscript. NPT contributed to experimental design,implementation of the LD-weighting algorithm, and helped draft the manuscript. KJKcontributed to experimental design, statistical analysis, and helped draft themanuscript. HS created the A#m scoring metric. SB genotyped and performed qualitycontrol on the Malmo Cohort. JKB, TT, YN, MK, MT, NAL, LHC, MP, JAJ, and TEKgenotyped and performed quality control on the IWPC African American GWAS data. RBAcontributed to experimental design and drafted the manuscript. All authors read andapproved manuscript.Additional tables can be found in the Supplementary section, in the supplementaryfile.Click here for file


Admixture mapping is a popular tool to identify regions of the genome associated with traits in a recently admixed population. Existing methods have been developed primarily for identification of a single locus influencing a dichotomous trait within a case-control study design. We propose a generalized admixture mapping (GLEAM) approach, a flexible and powerful regression method for both quantitative and qualitative traits, which is able to test for association between the trait and local ancestries in multiple loci simultaneously and adjust for covariates. The new method is based on the generalized linear model and uses a quadratic normal moment prior to incorporate admixture prior information. Through simulation, we demonstrate that GLEAM achieves lower type I error rate and higher power than ANCESTRYMAP both for qualitative traits and more significantly for quantitative traits. We applied GLEAM to genome-wide SNP data from the Illumina African American panel derived from a cohort of black women participating in the Healthy Pregnancy, Healthy Baby study and identified a locus on chromosome 2 associated with the averaged maternal mean arterial pressure during 24 to 28 weeks of pregnancy. Admixture mapping, also known as mapping by admixture linkage disequilibrium, has become an important tool for localizing disease genes. A number of admixture mapping studies have successfully identified candidate loci associated with common complex traits and biomarkers , such as single-nucleotide polymorphisms (SNPs), which vary in frequency across ancestral populations. AIMs tag the status of an ancestry block, similar to that of tagSNPs, which are used to characterize common haplotypes in a chromosomal region. In the African-American population, the linkage disequilibrium due to admixture extends for a much wider region than the linkage disequilibrium between haplotypes . Moreovevs. the one under the null hypothesis, for cases and controls respectively. Given the local ancestries of each individual, several hypothesis testing-based approaches have been proposed to test, one locus at a time, the null hypothesis that the AIM is unlinked to the complex-trait/disease for a dichotomous trait within a case-control study design. q%  of the quantitative trait value as cases and controls; The remaining subjects with in-between quantitative trait values are then discarded  traits and Poisson regression for count traits. The predictors in GLM include local ancestries at the given AIM loci and other risk factors. The local ancestry is defined as the number of alleles from the high-risk ancestral population, for example, 0, 1, or 2 alleles from African ancestry at a given AIM locus. The association examined in GLEAM can be adjusted by other risk factors. We assume for complex genetic traits that most loci have no association with the trait, a few loci may have small to modest association , and the loci with greater proportions of disease-causing alleles from the high-risk population would possibly have stronger association with the traits. This prior knowledge is incorporated into GLEAM by using a quadratic normal moment (QNM) prior  with the benefit of reducing the type I error while increasing the power, as demonstrated by the simulations in Results.With these motivations, we propose regression-based generalized admixture mapping (GLEAM) for both quantitative and qualitative traits. The new approach is able to examine the association between the complex trait and single or multiple loci simultaneously while also adjusting for other risk factors. GLEAM is based on generalized linear models (GLMs) , with liM) prior  for the The number of AIMs (1500~3000)  and commDifferent from the association mapping based on the SNPs that are directly measured, the local ancestries are unobserved and are inferred on the basis of the AIMs via use of the Hidden Markov Model (HMM) detailed in the Appendices. At each AIM locus, the number of alleles from the high-risk ancestral population is imputed multiple times for every subject, using an Markov chain Monte Carlo (MCMC) algorithm. By using the multiple imputed datasets of local ancestries, we are able to assess the association between the traits and local ancestries directly while taking imputation uncertainty into account through Bayesian averaging. Importantly, our multiple imputation approach preserves the admixture linkage disequilibrium between the AIM loci, which is crucial for multilocus admixture mapping in GLEAM. In addition, GLEAM can also use the local ancestries sampled by other local ancestry inferring methods, such as HAPMIX ′. Specifically, we use the linear model for continuous traits,p local ancestries Si = ′ are considered and centered to have mean zero, β = ′ and α = ′ are the regression coefficients for Si and Ei respectively, and H1: jβ ≠ 0 for j = 1, …, p, and null hypothesis, H0: jβ = 0 for j = 1, …, p. Marginal likelihoods remove the parameters from the likelihood by integrating over the prior distribution. The larger the Bayes factor, the stronger the evidence in favor of H1.GLEAM is a regression method that extends the current approaches in various ways. The most obvious extension is to accommodate both quantitative and qualitative traits yβ under H1, we use the QNM prior having densityp-dimensional multivariate normal distribution with the mean vector m and covariance matrix V, and τ is the dispersion parameter. The QNM prior is able to incorporate the case with a large number of loci of tiny effect. As shown in τ. For illustration purposes, we only showed a particular value of τ = 0.01, but as we decrease this value, tiny effects are accommodated. For data containing a large number of loci of tiny effect, the empirical Bayes approach should estimate a very small value, and the QNM prior will concentrate on very small effect sizes. Usual priors face major problems in distinguishing the signal from the noise, and we argue that nonlocal priors such as the quadratic normal provide more accurate results for genetic effects on complex traits. Hence, The QNM prior increases the evidence in favor of both the true null and true alternative hypothesis, compared to other prior distributions  (σ2Σ as the covariance matrix of the (iterative weighted) least square estimation of β in the GLM. This choice not only leads to convenient computation but also easily incorporates the prior knowledge about the effect of local ancestry on the trait. For example, when Si is orthogonal to Ei, Σ = (S′S)−1 with S = ′ in the linear model for the continuous trait. As illustrated by the right panel of Σ = (S′S)−1 suggests that for each locus, the greater the proportion of alleles from the high-risk population (ap), on average the larger the risk effect of local ancestry. Such relationships frequently are observed in admixture mapping but not in association mapping based on SNPs in general. More importantly, when we investigate multiple loci simultaneously, it is crucial to take the correlation  between the local ancestries into consideration. As a prior distribution for  priors) . Moreoveβ, the Bayes factor is simplyβ, adjusted by other risk covariates when necessary, Under the QNM prior for J AIM loci. The loci at which log10BF(y) > δ are considered susceptibility loci. Although the “one locus a time” approach explores the marginal association and is widely used, marginal association only reflects part of the relationship between the AIM loci and the trait. Several loci in different regions may show associations with the trait. Thus, it is desirable to quantify the evidence for joint association of multiple loci with the trait. For this reason, in the second stage, we list all possible combinations of susceptibility loci selected in the first stage. For each set of susceptibility loci, we can again calculate the Bayes factors for the joint association at those loci simultaneously. The most significant ones are reported. The local ancestries at the AIM loci are unobserved and imputed from the HMM. The imputation uncertainty could be properly accounted for by calculating weighted average of the Bayes factors for each imputed local ancestry dataset, which is similar to the strategy used by We propose a two-stage approach for GLEAM. In the first stage, we examine the marginal association between a single AIM locus and the trait, using the Bayes factors (3), one locus a time for http://genepath.med.harvard.edu/∼reich/Software.htm) as well as regularized regression methods Lasso and elastic net (Supporting Information folder online.We carried out simulation studies to assess the performance of GLEAM in terms of type I error rate and power under various scenarios and compared it with the method based on Bayesian likelihood ratio (BLR) by a posteriori (MAP) frequency estimates under the assumption of Hardy-Weinberg equilibrium. Ten sets of trait data were then generated such that we were able to assess the type I error rates under the genome-wide threshold level , by using the following null model for continuous traits: yi = iαE + iε and for binary traits, logit{Prob(yi = 1)} = iαE; where the continuous risk covariate iE and the measurement error iε followed standard normal distributions. We considered two situations whereby α = 0 in the absence of a covariate effect and α = 1 in the presence of a covariate effect.We started by investigating the type I error rates for the local ancestries that were scattered around different regions of the genome and in linkage equilibrium. Under this scenario, the falsely localized AIM locus would be in the region remote from the true disease causing locus, which leads to a false positive finding. We first randomly sampled 1000 AIM loci with replacement from 1296 AIM loci for 1000 subjects. At each AIM locus, we simulated the local ancestries measured by the number of alleles from the African ancestral population from their maximum iS, continuous covariates Ei and measurement error iε generated same as that for the null model, continuous traits were simulated from yi = iαE + iβS + iε and binary traits from logit{Prob(yi = 1)} = iαE + iβS. Under both models, the β was specified as β = c × proportion of African ancestral population which reflected the a priori observation that the locus with the larger proportion of the high-risk ancestral (here African American) population usually demonstrated stronger association with the traits. For continuous traits, we chose the values of effect size multiplier c as 0.2, 0.25, 0.3, 0.35, and 0.4 respectively, with the largest possible effect size equal to 0.3527. Similarly, we picked the c values as 0.4, 0.5, 0.6, 0.7, and 0.8 for binary traits with the largest possible odds ratio equal to 1.8537.We next examined power under the single locus alternative models. We simulated 100 sets of traits. Each set included 1000 subjects and one disease associated local ancestry whose location was randomly sampled from 259 AIM loci, where the proportion of African ancestral population ranged from 0.8321 to 0.8817 and was on the top 20% percentile among 1296 AIM loci. Given the local ancestry c values set at 0.7 for continuous traits and 0.35 for binary traits.We further considered a multilocus alternative model where two local ancestries were associated with the traits and there existed admixture linkage disequilibrium. To do so, we generated an artificial chromosome composed of two pieces from chromosome 1 and chromosome 4 with the length 139.50 Mb and 114.88 Mb, respectively, for 1000 subjects, based on empirical data on local ancestries from HPHB study. In the middle of each chromosome piece with 51 loci, there is one locus whose proportion of African ancestry population was among the highest in all 1296 AIM loci. In the simulations, those two loci are assumed to be associated with traits. We generated 100 sets of continuous and binary traits respectively, each of which was simulated similarly to the single locus alternative model except with two local ancestries involved and both effect size multiplier The simulated datasets were analyzed by the GLEAM and the BLR method. Because the BLR method was primarily developed for binary traits, the BLR method required transformation of continuous traits into binary ones, such as defining the subjects with top 20% traits as the cases and the one with bottom 20% traits as controls.log10BF(y) to control the genome-wide type I error rates. The regularization parameters of Lasso and elastic net are chosen with the minimal cross validation error. The loci with nonzero regression coefficients are regarded as the ones associated with the traits. As illustrated in −4 for GLEAM and 4.2 × 10−3 for the BLR method. In both cases, those type I error rates seem overly conservative. However, in the application to real data, slight admixture linkage disequilibrium between the AIM loci will significantly inflate the type I error rate close to the nominal levels , which is discussed in the later paragraphs. Comparing vs. control), which inevitably loses power. For all situations considered, the power of the GLEAM approach increases with the increment of the local ancestry effect size, most rapidly when the effect sizes are smaller and then levels off with larger effect sizes. In comparison, the power of the BLR method increases roughly linearly. Both GLEAM and BLR are less powerful than the regularized methods especially when the effect sizes are small. With the growth of the effect size, the power of GLEAM will quickly increase and be comparable to the ones of regularized regression.Power of the methods also was evaluated for binary and continuous traits under the single locus alternative model, with or without covariate effects. We considered various effect sizes of local ancestries with the results shown in To understand the impact of admixture linkage disequilibrium on type I error rates and to evaluate the ability of localizing multiple loci simultaneously, we generated a set of artificial chromosomes as described previously, where two loci were associated with the traits, named as Locus 1 and Locus 2. Besides Locus 1 and Locus 2, we divided the remaining loci into three regions: region 1 (REG1) with 42 loci and region 2 (REG2) with 35 loci, where the admixture linkage disequilibrium measured by the correlation coefficient between a given locus at these regions and Locus 1 or Locus 2 was larger than 0.12 respectively; and region 3 (REG3), the unassociated loci which did not belong to region 1 and region 2. Strictly speaking, the identified loci except Locus 1 and Locus 2 were all false positives. However, in contrast to the loci found in region 3, which were completely false findings, the loci identified in Region 1 and Region 2 were partially correct and could be regarded as low-resolution findings instead, because the true associated locus did exist in the nearby region. Therefore, we evaluated the false positives in three regions separately. An ideal method under the prespecified genome-wide threshold would lead to few completely false positives in region 3 and to a small number of partially false positives in regions 1 and 2, while being able to identify the true associated loci with high frequency.e.g., power 1 for detecting both locus 1 and 2 with type I error rates 0.023 of Lasso and 0.029 of elastic net at region 3 for the continuous trait.We applied our approach to data from the Healthy Pregnancy, Healthy Baby (HPHB) study, which is a prospective cohort study of pregnant women aimed at identifying genetic, social, and environmental contributors to disparities in adverse birth outcomes in the Southern United States (log10(Bayes factor) = 2.05 exceeding the threshold 2. With only one local ancestry localized, the second step of the generalized admixture mapping procedure was unnecessary. The same data were analyzed by the BLR method, which treated the subjects with averaged maternal MAP more than 93.67 (top 20% quantile) as cases and the ones with averaged maternal MAP less than 79.33 (bottom 20% quantile) as control. No local ancestry was identified as being associated with the averaged maternal MAP with this approach, presumably due to its relatively low power compared with the GLEAM approach.The proposed GLEAM approach was applied to this dataset to identify the local ancestry associated with the averaged maternal MAP, a continuous trait, while we adjusted for mother’s age. The local ancestries were multiply imputed based on the HMM. We first examined the marginal association between the trait and local ancestries, one locus a time. The results are summarized in When the admixture linkage disequilibrium is used, admixture mapping is an indispensable tool to localize the alleles that are associated with the qualitative or quantitative traits and diseases that vary in prevalence across the ancestral populations. In this article, we propose a flexible and powerful generalized admixture mapping approach, which is based on the generalized linear model and is able to incorporate admixture prior information by using the quadratic normal moment prior and to adjust for covariates. The proposed method is applicable to both qualitative and quantitative traits with satisfactory power while controlling the type I error rates at a low level, and is able to be easily implemented as we demonstrated with our HPHB example.In addition to the flexibility to handle different types of traits, other attractive generalizations include consideration of multiple loci simultaneously. It is known that admixture linkage disequilibrium extends much further than haplotype linkage disequilibrium. Consequently, if we only examine one locus a time, the local ancestries which are highly correlated to the true disease associated local ancestry tend to be identified as significant ones as well. As demonstrated by the simulations, those false positives can be significantly reduced by considering multiple susceptible loci simultaneously, which reduce the type I error rates and improve the mapping resolution. In addition, GLEAM specifies a hidden Markov model treating the recombination rates varying across the genome, which allows us to infer the recombination “hotspots” in admixture population. Moreover, within the generalized linear model framework, it is straightforward to extend the current method to populations with more than to two ancestral populations, such as Hispanic populations, by adding extra ancestry population covariates. It is also easy to consider the interaction between the local ancestries and covariates with the properly specification of the priors on interaction coefficients.