P<0.05) trait-marker associations were detected using mixed linear model (MLM) within Panel 1 in two years, among which 32% were identical with previously mapped QTLs, and 11 significant associations had >10% explained ratio of genetic variation; (2) A total of seven aforementioned trait-marker associations were verified within Panel 2 and 3 when using a general linear model (GLM) and 55 SSR markers of the 76 significant trait-marker associations. However, no significant trait-marker association was found to be identical within three panels when using the MLM model; (3) several desirable alleles of the loci which showed significant trait-marker associations were identified. The research provided important information for further mining these elite genes within rice landraces and using them for rice breeding.Mining elite genes within rice landraces is of importance for the improvement of cultivated rice. An association mapping for 12 agronomic traits was carried out using a core collection of rice consisting of 150 landraces (Panel 1) with 274 simple sequence repeat (SSR) markers, and the mapping results were further verified using a Chinese national rice micro-core collection (Panel 2) and a collection from a global molecular breeding program (Panel 3). Our results showed that (1) 76 significant ( Oryza sativa L.) feeds more than 50% of the world's population As a staple cereal crop, rice (Linkage mapping and association mapping based linkage disequilibrium (LD) are two main methods for locating genes or QTLs. The major limitations of linkage mapping are that only two alleles at any given locus can be studied in bi-parental crosses and a low mapping resolution Arabidopsis, maize, barley, durum wheat, spring wheat, sorghum, sugarcane, sugar beet, soybean, grape, forest tree species and forage grasses Association mapping has been widely used in plant research since it was firstly reported in maize The choice of appropriate germplasm to maximize the number of historical recombinations and mutation events (and thus reduce LD) within and around the gene of interest is critical for the success of association analysis ArabidopsisPopulation structure may cause false positives in association mapping. To overcome this problem, an approach using a mixed-model was proposed for association mapping, which take both population structure (Q) and kinship (K) into account for the reduction of false positives In our previous studies, a rice core collection (Ting's rice core collection) consisting of 150 accessions of rice landraces has been constructed based on 15 quantitative traits and 34 qualitative traits from 2262 accessions of rice landraces of the Ting's collection with an optimal sampling strategy Three rice collections, i.e. Ting's core collection (Panel 1), the Chinese national micro-core collection (Panel 2), and a collection from the core collection of a global molecular breeding program (Panel 3) were used in this study. Panel 1 was collected by the researcher Ying Ting during 1920–1964 from all over China as well as from Korea, Japan, Philippines, Brazil, Celebes, Java, Oceania, and Vietnam. The original collection comprises 7128 rice landraces All of the three panels were cultivated at the farm of South China Agricultural University, Guangzhou , during the late season (July-November) for two consecutive years (2008 and 2009). A randomized complete block design with three replications was used during each season. The space between rows and between plants was set to 20 and 16.5 cm, respectively. Thirty plants of each variety were grown in three rows with 10 plants per row. For each block, the five plants in the middle position of the second row of each variety were selected so that the marginal effect was avoided. 12 agronomic traits for these plants were investigated. Heading date (HD) was recorded as days from sowing to flowering time when 30% of the individuals of one variety started flowering. Plant height (PH), panicle length (PL), grain length (GL), grain width (GW), flag leaf length (FLL), and flag leaf width (FLW) were measured in centimeters. Seed set rate  was the percentage of filled grains divided by the total grains per plant. For 1000-grain weight (1000GW), 100 grains were measured in grams with three replicates and then its average was multiplied by 10. For grain length (GL) and width (GW), ten grains were randomly selected and measured with a digital vernier caliper.274 SSR markers evenly distributed across the 12 chromosomes of rice were selected to genotype all varieties in Panel 1 (Table S2 in 2H) was calculated as 2H = Means and standard deviation (SD) for 12 traits were calculated using Excel software. The percentage of phenotypic variation explained by population structure was calculated using a General Linear Model (GLM) with software SPSS 17.0 for Windows . The broad-sense heritability  did not show a clear cutoff point for the true K, an ad hoc measure ΔK was used to detect the numbers of subgroup. That run with the maximum likelihood was applied to subdivide the varieties into different subgroups based on the maximum membership probability. A Q-matrix was obtained from the membership probability of each variety. Our previous study indicated that there were two distinct subgroups in Panel 1, which were in accordance with the germplasm types of indica and japonica rice 10 (P) using software SAS version 9.0 (SAS Institute 2002), where observed P values were obtained from association mapping and expected P values from the assumption that no associations happened between marker and trait.Polymorphism information content (PIC) which measures the extent of polymorphism for marker gene(s) or marker sequence(s) was calculated using the program POWERMARKER V3.25. Software Structure V2.3.1 was used to infer population structure and get Q matrices www.maizegenetics.net/tassel). For the mixed linear model (MLM) method, both K and Q matrices were incorporated, whereas for the GLM method, only population structure information (Q-matrix) was used as a covariate. Significance of associations between loci and traits were determined by their P values (P<0.05) which were calculated by the statistical models, and the phenotypic variance explained by the significant loci was calculated through analysis of variance (ANOVA). Since MLM method performs better in controlling spurious associations than GLM method P<0.05) association from MLM and then compared the significance of these markers (P<0.05) in the permutation based on GLM association tests. For the comparison, we calculated and used other two significant thresholds (i.e. Minimum Bayes factor (BF) and Bonferroni threshold) besides the P value. BF was calculated using the following formula: BF = −e*P*ln(P) Association analysis was performed using the software TASSEL  positive correlations both in 2008 and 2009 were found between HD and PH, PH and PL, FLL and FLL/FLW, PL and FLL, PL and FLW, GL and GL/GW, GW and 1000GW, GL and 1000GW, HD and FLW, PH and FLL, SS and 1000GW, PH and FLW (P<0.01) negative correlations in both two years were found between HD and 1000GW, GW and GL/GW, FLW and FLL/FLW, FLW and PN.Extremely significant  trait-marker associations were found using the GLM model for the 12 agronomic traits both in 2008 and 2009, and 15 (∼10%) of 152 trait-marker associations were detected in the previous studies (P<0.05) trait-marker associations were identified using MLM in 2008 and 2009, respectively. Among them, 76 trait-marker associations were significant (P<0.05) both in 2008 and 2009. The number of significant loci associated with each agronomic trait in two years ranged from 0 (seed set rate) to 13 (plant height). Moreover, 24 (∼32%) of the 76 trait-marker associations were in the same or similar genomic regions where QTLs were detected in previous studies (http://www.gramene.org/), and the other 52 trait-marker associations were new associations which were not previously identified.152 significant ( studies . Further2R), i.e. HD (PSM184), PH , PL (PSM184), GL/GW (RM447), FLL (RM287), FLW (RM235), 1000GW , and PN (RM311) both in 2008 and 2009 . Similarly, in Panel 3, the association for marker RM590 with plant height had the highest 2R (39.96%). RM339 which showed significant associations with heading days, were reported by previous researches Association analysis was performed within the two Panels using both MLM and GLM approaches with the 55 SSR markers. A total of 20 and 31 significant trait-marker associations were detected using MLM within Panel 2 and Panel 3, respectively. Seven significant trait-marker associations which were detected in Panel 1 using MLM model were identical with those in Panel 2 and Panel 3 using the GLM model, respectively. However, there was no identical trait-marker association within the three Panels when using the MLM model . In PaneP<0.01) lower plant height and panicle length than those carrying other two alleles 205 bp and 215 bp (P<0.01) higher grain width and significantly (P<0.01) lower grain length/width ratio than those carrying other two alleles 100 bp and 117 bp. For RM469, the individuals carrying the allele 94 bp had a significantly (P<0.01) lower flag leaf length than those carrying other two other alleles 83 bp and 88 bp. For RM206, the individuals carrying the allele 162 bp had a significantly (P<0.01) higher 1000-grain weight than those carrying the other four alleles 123 bp, 125 bp, 130 bp and 143 bp. For RM311, the individuals carrying the allele 143 bp, 143 bp and 153 bp showed a significantly (P<0.05) higher panicle number per plant than those carrying other two alleles 147 bp and 157 bp. For RM235, the individuals carrying the allele 108 bp showed a significantly (P<0.05) higher flag leaf width than those carrying the alleles 115 bp, 117 bp, 121 bp and 123 bp, whereas the individuals carrying the allele 123 bp had a significantly (P<0.05) lower flag leaf width than those carrying the alleles 91 bp, 108 bp, and 115 bp. For RM277, the individuals carrying the allele 117 bp had a higher grain length than those carrying the allele 111 bp .Seven markers, i.e. PSM184, RM447, RM469, RM235, RM206, RM311, and RM277, were selected for analysis of trait performance relevant to different alleles of significant loci based on their high explained percentage of genetic variation and supported by several significant thresholds . For PSMd 215 bp . For RM4An appropriate population with maximized phenotypic variation is critical for the success of an association analysis P<0.05) LD was 46.8%; (2) LD decayed rapidly to the threshold, i.e. the 95% quantile of r2 between unlinked loci pairs, at 1.03 cM in the entire collection; and (3) there were many LD blocks. These previous results indicated that Panel 1 was an appropriate population for association mapping. Therefore, our association mapping was performed based on Panel 1.China is well known as one of the origin center of cultivated rice with abundant genetic resources for rice. As early as in 1920–1964s, Professor Ying Ting collected more than 7128 accessions of rice landraces from all over China as well as some countries which grow rice as a major crop. The collection is one of the earliest collections for rice germplasm resources and therefore was named Ting's rice germplasm collection The populations in previous studies for association analysis in rice included populations from the USDA core collection Our results indicated that there is a wide-range of phenotypic variation for 12 agronomic traits in Panel 1. For heading days, flag leaf length, flag leaf width, grain length, grain width, grain length/width and panicle length, there was less phenotypic variations than described in the research of Jin et al. There are two frequently used models (i.e. MLM and GLM) which were implemented in the software TASSEL for association analysis P value) must be set considerately in the association mapping. Using a smaller P value as threshold might lose more minor QTLs, while using a higher P value as threshold might get more false positive QTLs. To reliably interpret the MLM-derived significant associations in our study, we also used minimum BF estimation P values of MLM approach may help to understand the overall impact of the associations P<0.05, minimum BF, and the Bonferroni), which should be emphasized in future studies.Furthermore, the significance threshold  of the significant associations found using the MLM approach were also supported by the GLM approach in both years. The percentage of associations identical to previous reported QTLs was about 32%, which was higher than those in the research of Li et al. For heading days, two of the four significant trait-marker associations were identical to previous reported QTLs, i.e. RM341 and RM339, were identical to previous reported QTLs in the research of Mei et al. It is worthwhile to further verify the significant associations identified within one population in a different population We observed that there were no overlapping QTLs among the three panels with the GLM approach. The reasons might be (1) different compositions and origins of the varieties in three panels, where Panel 1 only consists of original rice landraces from China and some other rice growing countries which were collected during 1920–1964 before the emergence of hybrid rice, while Panel 2 consists of rice landraces as well as modern rice cultivars and maintainer lines in hybrid rice breeding from China, and Panel 3 is a worldwide collection and consists of modern rice cultivars including cytoplasmic sterile line, maintainer lines, and some landraces; (2) that different allelic frequencies might exist for the three panels which consist of different compositions and origins. The explanations were supported by our observations that (1) frequency of some alleles was different in the three panels and some alleles only exist in one panel  have been developed, genotyping large germplasm resources with high density markers and GWAS in such mapping populations has become possible. Because such an association could be further applied in rice breeding by molecular marker assisted selection, it would be promising to make use of the elite genes in the diverse germplasm resources by the current strategy.File S1Table S1, Accessions, variety names, origin, germplasm types of 150 rice varieties in Panel 1. Table S2, Summary statistics of the 274 SSR markers used in this study. Table S3, Allele frequency of the 55 significant markers in three panels. Figure S1, Frequency distribution of heading days, plant height, seed set rate and panicle length in Panel 1 in 2008. The height of black bar represents the number of varieties in different range of traits. Figure S2, Frequency distribution of grain length, grain width, grain length/width and 1000 grain weight in Panel 1 in 2008. The height of black bar represents the number of varieties in different range of traits. Figure S3, Frequency distribution of flag leaf length, flag leaf width, flag leaf length/width and panicle number per plant in Panel 1 in 2008. The height of black bar represents the number of varieties in different range of traits. Figure S4, Frequency distribution of heading days, plant height, seed set rate and panicle length in Panel 1 in 2009. The height of black bar represents the number of varieties in different range of traits. Figure S5, Frequency distribution of grain length, grain width, grain length/width and 1000 grain weight in Panel 1 in 2009. The height of black bar represents the number of varieties in different range of traits. Figure S6, Frequency distribution of flag leaf length, flag leaf width, flag leaf length/width and panicle number per plant in Panel 1 in 2009. The height of black bar represents the number of varieties in different range of traits. Figure S7, Distribution of pairwise relative kinship values in Panel 2 and 3. The height of black bar represents the percentage of varieties in different range of kinships. Figure S8, Delta K change according to different K among Panel 2 and Panel 3 identified by STRUCTURE under Admixture model.(DOC)Click here for additional data file.


Recent studies of eukaryotes including human and Neandertal, mice, and butterflies have highlighted the major role that interspecific introgression has played in adaptive trait evolution. A common question arises in each case: what is the genomic architecture of the introgressed traits? One common approach that can be used to address this question is association mapping, which looks for genotypic markers that have significant statistical association with a trait. It is well understood that sample relatedness can be a confounding factor in association mapping studies if not properly accounted for. Introgression and other evolutionary processes  typically introduce variation among local genealogies, which can also differ from global sample structure measured across all genomic loci. In contrast, state-of-the-art association mapping methods assume fixed sample relatedness across the genome, which can lead to spurious inference. We therefore propose a new association mapping method called Coal-Map, which uses coalescent-based models to capture local genealogical variation alongside global sample structure. Using simulated and empirical data reflecting a range of evolutionary scenarios, we compare the performance of Coal-Map against EIGENSTRAT, a leading association mapping method in terms of its popularity, power, and type I error control. Our empirical data makes use of hundreds of mouse genomes for which adaptive interspecific introgression has recently been described. We found that Coal-Map’s performance is comparable or better than EIGENSTRAT in terms of statistical power and false positive rate. Coal-Map’s performance advantage was greatest on model conditions that most closely resembled empirically observed scenarios of adaptive introgression. These conditions had: (1) causal SNPs contained in one or a few introgressed genomic loci and (2) varying rates of gene flow – from high rates to very low rates where incomplete lineage sorting dominated as a primary cause of local genealogical variation.The online version of this article (doi:10.1186/s12864-015-2298-2) contains supplementary material, which is available to authorized users. At time t2, a new hybrid population was formed by hybridization between species A and B. We assume that ploidy is preserved across the phylogeny. In a first generation hybrid offspring, half of the alleles in its genome are expected to come from a parent individual in species A and the other half from a parent individual in species B. A locus in a first-generation hybrid genome has ancestry either from species A or from species B, depending upon the outcome of genetic recombination. We refer to a contiguous genomic subsequence with ancestry from a single parental species as a tract. The evolutionary history of a tract in a first-generation hybrid is represented by either the blue or the green genealogy shown in Fig. Adaptive interspecific introgression has played a key role in the evolution of novel traits in many eukaryotic organisms. Examples include hemoglobin concentration in Tibetans as an adaptation to high-altitude environments , 2, mimeMus musculus and its sister species Mus spretus [Vkorc1 gene which are known to contribute to resistance and susceptibility to warfarin [Recently in collaboration with others, we used PhyloNet-HMM to uncover genome-wide signatures of introgression between natural populations of  spretus . Dozens warfarin , 12, a wGenome-wide association (GWA) mapping methods can be used to obtain important clues concerning these questions. GWA methods are widely used throughout the life sciences to investigate the genetic architecture of complex traits, particularly in natural human populations and laboratory strains of model organisms . The goaThe statistical methodologies used in GWA studies can also be used to investigate the genomic architecture of traits involved in adaptive introgression between different species. However, the sample structure is typically more complex than in human populations and artificial laboratory organisms such as classical and wild-derived mouse strains. Two contributing factors are: (1) greater evolutionary divergence involving heterogeneous evolutionary processes such as gene flow, recombination, lineage sorting, and natural selection, and (2) genealogical histories of different loci within genomes can vary significantly not only in terms of branch lengths but also topologies. The latter can cause sample relatedness in one locus to differ from other loci as well as the genome as a whole.Exactly how to account for sample relatedness remains a subject of major debate. The most widely used GWA methods adopt a range of approaches, broadly categorized in terms of their complexity. On one end of the spectrum, a genomic control approach involves computing an inflation factor based on the degree of sample relatedness, which is then used to correct association statistics . On the More recently, GWA studies have begun to examine admixed human populations (reviewed by ), introdAs suggested by , the truγ=0.5). Coal-Map offered better power than EIGENSTRAT across the different model conditions. The performance improvement was significant in terms of area under ROC curve (AUROC) for all model conditions , with P values of 2∗10−14, 5∗10−5, and.006 for the single-causal-locus, two-causal-loci, and all-causal-loci model conditions, respectively. As measured by AUROC, Coal-Map’s performance advantage over EIGENSTRAT was largest on the single-causal-locus model condition  and smaller as more loci contributed causal SNPs. This can also be seen based on each method’s power at typical false positive rates. At a false positive rate (FPR) of 0.05, Coal-Map’s TPR improved upon EIGENSTRAT’s by 0.152 and 0.054 on the single-causal-locus and two-causal-loci model conditions, respectively; on the all-causal-loci model condition, the TPR difference between the two methods was less than 0.039.The simulation study included model conditions with adaptive gene flow. A range of genetic architectures were simulated, where one, two, or all loci contained causal markers. Figure al. test , α=0.05)γ=0.01 to 0.5 and intra-locus linkage that emulated selective sweep effects (but did not directly incorporate positive selection). The synthetic traits incorporated genetic contributions from one, two, or all loci. In Fig. γ=0.5) is shown using ROC curves. Across the different trait architectures , Coal-Map offered comparable or better power than EIGENSTRAT for a given false positive rate. The performance improvement was significant in terms of area under ROC curve (AUROC) for the single-causal-locus and two-causal-loci model conditions but not for the all-causal-loci model conditions . Coal-Map’s performance advantage over EIGENSTRAT was largest on the single-causal-locus model condition: the methods had AUROC values of 0.938 versus 0.870, respectively, and Coal-Map’s TPR improved upon EIGENSTRAT by 0.111 at an FPR of 0.05. As more loci contributed causal SNPs, Coal-Map’s performance advantage was smaller. Overall, Coal-Map reported smaller p-values at causal SNPs compared to EIGENSTRAT RAT Fig. .Fig. 5Cγ from 0.5 to 0.01 . Thus, on the model condition with negligible gene flow , virtually all local genealogical variation was due to incomplete lineage sorting. At an FPR of 0.05, Coal-Map’s TPR improved upon EIGENSTRAT by 0.211, 0.171, and 0.242 on single-causal-locus model conditions with γ settings of 0.25, 0.1, and 0.01, respectively; on two-causal-loci model conditions, the corresponding TPR improvements were 0.036, 0.032, and 0.094, respectively. The performance of the two methods on the all-causal-loci model conditions was similar regardless of the amount of gene flow, as measured by either AUROC or TPR at a typical FPR level.As we examined single-causal-locus and two-causal-loci model conditions with smaller levels of gene flow, we observed that Coal-Map’s performance advantage over EIGENSTRAT did not diminish and in fact remained roughly the same. As shown in Table al. test , α=0.05)We explored the sensitivity of Coal-Map to the number of covariates (five and twenty) used to represent the sample structure. We found that Coal-Map’s performance was robust to the number of covariates used to represent sample structure . At an FPR of 0.05, Coal-Map’s TPR improvement over EIGENSTRAT was 0.076 and 0.166 for single-causal-locus traits, respectively, and 0.030 and 0.057 for two-causal-loci traits, respectively  will predominate. We note that, in prior genomic studies of adaptive introgression , 5, intrIn our simulation study, we found that Coal-Map’s performance advantage was retained across a wide range of gene flow – even on model conditions which had virtually no gene flow. In the latter case, we attribute Coal-Map’s improvement to modeling the variation in local sample structure contributed by incomplete lineage sorting. The breakpoint inference stage of Coal-Map’s methodological pipeline accounts for local genealogical variation due to gene flow as well as incomplete lineage sorting and other evolutionary processes. We note that the presence of incomplete lineage sorting in our performance study is unique compared to past performance studies of association mapping methods on admixed populations  recombination. We compared the performance of Coal-Map to EIGENSTRAT, a leading association mapping method. We consistently observed the same outcome across all of the datasets in our study: Coal-Map’s performance in terms of power and false positive rate was comparable or better than EIGENSTRAT in all cases. Thus, Coal-Map can be generally used in place of EIGENSTRAT and related association mapping approaches that do not explicitly model local variation in evolutionary relatedness. We found that the conditions under which Coal-Map’s performance was strictly better than EIGENSTRAT were those that most closely resembled empirical cases of adaptive interspecific introgression, involving: (1) traits with causal SNPs drawn from one or a few genomic loci with common introgressive origin, and (2) a range of gene flow levels. Perhaps surprisingly, Coal-Map strictly outperformed EIGENSTRAT even on model conditions where gene flow was nearly absent but incomplete lineage sorting was still a factor. We hypothesize that modeling the fine variation in sample structure due to incomplete lineage sorting may be useful to association mapping approaches outside of the multi-species evolutionary context considered in this study. These alternative contexts include traditional genome-wide association studies of human populations or inbred mouse strains.The pipeline-based design of Coal-Map is flexible. As noted above, richer coalescent-based modeling of the evolutionary origins of local genealogical variation may permit more accurate breakpoint inference in the first stage of Coal-Map.We explored the use of forward selection for our model selection approach, which was used to determine if local sample structure containing the test SNP was incorporated into the model or not. However, we found that forward selection is conservatively biased towards models with fewer parameters. As an alternative, we utilized an approach involving two nested models – one incorporating local sample structure and the other not – which uses a likelihood ratio test of each model against a null model (positing that the test SNP has no effect), and then selects the model with the smallest test statistic. We note that, using this approach, the resulting association score is at least as significant as a likelihood ratio test using one of the two nested models by itself. Thus, the number of positives  reported using the approach can be no smaller than the number reported using one of the two nested models, and the number of false negatives can be no larger. In practice, our results suggest that the approach yields a comparable false positive rate and a substantially improved true positive rate compared to forward selection and other model selection techniques such as information criteria –41.Recently, Shriner et al. and Pasaniuc et al. proposed BMIX and MIXSCORE, two methodologies for genome-wide association studies of admixed populations , 28. TheWe conclude with discussion of future research directions. To our knowledge, our study is the first to explore association mapping performance using many hundreds of genomes with adaptive interspecific introgressive origins. Compared to human genome sequence data in public databases, a relative paucity of genomic sequence data is available to explore this question. Genomic sequence data is available for less than a thousand samples from natural populations of house mice –47, and n by k multiple sequence alignment X containing genotypic data for n aligned sequences and k sites, (2) local partition breakpoints b in ascending order , and (3) a phenotypic vector y with n observations. The ith row in alignment X and the ith entry in the phenotypic vector y correspond to the genomic sequence and phenotypic value of taxon si for 1≤i≤n. A local partition Xℓ is the alignment consisting of all sites in alignment X contained in the closed interval with endpoints equal to the breakpoints bℓ and bℓ+1. Each local partition Xℓ represents a contiguous genomic region where introgressed tracts in the region had a common introgressive origin  and phenotypic vector y for 1≤j≤k.The input to Coal-Map consists of: (1) an onet-HMM  in the gpj for a SNP xj is calculated under the following linear mixed model (following the notation of [The association score ation of ): \docuxj has effect size β. The fixed effects Wj includes covariates that account for global sample structure . Additional covariates that account for local sample structure  may be added using a model selection approach (described below). The covariates have coefficients α. The error term ε follows an n-dimensional multivariate normal distribution with mean 0 and variance τ−1In. We obtained MLE estimates pj is computed using a likelihood-ratio test of the fitted model against a null model of no SNP effect.The test SNP 1.1 from . The assWglobal, obtained as follows. Following the approach of [X excluding the local partition Xℓ and the top five principal components are used as the covariates w1,w2,…,w5. Local sample structure in a local partition Xℓ containing the test SNP xj is represented similarly, resulting in five additional covariates w5,w6,…,w10. We chose to use at most ten covariates to represent sample structure based on the empirical findings of [We chose to model sample structure using fixed effects instead of random effects due to the popularity of fixed-effect association mapping approaches and their accuracy , 34, 53.roach of , a princdings of . We alsoXℓ (containing the test SNP) are modeled as a polygenic effect based on covariates computed from global sample structure since it aggregates over all partitions. Covariates computed from local sample structure contribute to the linear mixed model when the local partition Xℓ contributes to the phenotypic vector y , but otherwise not. Coal-Map selects between the two resulting models: one using the covariates P<0.05). We also evaluated an alternative approach which performs the likelihood-ratio test of each alternative model against a null model of no SNP effects and then chooses the model with smaller P value. Since the forward selection approach can be conservative, we focus on the latter approach.The basic idea behind our use of fixed covariates to capture sample relatedness is as follows. Causal loci outside of the local partition s=0.56 which was based upon previously reported estimates from natural mouse populations that were involved in adaptive introgression [t1. At time t2, the ancestral populations of A and B hybridized to form the ancestral population of H. We based the divergence time t1=3.0  on prior population genetic estimates in two Mus species , the local partition breakpoints required as input to Coal-Map were inferred using the Four-Gamete Test [Our performance evaluation of Coal-Map utilized simulated genotypic sequences and traits where local genealogical variation was due to gene flow and incomplete lineage sorting, two evolutionary processes with first-order effects in prior studies of introgressed eukaryotic genomes , 31, 54.ble 1 in ), corresete Test , 59.yi is the trait value for the ith individual, π is the proportion of trait variation contributed by genotypic effects, Qi,j is 1 if the ith individual carries the derived allele at site j or 0 otherwise, the environmental contribution is a random effect with normal distribution N, and Δ is the set of causal SNPs. Twenty causal SNPs were selected uniformly at random from either one, two, or all loci, where loci were chosen uniformly at random in the case of a single or two loci contributing causal SNPs. We refer to the resulting model conditions as single-causal-locus, two-causal-loci, and all-causal-loci model conditions, respectively. Additionally, causal SNPs were selected to have minor allele frequency ranging between 0.1 and 0.3 . In theMus musculus and Mus spretus populations [Vkorc1 gene that PhyloNet-HMM inferred as introgressed in origin. Crucially, PhyloNet-HMM performs probabilistic inference to ascribe local genealogical variation to one of several evolutionary processes: interspecific introgression, incomplete lineage sorting, recombination, back mutation, and any combination thereof. Thus, local sample structure will often vary within introgressed tracts that are shared across a common subset of samples .Two main factors affecting association mapping power are effect size and minor allele frequency of causal SNPs  – both ogitlab.msu.edu/liulab/coal-map.Open-source software and open data are available at


Multi-marker approaches have received a lot of attention recently in genome wide association studies and can enhance power to detect new associations under certain conditions. Gene-, gene-set- and pathway-based association tests are increasingly being viewed as useful supplements to the more widely used single marker association analysis which have successfully uncovered numerous disease variants. A major drawback of single-marker based methods is that they do not look at the joint effects of multiple genetic variants which individually may have weak or moderate signals. Here, we describe novel tests for multi-marker association analyses that are based on phenotype predictions obtained from machine learning algorithms. Instead of assuming a linear or logistic regression model, we propose the use of ensembles of diverse machine learning algorithms for prediction. We show that phenotype predictions obtained from ensemble learning algorithms provide a new framework for multi-marker association analysis. They can be used for constructing tests for the joint association of multiple variants, adjusting for covariates and testing for the presence of interactions. To demonstrate the power and utility of this new approach, we first apply our method to simulated SNP datasets. We show that the proposed method has the correct Type-1 error rates and can be considerably more powerful than alternative approaches in some situations. Then, we apply our method to previously studied asthma-related genes in 2 independent asthma cohorts to conduct association tests. Genome wide association studies (GWAS) have generated a wealth of information about genes and genetic variants influencing various diseases and traits.  The vastGenes are the basic functional units of the genome and multiple polymorphisms within or near a gene can jointly affect its products. Thus, multi-marker association tests can realistically model the multiplicity that occurs biologically. While individual causal variants might show only a marginal signal of association, jointly utilizing all informative SNPs within a gene may detect their manifold effects. Testing genes also reduces the burden of multiple testing from millions of individual SNP tests to around 20,000 genes. Gene-based methods may also be less sensitive to differences in allele frequency and linkage disequilibrium patterns between population groups .p value based on the individual SNP association tests. Versatile gene-based association study (VEGAS) is a gene-based method that combines the chi-square test statistics of individuals SNPs, while accounting for their dependence [p value by integrating the p values of individual variants while accounting for pairwise correlations between variants when calculating the effective number of independent tests [To date many gene-based association tests have been proposed –10. Mostpendence . Li et ant tests . SKAT isnt tests ,8.p values in gene-based tests can be divided into 2 categories: best-SNP picking and all SNP aggregating tests. Best-SNP picking tests use only one SNP-based p value after accounting for multiple testing adjustment. GATES is an example of a testing method that falls within this category. All-SNP aggregating tests, such as VEGAS-SUM and SKAT, attempt to accumulate the effects of all SNPs into a test when determining the overall p value. HYST is a recently developed hybrid method that use both these kinds of approaches in its calculations [Generally, the methods used for combining ulations .p value for variants within a gene or integrate the p values or test statistics from individual variants to determine the overall gene-level p values. However, this may not be optimal in terms of utilizing the information available in the data [Many existing gene-based approaches either use the minimum the data  and it mthe data –16. Thusthe data . In prinm predictors is chosen as split candidate from the full set of p predictors. The split is then allowed to use only one of these m predictors. This has the effect of decorrelating the trees and predictions from many trees are averaged to generate the final prediction. Random forests can model non-linear relationships and interaction effects between input variables.We propose to use Random Forests –13, SuppSupport Vector Machines are supervised learning algorithms that can be used for both classification and regression. Formally, a support vector machine constructs a hyperplane in high-dimensional space based on the training data and this can be used to perform classification, and regression. Informally, the objective is to find a hyperplane that has the largest distance to training data points from any class. The larger this margin, the better is the accuracy of the classifier. In addition, SVMs have the ability to perform a non-linear classification using kernels that implicitly map their inputs into high-dimensional feature spaces.Here, we show how machine learning algorithms can be used to construct powerful tests for multi-marker association analysis. We then show how to construct tests of association in the presence of genetic or non-genetic covariates and how to construct a multi-marker test of interactions under this framework. We first apply our method to simulated datasets to demonstrate its power and correctness. Lastly, we apply our method to previously studied asthma-related genes in two independent asthma cohorts to conduct gene-based association tests.The Henry Ford Health System Institutional Review Board approved this study. Patient records and information were anonymized and de-identified prior to use in this analysis.Here, we present an overview of our approach to predict phenotypes from genetic and clinical variables through the use of multiple machine learning algorithms. First, we create a list of all genetic variants and clinical covariates that can potentially influence the phenotype of interest such as a disease or drug response. Next, we perform a feature selection step where we identify a subset of variables, which are useful for building a predictive model . This can be done in many ways such as using variable importance scores from a random forest algorithm or Pearson’s correlation coefficient with the phenotype. Different machine learning algorithms  are used for training the algorithm and learning the model parameters. Subsequently, this model is applied to generate phenotype predictions for the samples in the test set. This process is repeated for each of the k parts to generate phenotype predictions for all the samples.Generate a set of all genetic variables.1, f2…fn) for phenotype prediction. This can be performed using either pairwise correlation coefficients between variables and phenotype or by using random forest variable importance scores to rank the variables. Then, we can use the top 10–30% of the variables in a prediction model.Perform feature selection on the training data in order to identify an informative subset of variables  on “out of the bag” samples (i.e. those not used in training) for asthma drug response.The choice of mfound in ). We con2 or Mean Squared Error between observed and predicted values) for the dataset under consideration. In general, the goal is to maximize the prediction accuracy (or minimize prediction error) while maintaining a reasonable computing time and roughly correct false positive rate. We chose the parameters for each component algorithm  by maximizing the marginal prediction accuracy. However, there are no hard and fast rules for choosing a set of machine learning algorithms and we expect that many different variations under the ensemble learning framework  and observed  values and determine the corresponding p values. For case-control studies, we perform a standard logistic regression that uses all genetic variables as well as Pfinal as explanatory variables and Pactual as response. A chi square based likelihood ratio test can then be used with respect to a null model with no variables to generate p values. If lik denotes the log likelihood of a model, the test statistic is given by: 2(likfull—liknull) which follows a chi square distribution with g + 1 degrees of freedom where g is the number of genetic markers.Once we have estimated a model using any of the algorithms described in the previous section and predicted phenotypes for all individuals using cross-validation, we can construct tests of association in the following manner. For continuous traits, we can calculate the Pearson’s correlation coefficient between predicted  for all the samples in our data. This prediction is generated using k-fold cross-validation as described previously. For case-control phenotype, the test statistic is based on a standard logistic regression model that uses all the SNPs as well as Pfinal as explanatory variables making use of all the samples. For continuous phenotype, we perform a test of correlation between Pfinal the predicted phenotype value and Pobserved the actual phenotype values using all the samples.Note that the final test statistic that we calculate, makes use of all the samples in our data and not just the testing set. The first step in our multi-marker association test is generating phenotype predictions (Pp(j) denote the p value for the jth SNP and assume that values are in ascending order. Letm denotes the total number of SNPs in the gene. We perform simulation studies to compare the Type-1 error rate and statistical power of the ensemble learning approach with the following alternative gene-based tests:Let p value is calculated using a chi square test statistic that is based on the log likelihood ratio comparing the full model with all available SNPs and null model with none.Each SNP is coded as 0, 1, or 2 for the number of copies of the minor allele in the genotype and the response variable is the disease status coded as 1 (case) or 0 (control). The gene-based T = −2∑lnp(j), where the summation is from 1 to m. This statistic has a chi-square distribution with 2m degrees of freedom under the null hypothesis. m denotes the total number of SNPs in the gene and the tests are assumed to be independent. [The test statistic is given by pendent. p value is given by PS= min(mp(j)/ j). For independent tests, PS is uniformly distributed between 0 and 1 under the null hypothesis [In this test, gene-based pothesis . When mam SNPs in a gene, the overall gene-based p value is given by: PG= min(mep(j)/ me(j)), where me is the effective number of independent p values among the m SNPs and me(j) is the effective number of independent p values among the top j SNPs. j can vary between 1 and m. The effective number of tests is calculated using a formula that uses the correlation coefficients between SNP-based association test results.GATES is a rapid gene-based association test that uses extended Simes procedure . The tesA versatile gene-based test for genome-wide association studies (VEGAS) was recently proposed in . The tesp value. The test also allows adjustment for covariates. The kernel machine has the ability to model complex and non-linear relationships between dependent and independent variables.This test , 8 uses final-all be the predicted phenotype values. Then, remove the SNP variables and rerun the phenotype prediction algorithm. Let Pfinal-covariates be the predicted phenotype values. For continuous traits, we first calculate the Pearson’s correlation coefficient for these predicted variables with the true phenotypes . The strength of association for the genetic variables with continuous traits can then be calculated using the Steiger’s Z test [12 and r13 denote the Pearson’s correlations between the true phenotype  and Pfinal-covariates and Pfinal-all respectively. Let r23 denote the Pearson’s correlation between Pfinal-covariates and Pfinal-all. The Steiger’s test computes p values based on the following test statistic that is assumed to be standard normally distributed:Association testing in the presence of covariates  can be done in the following manner. First, consider both non-genetic covariates and genetic variables together for phenotype prediction according to any of the ensemble learning algorithms described earlier. Let Ps Z test  for the 12 and Z13 are Fisher’s transformations of r12 and r13, and Here, Zfinal-all and Pfinal-covariates as explanatory variables in a logistic regression model. We then use a chi square likelihood ratio test to compare the former model with a model without any genetic variables  to calculate a p value for the genetic contribution. If lik denotes the log likelihood of a model, the chi square test statistic is 2 for case-control data, which follows a chi square distribution with g + 1 degrees of freedom where g is the number of genetic markers.For case-control studies we can use both non-genetic covariates, genetic variables, Plinear be the predicted phenotype values. Then, generate phenotype predictions for all individuals using any of the ensemble learning algorithms described previously. Let Pensemble denote the predicted phenotype values. For continuous traits, we will use all markers as well as Pensemble and Plinear as explanatory variables in a multiple regression model (Model 1) and perform a F test with a model (Model 0) without interactions  to calculate the p value. We compare the sum of the squared errors (SSE) of prediction to construct an F statistic with  degrees of freedom. Here:We can test for interactions between a set of markers in the following manner. First, consider all of the SNPs together in a linear or logistic regression model (for continuous or case-control phenotype respectively) and generate phenotype predictions using cross-validation for all individuals. Let PModel1 denotes the total number of explanatory variables in model 1. For case-control studies, we will use all markers as well as Pensemble and Plinear as explanatory variables in a logistic regression model and perform a chi square likelihood ratio test with a model without interactions  to calculate the p value. The test statistic has 1 degree of freedom. Note that this test assumes normality of residuals and homoscedasticity. Violation of any of these assumptions may affect the Type-1 error rates for the test.N denotes the number of samples and Vp values (i.e. p < 0.05).We tested the performance of the proposed gene-based test by simulating genotype data for 30 biallelic SNPs assuming Hardy Weinberg equilibrium. We assumed the following 3 scenarios of linkage disequilibrium (LD) for the 30 SNPs: i) SNPs are within blocks with high LD (r = 0.9 or 0.8 within blocks); ii) SNPs are within blocks in moderate LD (r = 0.5 or 0.4); and iii) SNPs are completely independent of one another and in linkage equilibrium. The choice of simulation settings were similar to what has been used previously  . We compared our result with a gene-based test using multiple linear regression, a gene-based test using GATES [p values were obtained using a F test statistic.The simulations in the previous section assumed that the effect of various disease susceptibility SNPs were independent of one another and that they increased the risk additively or multiplicatively. To explore the effect of pairwise and higher order interactions between genetic variants, we also compared the performance of methods for data simulated under models with interactions. We simulated a quantitative trait for many different models with one or more interactions among variants in addition to main effects. In addition, we also considered scenarios where there is pure epistasis (i.e. where the effect of a group of SNPs is simply due to their interactions and there are no main effects). We simulated samples of 3,000 individuals and genes with 5 or 10 SNPs assuming linkage equilibrium ; p values were based on an F test statistic with two parameters as described previously.For all the models simulated in the previous section, we also constructed a multi-marker test for interactions as described previously and estimated the power of such a test. We simulated samples of 3,000 individuals and genes with 5 or 10 SNPs assuming linkage equilibrium. The phenotype was drawn from a complex distribution involving the sum of a standard normal variable and interaction terms involving many SNPs. Power and Type-1 error rates were estimated based on 1,000 simulated datasets. For each model with interactions, we calculated the fraction of simulated datasets for which the multi-marker test of interactions generated a significant We applied the methods developed in this paper to data from 2 independent studies . After data quality control, genotype information was available on 586,952 SNPs for 1,099 individuals with asthma and 328 healthy controls . All of The GALAII study is a case control study to identify gene-environment interactions contributing to asthma. Children of Latino descent age 8–21 years were recruited from New York City, Chicago, San Francisco, Houston, and Puerto Rico. Children with asthma had a physician diagnosis of asthma and either a 12% increase in forced expiratory volume at one second following the administration of albuterol or a positive methacholine challenge test. Genome wide genotype data was available on 3,772 individuals . Genomic DNA was genotyped on the Axiom Genome-Wide LAT array. After data cleaning, information was available for 747,075 SNPs genome wide.The following are the assumptions made in simulations for our multi-marker association test:We assume that the samples are unrelated and that there is no population stratification.For simulations in Tables For simulations in Tables For models with epistasis , we inclFor models with epistasis, the markers are assumed to be in linkage equilibrium.For Type-1 error rates, we assume that phenotype is normally distributed for continuous traits.p values < 0.05, in around 5% of the simulated datasets due to chance alone. For the ensemble learning and logistic regression methods, we can also see that power is not strongly sensitive to the strength of linkage disequilibrium. Thus, for both additive and multiplicative models, power estimates do not appear to change much across Tables Tables In Note that for models with moderate or strong LD, the Fisher’s combination test has significantly inflated Type-1 error rate and therefore is no longer a valid test. In contrast, the VEGAS-SUM test shows the correct Type-1 error in all scenarios and appears to be significantly more powerful than the ensemble learning approach and logistic regression, when LD is strong. However, note that LD based pruning or principal component analysis can reduce the number of variables (and degrees of freedom when constructing association tests) and improve the power for both our approach  includes the effects of interactions and is always used when constructing the final association test and determining p values for both continuous traits and case-control data.Note that the improved power of the ensemble learning approach for models with epistasis comes from its ability to model non-linearity and interactions between features. The models learned under the ensemble learning framework incorporate pairwise and possibly higher order interactions and when such effects are actually present, the machine learning based association test can be considerably more powerful than other simpler approaches which do not incorporate interactions. The predicted phenotype variable  from the SAPPHIRE cohort and 3,772 Latino children  from the GALA II study. IL33 was significantly associated with asthma in Latino children using the ensemble learning gene-based test, but this gene was of borderline significance using the other 2 approaches. Analysis of local ancestry for all these tested gene-regions did not indicate any unusually high correlations with phenotypes for both the African American and Latino population samples used in this study (Results not shown here).We tested 9 previously studied asthma-related genes –25 to seWe have introduced a new method for assessing gene-based associations using genome wide genotype data. This method uses diverse machine learning algorithms to construct predictive models for the phenotype using the SNP variation within a gene and then uses these predictions to construct tests of association. Machine learning algorithms represent powerful tools for inferring the relationship between multiple explanatory variables and a phenotype while accounting for high-order interactions between the former. Because the “true” multivariable relationship between a set of variables and a trait like disease or drug response is not known in advance, we can better approximate this relationship by first learning from the data. The use of ensemble learning-based predictions leads to novel multi-marker tests of association. In addition to gene-based tests of association, these methods could also be applied for pathway-based analysis  or to any other set of polymorphic variants defining a region of interest or a functional class.a priori assumptions about the genetic model for a SNP . When constructing our tests, we can include 3 variables for each SNP where the variants are encoded according to these 3 models . Thus, we can include heterogeneous effects across SNPs. A second advantage is the ability to include any number of covariates (genetic or non-genetic) and model higher level interactions between them. This feature makes machine learning particularly suited for assessing gene-environment or gene-gene interactions. Third, creating an ensemble of diverse multivariate models with meta-features makes our method less restrictive and capable of approximating the phenotype more accurately. Collectively, these novel aspects can boost statistical power and result in novel genetic discoveries.There are three key advantages of using our gene-based approach compared to existing approaches. First, our method does not make p values obtained from our ensemble learning based test of common variants with any currently used rare variant multi-marker tests (e.g. SKAT) using Fisher’s method or the Original Simes procedure. Ideally, we want to include both common and rare variants  in an ensemble learning based phenotype prediction framework and subsequently construct association tests based on such predictions.It should be noted that the ensemble learning based association test is not affected by the relative direction of effect of the different variants in the genes. Since the ensemble learning approach is based on generating phenotype predictions, in principle the direction of effect of particular SNPs is not expected to adversely influence the accuracy of this variable. As long as a gene contains SNPs that are associated with the phenotype, we expect that it will add to the overall prediction accuracy of the models that are learned and help us to detect associations with a gene-region. Furthermore, since the overall goal of multi-marker association tests is to find regions associated with phenotype, it is desirable to construct tests that can look at the combined effects of all variants, both common and rare . Incorpop values. Subsequently, we can obtain an overall p value from these individual p values using the TATES multi-trait association method [Extensions of these methods towards the case of multiple correlated phenotypes should also be straightforward. If instead of a single phenotype, we are interested in many phenotypes that are correlated with one another in some manner, we can construct a joint association test for all of them in the following manner. First, we will apply the ensemble learning based gene-based association test to each phenotype individually and obtain their corresponding n method , which iWe applied our method to both simulated and empirical datasets to demonstrate its power and utility. For models without interactions between variables, the ensemble learning approach worked similarly when compared with other previous gene-based association tests. In contrast, for models dominated by interactions, our simulation studies suggested that the ensemble learning test can be considerably more powerful than other methods. Thus, for situations where epistatic or gene-environment effects are likely to be important, our association test is more likely to detect associations as compared to many of the alternative methods described.There are a number of potential limitations to our approach that require mentioning. First, computational time can be a limitation factor when applying an ensemble learning algorithm based association test to thousands of genes. LD based pruning of SNPs, dimensionality reduction using principal component analysis within haplotype/LD blocks, and parallelization (when computing clusters are available) can all help to boost computational efficiency so that gene-based association tests can be implemented within a reasonable time. LD based pruning of SNPs or principal component analysis also ensures that the top selected features are not highly correlated with one another. When samples used are not unrelated , we can estimate pairwise relatedness between individuals and subsequently choose the largest subset of people who are not too closely related to one another (e.g. no first and second degree relatives) for analysis. Next, we cannot state with certainty that the genes assessed here are involved in asthma pathogenesis, since many of these genes were identified in association studies and their function (as it relates to asthma) has not yet been elucidated. Therefore, while we assume that these genes represent true-positives, this portion of our analysis may not represent an actual demonstration of statistical power unless more detailed functional studies are conducted for the relevant genes to directly demonstrate their role in asthma. Lastly, it should also be mentioned that while our multi-marker tests can detect associations or the presence of interactive effects, they do not attempt to pinpoint the specific variants contributing to such effects.In summary, ensemble learning algorithms provide a general and flexible framework for conducting association analysis. We have shown how phenotype predictions made by such algorithms can be used for many common tasks encountered in association analysis, such as multi-marker association tests, adjusting for genetic and non-genetic covariates, and tests of interaction. Because machine learning is a highly developed area of study, prediction of response from many input variables is a well-studied problem and numerous well-established algorithms are already available which can be readily incorporated as components in an ensemble learning framework to maximize prediction accuracy and construct powerful tests of association.S1 Appendix(DOCX)Click here for additional data file.S2 Appendix(DOCX)Click here for additional data file.S3 Appendix(DOCX)Click here for additional data file.S4 Appendix(DOCX)Click here for additional data file.S1 Archive(ZIP)Click here for additional data file.S2 Archive(ZIP)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S6 Table(DOCX)Click here for additional data file.S7 Table(DOCX)Click here for additional data file.S8 Table(DOCX)Click here for additional data file.S9 Table(DOCX)Click here for additional data file.


The implementation of genomic-based medicine is hindered by unresolved questions regarding data privacy and delivery of interpreted results to health-care practitioners. We used DNA-based prediction of HIV-related outcomes as a model to explore critical issues in clinical genomics.Genet Med18 8, 814–822.We genotyped 4,149 markers in HIV-positive individuals. Variants allowed for prediction of 17 traits relevant to HIV medical care, inference of patient ancestry, and imputation of human leukocyte antigen (HLA) types. Genetic data were processed under a privacy-preserving framework using homomorphic encryption, and clinical reports describing potentially actionable results were delivered to health-care providers.Genet Med18 8, 814–822.A total of 230 patients were included in the study. We demonstrated the feasibility of encrypting a large number of genetic markers, inferring patient ancestry, computing monogenic and polygenic trait risks, and reporting results under privacy-preserving conditions. The average execution time of a multimarker test on encrypted data was 865 ms on a standard computer. The proportion of tests returning potentially actionable genetic results ranged from 0 to 54%.Genet Med18 8, 814–822.The model of implementation presented herein informs on strategies to deliver genomic test results for clinical care. Data encryption to ensure privacy helps to build patient trust, a key requirement on the road to genomic-based medicine.Genet Med18 8, 814–822. The clinical use of genomic data has the potential to improve health care by allowing for more individualized preventive and therapeutic strategies. However, applying genetic knowledge clinically raises critical issues regarding the protection of genetic data, predictive power, and interpretation as well as delivery of results.1 In addition, many of the approaches used in research  are not applicable to genetic information because the genome is the ultimate identifier for each individual. Thus there is a requirement for additional strategies that preserve the privacy of genomic data while not compromising the accuracy of results.The majority of clinical genetic testing currently consists of targeted genotyping of one or a few markers. However, it is likely that future testing will involve the in silico selection of relevant markers from a large set of previously genotyped variants . Large-scale genetic data will thus be stored and analyzed routinely in a clinical context; still, they have specificities that differentiate them from the rest of health-related information: genomic data have the potential to inform on identity, ancestry, and risks of multiple diseases in a given patient and among their relatives.HLA-B*57 and severe hypersensitivity reaction to abacavir3). However, other variants are largely nondeterministic  and are best summarized by genetic risk scores, and reported as modifying an individual's basal risk. Thus a real-world framework for genomic testing needs to provide a calculation and reporting infrastructure that incorporates both classes of results.Clinical genetic tests vary in number of informative markers and overall predictive power. Some tests are deterministic (or nearly deterministic), and thus are associated with a clear interpretation , response to therapy,5 adverse events,6 and susceptibility to metabolic disorders.9 Today, decisions for clinical care of HIV are based on guidelines, local preferences, clinical and demographic data, viral resistance analyses, and, increasingly, cost.10 The fact that there are now multiple alternatives for first- and second-line treatments sets the stage for more informed treatment decisions.In this study we chose clinical aspects of HIV care as a model setting for an implementation of privacy-preserving genetic testing and results reporting in the clinic. Human genetic variation affects multiple aspects of HIV disease, including rate of disease progression off therapy  involves four parties: (i) the patients; (ii) a certified institution (CI) responsible for genotyping, management of cryptographic keys, and encryption of patients' genetic data; (iii) a storage and processing unit (SPU) where the encrypted genetic variants are stored; and (iv) health-care practitioners, or medical units (MUs), wishing to perform genetic tests on the patients. We note that, since sequencers generating encrypted data do not exist yet, the CI currently would have access to unprotected raw genetic variants and therefore must be a trusted entity. In addition, we are assuming a model where the encrypted genetic variants are stored in a centralized SPU rather than at an MU, which maximizes efficiency and security. This is similar to applications used in business and government where the trust in the server (SPU) is much higher than in the client (MU) and allows access to be provided to several different clients (MUs) from a trusted central resource whose key task is preserving security.The proposed system . In particular, both the MU and the SPU honestly follow the protocols without altering the data—but they might try to passively infer sensitive information about the patients. The honest-but-curious adversary model is a realistic assumption in health care where, on a daily basis, different MUs honestly collaborate and share sensitive data about patients based on mutual trust and privacy policies. Moreover, as recently discussed in ref. 13 using additively homomorphic encryption, deterministic encryption, proxy re-encryption, and secure two-party protocols for comparison and multiplication in the ciphertext domain (see Supplementary Text S1 online). The algorithm consists of an “offline” phase and an “online” phase. In the offline phase, the CI generates a pair of cryptographic keys (public and private) for each patient. Each private key is randomly split into two shares, with one share assigned to the SPU and the other to the MU such that neither site can individually decrypt the data. Given the noncollusion assumption between these two parties, such a technique prevents the genomic privacy of patients from being compromised if one share of the key is leaked or stolen. The CI encrypts each genetic variant with the public key of its owner and then sends the encrypted data to the SPU for secure storage. To encrypt the genetic variants, the CI applies a probabilistic encryption scheme that is additively homomorphic. Probabilistic encryption provides semantic security  by using randomness in the encryption algorithm so that encrypting the same message several times yields different ciphertexts. Homomorphic encryption allows computations to be carried out on encrypted messages without decrypting them. Note that, despite its critical role of key manager and genotyping facility, the CI has no incentive or motivation to directly perform the genetic tests on the raw data on behalf of the MU. In the online phase, the MU and the SPU collaborate to privately infer ancestry information and perform genetic tests such that the MU obtains only the final result of the computation without directly accessing the raw genetic data.Data processing to infer ancestry and calculate medical test results used modified versions of previously devised privacy-preserving algorithms,14) was selected as a training data set, and a principal components analysis along with a k-means clustering were applied to identify the main ancestry groups in continental populations. Encrypted principal components for each patient were then computed at the SPU using the same set of variants through homomorphic operations. A secure similarity protocol was performed to privately compare encrypted principal components and cluster means to identify the correct ancestry group for each individual (for further details see Supplementary Text S1 online).To infer ancestry from encrypted data, we used a secure two-party protocol between the MU and the SPU. The ancestry inference algorithm is performed only once at each MU after genetic variant encryption. A reference panel of publicly available genotypes (HapMapSNPj represent the unique identifier (ID) of the jth single-nucleotide variant, SNPjP represent the genotype value of SNPj for P, and [SNPjP] denote its encryption under the homomorphic encryption scheme. Let [AP] be the homomorphic encryption of P's ancestry information. To compute a specific genetic test for condition X on P, including ancestry information, the MU sends the set of encrypted IDs (ϕ) of the single-nucleotide polymorphisms correlated with X to the SPU. The SPU then sends P's corresponding encrypted variants and encrypted ancestry information back to the MU. Computation of the genetic risk score G(X), generally assuming an additive model, is then performed at the MU using the encrypted data; that is, the MU calculates [G(X)] through the homomorphic properties of the encryption scheme, as shown in equation (1):Privacy-preserving computation of the genetic risk test on encrypted data for patient P is performed as follows. Let βj represents the contribution of SNPj to condition X , α represents the baseline risk, and ⊗ represents a secure two-party multiplication protocol (see Supplementary Text S1 online for more details). Note that to prevent the SPU from inferring the nature of the test based on the number of requested variants, the MU can include an arbitrary number of “dummy” variants with a null contribution to X . Finally, after partial decryption of [G(X)] at the SPU (with SPU's share of P's private key), the MU completes the decryption of G(X) with its share of P's private key to generate the final report.where 15 Clinical toxicity was assessed at baseline and 1 month (+15 days) and 1 year (+3 months) after treatment initiation using an adapted toxicity questionnaire.17 In the case of a treatment discontinuation, modification, or dose change, a stop questionnaire was completed. Plasma drug concentrations were measured 1 month after antiretroviral therapy initiation by liquid chromatography coupled to tandem mass spectrometry using an adaptation of previous methods.19 Measured laboratory parameters included total bilirubin, triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and glucose and were collected at baseline, 1 month, and 1 year. Laboratory measurements below the limit of detection were set to the lowest detectable value. All patients signed consent for genetic testing, and the institutional review boards of the Swiss HIV Cohort Study centers approved the study.Patients were treatment-naive HIV-infected individuals starting antiretroviral therapy and were enrolled in the Swiss HIV Cohort Study.24 and response to therapy29; (ii) pharmacokinetics of efavirenz,34 nevirapine,31 etravirine,35 or lopinavir36; and (iii) metabolic traits including vitamin D deficiency,7 coronary artery disease,37 cholesterol and triglyceride levels,38 and type 2 diabetes.9 Testing included single and multimarker deterministic tests, where the presence of a risk variant or combination of variants is highly likely to cause the associated trait, and multimarker risk scores, where several variants combine together to moderately affect trait risk. The prediction scheme for each reported results is provided in Supplementary Text S2 online. Additional markers that are predictive of patient ancestry (n = 111),39 or HLA type (n = 250) also were incorporated. Markers capturing variation across a set of absorption metabolism distribution and excretion genes  also were included.40 Though these variants were not used for clinical prediction, they were used to improve the precision of ancestry inference.We identified from the literature 71 markers that were informative for 17 traits relevant to HIV outcomes. Clinically informative markers fell into three categories: (i) HIV/hepatitis C virus progressionCCR5Δ32 (rs333), CYP2B6*6 (rs3745274), UGT1A1*28 (rs8175347)) were genotyped by TaqMan allelic discrimination from Applied Biosystems, Foster City, CA or fragment size–based analysis.41 Samples and variants were filtered out if they did not pass quality thresholds for genotyping rate and Hardy-Weinberg equilibrium. A second method was used to confirm genotyping for two individuals per genotype (Supplementary Table S1 online). Four-digit classical class I HLA allele genotypes were imputed for individuals with inferred European ancestry using the SNP2HLA pipeline.42 Since currently it is not feasible to perform this operation on encrypted data, this step was performed outside of the privacy-preserving framework, although it was included in the text report provided to physicians because of the high relevance of HLA types in relation to HIV progression. Only alleles with an imputation quality above 0.98 were reported.The majority of variants were genotyped using a custom array on the Illumina Infinium platform. Informative variants that could not be included on the genotyping array because of technical issues (Supplementary Text S2 online). Results were returned to physicians as a standardized text report. Predictions were reported to indicate increased or decreased risk of the trait due to genetic factors, or a result of “no relevant alleles found” was reported. Concurrently, physicians were asked to complete a survey aimed at gauging their acceptance and interest . Each report included a disclaimer indicating the investigational nature of the study. Importantly, the release of genetic data to the clinics was delayed and, by design, not meant to modify choice of treatment.Interpretation was defined a priori and fully documented . Plasma drug concentrations and laboratory parameters were compared using linear regression.Statistical analyses were performed using R version 2.15. Survival analysis was performed using the R Survival package version 2.37 (Supplementary Table S2 online.) To assess the feasibility of applying genetic testing in the clinical setting, we performed all operations  on encrypted data based on the framework outlined in Figure 1. We used a modified version of the Paillier cryptosystem43 supporting both additively homomorphic encryption and proxy re-encryption to encrypt the genetic variants of each patient, and we used the CCM mode44 of the advanced encryption standard45 to deterministically encrypt their identifiers. We tested the performance on off-the-shelf hardware  by using a Paillier's security parameter 4,096 bits in size. The encryption time for a single marker was 171 ms with a storage size of 1 kB. Thus, total encryption time per patient for all genotypes took ~12 min, generating a ciphertext size of 4 MB. We note that initial encryption is required only once in the “offline” phase of the protocol and could be accelerated through parallel computing.A total of 230 HIV-infected individuals initiating antiretroviral therapy were included in the study and were genotyped for 4,149 variants. . For the remaining individuals, a result of “prediction not available for this population” was reported for the ancestry-limited tests. Predicted ancestry was highly similar to self-reported ancestry (94%) and was incorporated solely to determine which test results were valid on an individual basis; this was not reported to the clinician or patient.After ancestry inference, a set of 169 individuals predicted to be of European ancestry and for whom full results and HLA alleles could be reported was identified . An example report returned to physicians is shown in Figure 3.To maximize clinical utility, clinicians were provided with interpreted test results for each trait, rather than the raw patient genotypes. Semantics were adapted to indicate the confidence of each test individually. Thus, when significant genetic markers were observed, an alert specific to the test was returned; otherwise a result of “no significant alleles found” was given (Supplementary Text S2 online). The proportion of positive results returned for all tests ranged from 0 to 54% (Table 1). Considering all tests, 226 patients (98%) had at least 1 positive result. Though this study was not designed to assess the predictive value of the included genetic variants, we did observe consistency between their reported effects in the literature and drug plasma concentrations  and levels of measured laboratory values  in this sample. In addition, we observed a shorter time to treatment discontinuation for individuals with a gene–drug conflict  compared with those without .In total, we tested 17 phenotypes relevant for patients with HIV. The number of single-nucleotide polymorphisms that are informative for a single trait ranged from 1 to 22 , 65% (HLA-B), and 96% (HLA-C) of alleles in Europeans with ≥ 98% confidence. The relatively low proportion of imputed HLA-B alleles is probably due to the extreme diversity across this gene.42Given the importance of HLA class I alleles in influencing HIV disease progression,Supplementary Figure S1 online). Although the majority (53%) of physicians reported that the test results were useful or potentially useful, only a minority (42%) reported that they would discuss these results with the patient . In addition, when a positive genetic result was returned and the patient had been prescribed the contraindicated medication, only 10% of physicians reported that they would have prescribed a different first-line regimen if given the genetic results in advance.To address the utility of and interest in the pharmacogenetic report, we asked all physicians to respond to an acceptability questionnaire  within an encrypted environment.12 .The design of the study included the genotyping of several thousand markers and the reporting of a number of potentially actionable HIV-related variants. Specifically, the panel of genetic tests addresses some recognized issues in HIV care: abnormal drug concentrations and toxicity, HIV- and treatment-associated metabolic disorders, HIV/hepatitis C virus coinfection and prediction of disease progression. For example, tests included deterministic information , as well as informative results on particular predispositions . The language was controlled to indicate this difference. Importantly, this framework could easily be extended to incorporate demographic, behavioral, and laboratory parameters to more precisely estimate a patient's risk of a particular outcomeSpecific aspects of the predictive value of individual tests were assessed, although the study was not designed to formally test their validity (which has been confirmed by larger studies). A central outcome of this study is the delivery of interpreted genetic data. Processes such as correction for ancestry, imputation of HLA alleles, and calculation of genetic scores were performed in the background, and clinicians received only a fully interpreted report rather than raw genetic data. However, the testing framework was made available to clinicians so that they could evaluate the evidence for each test based on their interest level. We deployed a real-life clinical application by using a privacy-preserving framework in which reports were generated from encrypted genetic data without significant additional cost in terms of computation and storage overhead.n bits can be broken in an average time of 2n−1). We used a 4,096-bit key, a size that is compliant with the recommendations of the National Institute of Standards and Technology and will provide security for the next 30-plus years based on the envisioned improvement in computing power.46 For some test results reported, however, there is a strong linkage between the results and the underlying causal genotype . Thus the inclusion of a large number of such tests may present its own risk to patient privacy. In the case where many such conditions are to be included in the same report, other techniques, such as result obfuscation, may be desirable.The security of the system relies on the security of the underlying cryptosystem that is based on the quadratic residuosity assumption. In our case, the proposed system may be susceptible to a brute-force attack . The feasibility of this type of attack depends on the length of the key used  would take ~200 h. Importantly, this initial encryption is required only once (in the offline phase) and could be expedited by precomputation of certain exponents that are required for encryption and parallel computation, resulting in an encryption time on the order of minutes. Though current computational limitations are prohibitive for the performance of certain sophisticated operations, such as genotype imputation, fully homomorphic encryption has no theoretical bounds on possible mathematic operations or on scalability. Thus, as computation efficiency continues to increase, the scheme presented here will remain directly applicable.The strategy successfully implemented in this pilot study allows the secure storage and analysis of large-scale genetic data, as well as the targeted delivery of specific subsets of test results to the clinic.The authors declare no conflict of interest.