Shared genetic aetiology may explain the co-occurrence of diseases in individuals more often than expected by chance. On identifying associated variants shared between two traits, one objective is to determine whether such overlap may be explained by specific genomic characteristics . In clinical studies, inter-rater agreement approaches assess concordance among expert opinions on the presence/absence of a complex disease for each subject. We adapt a two-stage inter-rater agreement model to the genetic association setting to identify features predictive of overlap variants, while accounting for their marginal trait associations. The resulting corrected overlap and marginal enrichment test (COMET) also assesses enrichment at the individual trait level. Multiple categories may be tested simultaneously and the method is computationally efficient, not requiring permutations to assess significance. In an extensive simulation study, COMET identifies features predictive of enrichment with high power and has well-calibrated type I error. In contrast, testing for overlap with a single-trait enrichment test has inflated type I error. COMET is applied to three glycaemic traits using a set of functional annotation categories as predictors, followed by further analyses that focus on tissue-specific regulatory variants. The results support previous findings that regulatory variants in pancreatic islets are enriched for fasting glucose-associated variants, and give insight into differences/similarities between characteristics of variants associated with glycaemic traits. Also, despite regulatory variants in pancreatic islets being enriched for variants that are marginally associated with fasting glucose and fasting insulin, there is no enrichment of shared variants between the traits. Apparent links between disease susceptibilities may be explained by shared genetic aetiology, such that a variant may be associated with multiple traits. Besides identifying shared associated variants, a further objective is to determine whether the overlap of associated variants between the traits may be related to SNP (or trait × SNP)-specific characteristics. Identification of specific characteristics that are predictive of overlap enables refinement of the set of variants in further searches for predisposing variants of both traits. Moreover, Bayesian priors may be defined such that a SNP belonging to a predictive category has a higher prior probability of association than SNPs outside that category; priors may also be allowed to differ so that the prior probability increases with the number of predictive categories that the SNP belongs to. The overall purpose of the proposed method, corrected overlap and marginal enrichment test (COMET), is to determine whether agreement (overlap) between the verdicts of association between a SNP and a phenotype can be related to SNP-specific  or trait × SNP-specific characteristics, such as membership of known biological pathways.1 genetic analysis incorporating pleiotropy and annotation (GPA),2 and a method implemented in database for annotation, visualisation and integrated discovery (DAVID).3 All of these methods assess enrichment of annotations among trait-associated variants and, on application to shared variants between different traits, do not account for marginal enrichment of individual traits. Testing for annotation enrichment within trait-associated SNPs is the reverse of the proposed objective of testing for enrichment of trait-associated variants within annotations. In the latter, the number of associated variants is treated as the random variable, which aligns with the perception that we observe a number of associated variants and there are more to discover. In contrast, testing for annotation enrichment in a set of associated SNPs fixes the number of associations found and assesses annotation status among them; the annotation status is treated as the random variable in that approach.Several existing methods address similar, but distinctive, objectives; for example, GoShifter,P-value may be due to marginal enrichments.2 GoShifter uses a computationally intensive permutation approach1 and the test implemented in DAVID involves calculation of a hypergeometric probability.3 We apply DAVID to test for enrichment among shared variants, rather than variants associated with a single trait and demonstrate that it has an increased type I error rate. Owing to the inflated error, power comparisons are not carried out with DAVID.With regards to overlap enrichment extensions, any of the single-trait enrichment methods may be extended by considering the set of SNPs associated with two traits. However, this does not automatically account for enrichment due to chance, as the marginal distributions of the individual traits are not accounted for. The GPA approach uses annotation information to increase the statistical power to identify risk variants. The authors of the method recommend caution in interpreting the enrichment testing approach of GPA with respect to overlap variants, as a significant COMET requires only summary statistics and is applicable to case–control or quantitative trait studies that may or may not have overlapping individuals. Simulations demonstrate that any degree of overlap between studies does not inflate the type I error for detection of SNP characteristics that are predictive of concordant associations between the traits. As COMET only requires fitting several linear models and does not depend on permutations to assess significance, it is computationally efficient. The data only needs to be clumped once, and then may be quickly analysed with any set of covariates. On a Linux (64 bit) machine with X86-64 architecture, 32 cores, and 2 × 2.1 Ghz 12 core AMD 6272 CPU, on data that has already been clumped, COMET is able to run for one pair of traits and one set of five covariates in 3 min, 44 s for our data application, where the fitting of the models takes 36 s.P<5 × 10−6, as given by the National Human Genome Research Institute (NHGRI) Genome-Wide Association Study (GWAS) catalogue4) for 14 different diseases/traits. COMET is then employed with these covariates to assess whether any annotation class is enriched for variants associated with fasting insulin, fasting glucose or 2-h glucose, or enriched for shared associations between any pair of the three glycaemic traits . As more genome-wide significant loci have been identified for the glucose traits than for fasting insulin,5 an objective is to determine whether there are certain characteristics that are enriched for variants associated with either or both traits; such features may then be used for refinement of searches for further associated variants. On the basis of our results, we proceed with further analyses using COMET to test for enrichment of trait(s)-associated variants within tissue-specific regulatory regions. The software for COMET is freely available at http://www.sanger.ac.uk/science/tools/comet.There is flexibility in the covariates that may be incorporated in the analysis, leading to a range of potential applications. Before our real data application, we first examine the potential for a set of functional annotation covariates to differentiate between associated variants  that make a verdict or pronouncement  on the same subject, and adjust for agreement between raters that may occur simply due to chance. A two-stage inter-rater agreement model identifies covariate categories containing more concordance/discordance in verdicts than expected by chance, accounting for the marginal rater opinions.At each genetic variant, a binary variable is defined for each trait corresponding to evidence of association with the trait, based on a pre-specified significance threshold; this corresponds to the verdict of each rater. Analogous to comparing measurements taken by raters on the same individuals, we compare measurements of trait-association at each SNP. Rather than considering agreement for both traits , we focus only on both traits having association evidence, as lack of association evidence does not imply that the association does not exist .P-values or Bayes' factors (BFs). We focus on BFs, as BFs may be easily computed from summary statistics7 and have several advantages over P-values in the comparison of multiple studies.8 In both our simulations and data application, we used a Bayesian threshold of log10(ABF)>0.695 , corresponding to a P-value threshold of 0.004–0.01, depending on the study size;8 see Evidence of association for each trait with each SNP may be defined according to r2>0.1) the set of SNPs  >5%) that comprise the GWAS data for each trait. The MAF threshold of 5% was chosen as we focus on GWAS results, though in application to other data sets  lower MAF variants may be included. SNPs are clumped using r2>0.1 to satisfy the independence assumption required for the regression models. We make use of a joint association metric that accounts for the significance of a SNP with respect to each trait, maximising the retention of SNPs associated with multiple traits, rather than SNPs with high association evidence with one trait and not with the other8  associated variants. As the inter-rater methods assume independent subjects (with subjects here corresponding to SNPs), we first prune ; r=1, 2, and pir=Pr; r=1, 2; i=1,...,m. In the inter-rater model,6 agreement between the raters at subject i would be defined as Yi=Yi1Yi2+(1−Yi1) (1−Yi2). Instead, we focus on the concordance of associated SNPs, and therefore consider Yi=Yi1Yi2. The marginal models for conditional probability of a detected association given a particular trait  are:Let γ0r is the baseline probability of association, accounting for the probability of association that is not attributable to any of the covariates. An effect estimate that meets the significance threshold  and is positive suggests that SNPs within the coinciding covariate category tend to be associated with the trait ; negative enrichment is present if the significant effect estimate is below zero. Collectively, this model tests for covariate categories that are predictive of SNP-trait associations.The intercept term These marginal models are first fit independently for each trait, then the fitted models are used to obtain estimates of the log-odds of chance overlap term β0 would be suggestive of more agreement than expected by chance that is not accounted for by any of the covariates. For instance, if SNPs associated with one trait tend to be associated with the other trait, but this sharing of associations is not related to any of the covariates, then the intercept term would account for this agreement. This framework may easily be extended to identify predictive features of shared SNPs for R traits by defining agreement at SNP i as If overlap is due to chance alone, then all covariate effect estimates are not significantly different from zero and the probability of overlap is simply the product of the marginal probabilities, 2), as the offset term accounts for each of the marginal distributions when testing for enrichment among shared variants.The traits may be from studies composed of disjoint sets of individuals or possibly from studies that share some individuals in common. In particular, for two quantitative traits, measurements for both traits may be taken on a portion of individuals. In the usual inter-rater set-up, different raters have correlated responses by the nature of rating the same subject, which is akin to correlation between trait associations expected in the presence of shared individuals, when testing at a certain SNP. This may influence the overall probability of concordance between the ratings but, intuitively, although this will affect the intercept term, this should not affect the tests of whether or not any of the covariates explain the concordance in the ratings. In the scenario of two case–control studies, there is the possibility of shared individuals between the control sets of the two studies. These shared controls may influence the individual SNP association tests, but by similar reasoning to the quantitative traits case, only the intercept term is expected to experience an impact. On a similar note, the traits may be correlated  or linked through a phenotypic derivation  is removed and the two-stage models are fit to the data with one fewer subjects. However, as there are a large number of SNPs, there are negligible changes to the fitted models at the removal of each individual SNP. Therefore, for computational efficiency, we make use of the resulting coefficient estimates and standard errors from the model based on a known offset term. A flow chart for COMET is given in It has been noted that the variance estimates for each coefficient of the model for 9 Covariate categories that each SNP is positive for are determined by the Variant Effect Predictor  of Ensembl,10 which outputs all consequences of each variant on the protein sequence and gene expression, across all transcripts for the gene, so that a SNP may be positive for multiple covariate categories.Various SNP-specific covariates may be used to inform about overlap between traits, allowing flexibility in use of the method. A set of possible SNP-specific covariates is listed in 11 On pruning the common SNPs (MAF>0.05) on r2>0.1 (using PLINK v1.07), there are 208 780 approximately independent variants. As a reference to the general features of SNPs, we examine the distribution of SNPs from the 1000 Genomes CEU samples, phase 3 release.r2>0.1 in the 1000 Genomes CEU samples. Functional annotations for these SNP are obtained from VEP (v79). We focus on models that include five SNP-specific covariates that are listed in Each simulation is based on 208 780 approximately independent SNPs that remain after pruning the common SNPs on p12' of variants that are associated with both traits and belong to the enriched category. The overall proportion of overlap variants is denoted by p12, whereas the marginal proportions of SNPs associated with traits 1 and 2 are given by p1 and p2, respectively. The simulation algorithm, parameter selection, and technical details are given in the χ2 distribution). As a comparison, type I errors for enrichment testing of overlap variants are also determined via the DAVID software.3For assessment of power, only one of the five covariate categories (Q1 or Q5) is set as enriched for overlapping associations between the traits, though this does not restrict causal SNPs from belonging to other categories. We consider various proportions Before applying COMET to real data, we considered the distribution of the covariates among variants that are associated with fourteen traits/diseases. This pre-assessment illustrated that there is potential for the covariates to differentiate between trait-associated variants for different traits, as well as potential for identifying covariates that may be enriched for shared variants. Details and results on these comparisons are given in the www.magicinvestigators.org and details on this dataset are provided in the 12 In RegulomeDB, known and predicted regulatory DNA elements include regions of DNase hypersensitivity, binding sites of transcription factors, and promoter regions that have been characterised to regulation transcription.COMET was applied with the set of five functional annotation covariates to each pair of fasting insulin, fasting glucose and 2-h glucose, which were all measured on non-diabetic European-ancestry individuals (from MAGIC). The summary statistics from these glycaemic traits were downloaded from 13 In addition, liver, adipose tissue, and skeletal and cardiac muscles develop insulin resistance as defence against damage from an excess nutrient load.14Of particular interest are tissues that are involved in metabolism, i.e. pancreas, liver, cardiac muscle, skeletal muscle, and adipose tissues. Pancreatic islet cells are central in the pathogenesis of type 2 diabetes (T2D) and active islet enhancer clusters have been demonstrated to be enriched in T2D risk-associated and fasting glucose-associated variants.r2<0.1) that are regulatory in each tissue type are 0.0768 (pancreas), 0.0666 (pancreatic islets only), 0.0779 (liver), 0.0275 (cardiac muscle), 0.116 , 0.0012 (adipose), and 0.0955 (liver cancer). On considering all (5) tissues involved in metabolism, the proportion is 0.166, or 0.162 if pancreatic duct tissues are excluded. Among all available tissues, the proportion of regulatory variants is 0.693.Owing to the likely collinearity between the tissue-specific regulatory covariates, we ran separate models including one regulatory covariate annotated by RegulomeDB, for several filtrations on the tissue type(s); details of the specific cell/tissue lines within each tissue group are provided in the r  is composed of Nr cases and Nr controls; we consider study 1 with N1=3000 each of cases and controls and study 2 with N2=5000 each of cases and controls, as well as  taking values  and . In our null simulations, the proportions of trait-associated variants for trait 1 , trait 2  and shared between them are, respectively, p1=0.04, p2=0.02 and p12=5 × 10−4. For all five covariates, both sets of standardised effect estimates from the marginal models display a close alignment with the standard normal distribution  and Q1 (51.5% of variants) as being enriched for overlap, so that any impact of the category proportions may also be assessed. Covariate categories that are not designed as enriched for overlap each give additional type I error results and can be averaged over the simulation settings for each covariate ; individN1, N2) set at  or , the detection power is close to 100% at 20% enrichment, and is high at 10% enrichment; high power near 80% is attained for  when there is at least 10% enrichment. The enrichment setting of p′12=7 × 10−6 corresponds to the null hypothesis of no enrichment , fasting insulin (FI) and 2-h glucose (2G) are given in In addition, SNPs in mature miRNAs that have a regulatory effect  tend to be enriched for variants associated with each of the three glycaemic traits. Nonetheless, there are not more shared variants than expected by chance, considering these marginal enrichments; Our results also indicate that there is positive enrichment of variants associated with FG and with FG-2G among SNPs that overlap potentially regulatory or regulatory regions. Consequently, we tested tissue-specific regulatory annotations for positive enrichment in an additional analysis.P-value to 0.044 (pancreas tissues), suggesting enrichment. This illustrates that marginal predictive factors are not necessarily predictive of overlap variants, with the offset term able to account for any perceived overlap that may in fact be due to chance. FI and FG associated variants are enriched in liver tissue regulatory variants, though 2G variants are not. COMET also detected that regulatory variants in cardiac muscle are enriched for FG and those in cardiac and skeletal muscle are each enriched for the FG-2G overlap.Results for tissue-specific analyses are shown in Considering the five metabolic tissues collectively, there is enrichment of each individual trait, as well FG-2G, though these signals disappear when all available tissues are considered collectively. There is an absence of FI-FG enrichment signals in tissue-specific analyses and the collective tissue analysis suggests enrichment, but such overlap variants are regulatory in a range of tissues that may be contributing to the signal. The FI-FG SNPs (GRCh37/hg19 assembly) that are regulatory in at least one metabolism-involved tissue are listed in 10(ABF)>0.695  that corresponds to a P-value threshold of 0.004–0.01, depending on the study size.8 This lenient threshold allows us to highlight new overlapping variants not already known to be genome-wide significant, and such variants that fall within an identified enrichment category  may have a stronger prior probability for having true associations with each trait. Enrichment categories may also indicate a direction of refinement for future searches for overlap variants. For example, our analysis suggests that being a potentially deleterious variant is a predictive factor for shared associated variants between glycaemic traits. Therefore, further shared associations may be revealed through the analysis of whole-exome or whole-genome data, which are enriched for potentially deleterious variants that are generally poorly represented in other genome-wide association arrays.We have proposed COMET as a computationally efficient method that makes use of GWAS summary statistics to test categories for enrichment of variants that are associated with multiple traits, accounting for chance overlap due to the marginal associations of each trait; individual trait-specific tests of enrichment are also encompassed. In the association classification of variants we used a Bayesian threshold of logP<5 × 10−6) for an assortment of traits. However, by considering the proportion of associated variants that are positive for each covariate there is a range of confidence interval sizes for the traits, as the confidence interval depends on the number of associated variants that are listed in the NHGRI-EBI GWAS catalogue.15 A further limitation is that the results in the GWAS catalogue rely on a variety of studies, having a range of sample sizes, which in turn influences the ability to detect trait associations within each study. Therefore, the ability to detect enrichment based on these proportions is heavily influenced by the number of listed trait-associated variants. This pre-assessment gives further support for our approach of detecting enrichment of associated variants within covariates, rather than detecting enrichment of covariates within associated variants.As a means of pre-assessing the usefulness of a set of functional annotation covariates for our model, we compared the proportion of covariate-positive trait-associated variants  within several functional annotation classes, and identify well-established positive controls, together with their biological support. The two glucose traits appear to have more overlapping variants falling within some categories than expected by chance, suggesting that these two traits are similar to each other, as expected.16 2G,17 blood metabolite levels, cardiovascular disease risk factors, metabolic and lipid traits, gout, liver enzyme levels, and chronic kidney disease.15 Additional variants within GCKR are genome-wide significant for FI-related traits16 and Crohn's disease. An additional missense variant rs13266634  is associated with both FG and 2G, and genome-wide significant for T2D,18 FG,16 fasting proinsulin levels,19 and glycated haemoglobin levels.20 These results are positive controls, since the variants were known to be genome-wide significant for the traits and our method both detects this overlap and suggests that these numbers are greater than expected by chance.The missense variant rs1260326  is associated with all three traits, and genome-wide significant for FG,TCF7L2 is known to be associated with T2D and glycaemic traits13 and within it we identify two overlap SNPs that are in low LD (r2=0.089) with each other: rs7903146 is detected for each pair of traits and rs7079711 is identified for FI-FG. The SNP rs7903146 acts as a positive control, since it is the lead SNP in TCF7L2 for associations with T2D,18 FI-related traits (interaction with BMI),5 and FG-related traits (interaction with BMI)5 and is also genome-wide significant for 2G16 and FG;16 this SNP is also our top signal for the FI-2G overlap and for each of FG and 2G.The gene ADCY5), which is known to be associated with FG16 and is in LD with a known 2G-associated SNP rs2877716 (r2=0.807).17 Each FI-2G variant that is regulatory in a metabolism-involved tissue is within a gene containing FI- or T2D-associated variants (P<5 × 10−6).A further positive control is detection of the FG-2G variant rs11708067  and highly significant for FI ; rs6984305 is also in LD (r2=0.614) with a known genome-wide significant FG (interaction with BMI)-associated SNP, rs4841132.5The top FI-FG signal is rs6984305 (in RP11-115J16.1), which is regulatory in tissues from the pancreas, liver, cardiac muscle and skeletal muscle. In the MAGIC data under analysis, this SNP is genome-wide significant for FG  with more than one glycaemic trait. The exception is rs17036328 (within PPARG), which is in perfect LD with several variants that meet significance for each of FG, FI (genome-wide level) and 2G; two of these perfect LD variants are regulatory in cardiac and skeletal muscles.Several SNPs are of interest for further investigation, as they (and SNPs in LD with them) have not been previously identified as associated with glycaemic traits. The SNP rs4736324  is regulated in pancreas tissue/islets and is a FG-FI variant. Likewise, rs2014712 (in KCNK9 and regulated in liver tissue) is an FG-FI variant and variants in KCNK9 are associated with adiponectin levels, cholesterol and CAD. Variant rs598725 (downstream RP4-60717.1) is a FG-2G variant and is regulatory in both skeletal and cardiac muscles. Most of the overlap SNPs that are regulatory in a non-metabolic-involved tissue are not in LD with a variant that is associated  have normal to slightly reduced hepatic insulin sensitivity.21 This suggests that the liver plays a relatively more important role in influencing FG than 2G. Enrichment of FI-associated variants in liver tissue may coincide with insulin regulating glucose production in the liver during the fasting state. Enrichment of glucose trait variants in cardiac and skeletal muscle is likely linked with muscle being a target organ for insulin.Enrichment of variants associated with FG, FI, 2G, and FG-2G among regulatory variants in pancreatic islets concurs with the result that islets are enriched in loci that are associated with FG and T2D.A possible limitation of the proposed approach is that the SNPs included in the analysis need to appear in both trait data sets, though imputed results are often available, so this may not have a significant impact. It is possible that, as we are limited by the set of SNPs available in both studies, the associated SNP may be a tag SNP for the causal variant, which is in a different covariate category, so that the enrichment category does not contain this causal variant. However, for covariate categories with a proportion of SNPs >1%, there would need to be some number of associated variants within the category in order for enrichment to be detected. It is highly unlikely that the majority of associated SNPs in the detected enrichment category are each a tag SNP for a causal variant in a different category. Therefore, even if this is true for an associated SNP, there is no change to the general biological interpretation of the covariate category being enriched for associated SNPs, as a set of associated SNPs has been detected in the category.P<5 × 10−8), or a less stringent classification (5 × 10−4<P<5 × 10−8), to increase the chances of finding novel results.Alternative covariates to functional annotations may be trait × SNP-specific, to inform about whether overlap SNPs occur more likely than by chance within a certain trait feature, such as previously identified trait-associated SNPs (using information obtained from NHGRI-EBI). Additional covariate possibilities include SNP presence/absence in at least one gene (+/−50 kb buffer region) that has been identified as harbouring a trait-associated variant , a covariate may be defined according to presence/absence of the variant within at least one gene (+/−500 kb buffer) in the pathway; an additional covariate may be defined as presence/absence of variant 500 kb away from gene and closer than 1000 kb. This pair of covariates may be used in a separate overlap model for each pathway (or pathway group) of interest.In conclusion, our proposed procedure for identifying features predictive of overlap informs biological interpretation and enables refinement of the set of variants considered in further searches for predisposing variants for both traits.


A primary goal of polygenic scores, which aggregate the effects of thousands of trait-associated DNA variants discovered in genome-wide association studies (GWASs), is to estimate individual-specific genetic propensities and predict outcomes. This is typically achieved using a single polygenic score, but here we use a multi-polygenic score (MPS) approach to increase predictive power by exploiting the joint power of multiple discovery GWASs, without assumptions about the relationships among predictors. We used summary statistics of 81 well-powered GWASs of cognitive, medical and anthropometric traits to predict three core developmental outcomes in our independent target sample: educational achievement, body mass index (BMI) and general cognitive ability. We used regularized regression with repeated cross-validation to select from and estimate contributions of 81 polygenic scores in a UK representative sample of 6710 unrelated adolescents. The MPS approach predicted 10.9% variance in educational achievement, 4.8% in general cognitive ability and 5.4% in BMI in an independent test set, predicting 1.1%, 1.1%, and 1.6% more variance than the best single-score predictions. As other relevant GWA analyses are reported, they can be incorporated in MPS models to maximize phenotype prediction. The MPS approach should be useful in research with modest sample sizes to investigate developmental, multivariate and gene–environment interplay issues and, eventually, in clinical settings to predict and prevent problems using personalized interventions. Another use, the focus of the present research, is to estimate genetic propensities of individuals to predict individuals’ future problems and potential and, eventually, to develop personalized interventions that meet individual medical, psychiatric and educational needs. Both goals have been hindered by the ubiquitous GWA finding that the largest effect sizes are extremely small.2 For example, the largest population effect sizes found for common variants in height or body mass index (BMI) account for only ~1% of the variance.4 We know empirically that the vast majority of common genetic variants for most traits have a markedly lower effect than 1%.2Genome-wide association studies (GWASs) have been successful in identifying thousands of associations for hundreds of complex traits and common disorders.6 Rather than just using single-nucleotide polymorphisms (SNPs) that reach genome-wide significance, a recent development is to aggregate a much larger number of SNPs, weighted by their GWA effect size estimate, as long as together they increase the prediction in an independent sample, even if some SNPs have no real effect.7 For example, for height, a polygenic score that aggregates the effects of ~2000 SNPs accounts for 21% of the variance of height in independent samples.3The highly polygenic nature of complex traits and common disorders poses an immense challenge for understanding the biological mechanisms linking single variants with phenotypes. However, when the priority is phenotypic prediction, polygenic scores can be used to aggregate the effects of many DNA variants in order to investigate their joint predictive power.11The other defining characteristic of complex traits and common disorders is the abundance of genetic correlations between them. There is consistent evidence for genetic correlations between psychiatric disorders, between anthropometric traits and between educational and cognitive traits, as well as for genetic correlations across these categories.8 Genetic correlation can also reflect shared biological pathways or more indirect linkage.12 Regardless of its cause, genetic correlation between different traits means that a polygenic score based on one trait can predict a different outcome trait, with predictive accuracy a function of the shared genetic signal between them. Therefore, when the aim is prediction, genetic correlation can be exploited for trait prediction while remaining agnostic to the underlying mechanisms.Genetic correlation can arise from pleiotropy, the phenomenon of multiple traits being associated with the same gene or genetic variant.A primary goal of polygenic scores, which aggregate the effects of thousands of trait-associated genetic variants discovered in GWAS, is to estimate individual-specific genetic propensities. This is typically achieved using a single polygenic score, but here we use an approach to increase predictive power by exploiting the joint power of multiple discovery GWASs. We use a multi-polygenic score (MPS) approach that exploits genetic correlations between the outcome trait and a multitude of traits by using the joint predictive power of multiple polygenic scores in one regression model.13 We subsequently tested how well these models predict outcomes in an independent test set.We selected GWASs from a centralized repository of summary statistics—based on their statistical power and regardless of prior evidence for association with the outcomes—to predict three core developmental outcomes in our independent target sample: educational achievement, BMI, and general cognitive ability. Using repeated cross-validation, we trained and validated the prediction models using elastic net regularized regression, a multiple regression model suited to deal with a large number of correlated predictors while preventing overfitting.Here, we employ a MPS approach that uses publicly available GWAS summary statistics to estimate individual-level genetic propensities and predict developmental outcomes in an independent target sample. This stands in contrast to multi-trait approaches that rely on access to individual-level data in the discovery data sets because they make use of a method from animal breeding in which the total genetic effect  of each individual in a discovery data set is estimated from the best linear unbiased predictor in a multi-trait random-effects model that can be used for individual-level prediction in the validation data sets. These multi-trait methods are not applicable to GWAS summary statistics when genotype data are unavailable because of privacy or logistical constraints that are frequently the case.17 The current MPS approach allows for, but does not require, correlation among polygenic predictors.The declared aim of the current MPS approach is to maximize prediction of developmental outcomes, rather than investigating their etiology. This stands in contrast to multi-trait meta-analytic approaches of GWAS summary statistics that relies on substantial and consistent correlations between discovery GWASs and whose main aim is variant discovery.20 The project received approval from the Institute of Psychiatry ethics committee (05/Q0706/228) and parental consent was obtained before data collection. We processed the genotypes for the 6710 individuals using stringent quality control procedures followed by imputation of SNPs using the Haplotype Reference Consortium reference panel21 (The target sample comprised genome-wide SNP and phenotypic data from 6710 unrelated adolescents drawn from the UK representative Twins Early Development Study (TEDS). TEDS is a multivariate longitudinal study that recruited over 11 000 twin pairs born in England and Wales in 1994, 1995 and 1996. Both the overall TEDS sample and the genotyped subsample have been shown to be representative of the UK population. panel21 .LD hub, a centralized repository for summary statistics22 based on their statistical power—regardless of prior evidence for association with our outcome traits. Specifically, we included 81 GWAS summary statistics that were either publically downloadable or obtained via correspondence and had a linkage disequilibrium (LD) score23 heritability z-score >5, indexing good statistical power (which is a function of variance explained and sample size). We selected GWAS summary statistics from The published version of the child IQ GWAS included the present target sample of TEDS. Therefore, to avoid bias, the present analyses used summary statistics from a rerun of the GWAS meta-analysis excluding TEDS.We created 81 genome-wide polygenic scores for each of the 6710 individuals in the TEDS sample using summary statistics from the GWAS described above . After q24 to construct the scores. LDpred uses a prior on the markers’ effect sizes and adjusts summary statistics for LD between markers. Scores were standardized and adjusted for 30 principal components. More details on the construction of the polygenic scores are provided in We constructed polygenic scores as the weighted sums of each individual’s trait-associated alleles across all SNPs. We used LDpredTo illustrate the MPS approach, we selected three key developmental outcomes:Educational achievement operationalized as the mean grade of the three compulsory subjects  attained on the standardized United Kingdom General Certificate of Secondary Education (GCSE), taken by almost all (>99%) pupils at the end of compulsory education at age 16 years.General cognitive ability at age 12 years assessed by two verbal and two nonverbal cognitive standardized tests.BMI at age 9 years that was age and sex adjusted using external reference data.R2 in training data) was then entered into the multi-score model. These simple linear regression models were fit and validated in repeated 10-fold cross-validation (see section below for details) using the lm function implemented within the caret R package.25 Based on consistent evidence for extensive genetic correlations across complex traits and disorders, rather than summing up, the predictions of the single-score models were expected to substantially overlap.To estimate the separate prediction of each predictor, we fit a series of simple linear regression models for each of the 81 polygenic scores and each of the 3 outcomes. For each GWAS-outcome combination, three models were run using polygenic scores created with Gaussian mixture weights of 1, 0.1 and 0.01, respectively. The model that explained the most variance in the outcome . We used elastic net regularized regression13 to predict outcomes and by selecting predictors and estimating their contribution to the prediction. Regularized regression models are general linear models that employ strict penalties to prevent overfitting. Elastic net allows for estimating the joint predictive ability of a large number of variables while preventing overfitting. Elastic net uses a linear combination of two regularization techniques, L2 regularization (used in ridge regression) and L1 regularization (used in LASSO (least absolute shrinkage and selection operator)) by simultaneously implementing variable selection  and continuous shrinkage ; and it efficiently deals with multicollinearity by selecting or dropping groups of correlated variables.27Conventional multiple linear regression models in the presence of a large number of predictors are subject to overfitting, and stepwise regression suffers from upward-biased coefficients and In situations where predictors are non-independent or correlated  the elastic net has the advantage of including automatically all the highly correlated variables in the group (grouping effect).28Elastic net overcomes the limitation of LASSO that tends to select one variable from a group of correlated predictors and to ignore the others. R2.Final model coefficients are analogous to a conventional multiple linear regression output that allows for a ranking of predictors by the magnitude of their contribution to predicting the outcome. Overall variance explained by the model is indexed by the coefficient of determination, glmnet R package17 implemented within caret R package25 to conduct a series of linear elastic net regularized regressions and select polygenic predictors leading to an optimized final model for each outcome. Elastic net regularized regression employs two hyperparameters, alpha and lambda.13 As recommended to achieve optimized balance between variance explained and minimum bias, we fit models to tune over both alpha and lambda parameter values in repeated 10-fold cross-validation.29.We used Generally, a predictive model is considered powerful when the model is capable of predicting outcomes in ‘unseen’ data with high accuracy. The performance of a model can therefore be evaluated by testing how well it predicts phenotypes of individuals whose data were not included in the construction of the prediction model.Data splitting. We randomly split the data set into a separate training set and test set .Model training. We used repeated cross-validation on the training set to train and optimize the model via validation.Model testing and comparison. We applied the final model to the independent test set to obtain an unbiased estimate of model performance.Each model described in the preceding section was trained and tested using the following three-step strategy:29 We split the training data randomly into 10 equal-sized subsets, using 9 subsets to train the model and the remaining subset as validation. The cross-validation process was repeated 10 times, with each of the 10 subsamples used once as the validation data.The training set was used to train and validate the model, this included hyperparameter tuning for the elastic net models. In order to optimize the balance between variance explained and minimum bias, we tested each model in 10-fold cross-validation with resampling.31 Therefore, to minimize variation across validation data sets, we repeated the 10-fold cross-validation 100 times with random data set partitions.32Although cross-validation has been shown to produce nearly unbiased estimates of accuracy, variability of these estimates can be reduced by bootstrap methods, wherein available data are repeatedly sampled with replacement in order to mimic the drawing of future random sampling.R2train from the resampling distribution.The optimized or ‘final’ model is chosen based on the largest performance value . Predictors retained within the model and standardized coefficients index whether, and to what extent, they contribute to predicting the outcome. Model performance for the repeated cross-validation in the training set was summarized as mean-cv-R2test. Differences between mean-cv-R2train and R2test provide an index of out-of-sample error.To obtain unbiased estimates of model performance, we used the parameters from the final model obtained from the repeated cross-validation in the training set to predict outcomes  in the independent test set. To index prediction accuracy, we used the coefficient of determination, in the following referred to as H0: MPSR2test=best-single-scoreR2test, we compared the observed diffR2test (MPSR2test – best-single-scoreR2test) against an empirical null distribution of no difference in predictions between the MPS and the best single-score model. We tested the exchangeability of models by randomly selecting either the MPS or the best single-score model to generate predictions. We then calculated the difference in R2 for two models with shuffled predictions. The process was repeated 100 000 times, generating an empirical null distribution of diffR2 under exchangeability of model predictions.We used permutation to test the statistical significance of the difference in predictions between the MPS and the best single-score model. To test the null hypothesis of exchangeability of models, diffR2test value falls outside of those obtained when randomly exchanging models, this represents evidence against the null hypothesis of no difference in prediction between models. The statistical significance, as expressed in an empirical P-value, is calculated as the fraction of permutation values that are at least as extreme as the original diffR2test statistic observed in nonpermuted data.If the null hypothesis of no difference between models is true, it would not matter if we randomly exchange the model used for generating predictions. However, if the observed P=4e−03), 1.1% (P=2e−03) and 1.6% (P=1e−04), respectively.The MPS models showed better prediction in the independent test set than the best single-score models. The best single-score models were the large 2016 GWAS of years of education predicting 9.8% of the variance in educational achievement and 3.6% in general cognitive ability in the test set. For BMI, Obesity class 1 achieved the best single-score prediction, explaining 3.8% of the variance.  suggesting that 88% of the top 10% MPS group had a mean grade above that of the bottom 10% group, and there is an 80% probability that a person picked at random from the top 10% MPS group will have a higher score than a person picked at random from the bottom 10% group.38For cognitive ability, For BMI, We demonstrate that the MPS approach that combines summary-level GWAS data from multiple traits yields better individual-level phenotype prediction than single-score predictor models in independent test data.39 genetic variants associated with ulcerative colitis are not typically included in models estimating individuals’ genetic risk for increased BMI.The observation that a multitude of polygenic scores contribute to trait prediction in the MPS models highlights the complexity of the system being studied and the somewhat arbitrary way we divide it into phenotypic characteristics. We show that polygenic variation associated with traits other than the to-be-predicted outcome contributes to prediction. For instance, although there is a known association between ulcerative colitis and BMI,The predictors selected and coefficients estimated by the MPS models in the current study can be used to generate individual-specific composite estimates of genetic propensities in other and smaller samples. For a more parsimonious replication, future research in other samples could construct a simple multiple regression model using the top five predictors selected by the current analyses. The predictive power of such an MPS model can then be compared with that of the best single-score model. More generally, in addition to the likely improvement in MPS prediction as more and larger GWASs are being published, the MPS approach has the potential to be applied to a wide range of outcomes and samples, including psychiatric and medical outcomes in case–control samples.5 The MPS approach exploits the fact that even GWASs of genetically distantly related traits might contribute predictive power if their power is superior to GWASs of more proximal traits. For instance, most likely because of its much greater sample size, the years of education polygenic score predicted general cognitive ability better than any of the polygenic scores based on GWASs directly measuring general cognitive ability.The predictive power of a polygenic score is not only a function of the genetic correlation between discovery and outcome trait, but also of the statistical power present in the discovery GWAS on which it is based .40 the MPS approach is not suited for investigating etiology. Other methods have been developed to that end. For instance, multivariate twin studies are appropriate for investigating trait etiology, or multi-trait GWAS meta-analysis aims to disentangle effects of correlated traits at the level of genetic variants.45 In contrast, the declared aim of the MPS approach is to maximize trait prediction, without assumptions about the relationships among predictors.Because predictive power of polygenic scores does not simply reflect the genetic correlation between discovery and target trait, but depends on the genetic architecture of both traits and sample size ,The MPS approach will be useful whenever trait prediction is a priority. The primary reason for maximizing predictive power using the MPS approach is to predict phenotypes of individuals with as much accuracy as possible. Individual-specific genetic predictions will be useful in research with modest sample sizes to investigate developmental, multivariate and gene–environment interplay issues. Eventually, MPS models could be useful in both society and science to estimate genetic potential as well as risk in relation to all domains of functioning, including cognitive abilities and disabilities, personality and health and illness.This predictive power will raise concerns about potential early, even prenatal, prediction. It is important to begin discussions that are informed by the empirical data because genotype-based trait prediction is moving towards the point of practical relevance. Although concerns are warranted, these might be outweighed by the benefits that could result from being able to predict problems and potential early and develop stratified preventions and interventions accordingly.


Understanding the mapping precision of genome-wide association studies (GWAS), that is the physical distances between the top associated single-nucleotide polymorphisms (SNPs) and the causal variants, is essential to design fine-mapping experiments for complex traits and diseases.http://cnsgenomics.com/shiny/gwasMP).Using simulations based on whole-genome sequencing (WGS) data from 3642 unrelated individuals of European descent, we show that the association signals at rare causal variants  are very unlikely to be mapped to common variants in GWAS using either WGS data or imputed data and vice versa. We predict that at least 80% of the common variants identified from published GWAS using imputed data are within 33.5 Kbp of the causal variants, a resolution that is comparable with that using WGS data. Mapping precision at these loci will improve with increasing sample sizes of GWAS in the future. For rare variants, the mapping precision of GWAS using WGS data is extremely high, suggesting WGS is an efficient strategy to detect and fine-map rare variants simultaneously. We further assess the mapping precision by linkage disequilibrium between GWAS hits and causal variants and develop an online tool (gwasMP) to query our results with different thresholds of physical distance and/or linkage disequilibrium  contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) facilitated by high-throughput genotyping technologies have identified thousands of genetic loci associated with complex traits and diseases in humans . The cauy) and performed genome-wide association analyses of the simulated phenotype using genotype data from four different genotyping/imputation strategies (see “Methods”): (1) WGS data; (2) SNP-array data imputed to HapMap phase 2  ) and imp nref = 92. Theren) on mapping precision. We demonstrated by simulations under a simple scenario that the probability of causal variant being detected as the top signal in GWAS with sequencing data depends on NCP . This explains why the mapping precision slightly decreased with decreased n or q2 in either WGS or 1KGP-imputed data  using a relatively small sample size , we simulated causal variants of relatively large effect . Given n = 3642 and q2 = 2%, the NCP at any of the simulated causal variants was 74.3, which is approximately equivalent to a setting with n = 250,000 and q2 = 0.03% , suggesting that the conclusions we drew from our simulations can be applied in general to studies at the current scale  and that mapping precision at the known loci will be improved in the future with larger sample sizes. The conclusion has further been supported by evidence from simulations in the HRS dataset with a wider range of sample sizes and NCP  between causal variants and GWAS hits  [http://cnsgenomics.com/shiny/gwasMP).We have shown above results from simulations where the causal variants were randomly sampled from the sequence variants. In reality, however, it might not be the case. It has been suggested in previous studies that trait-associated or disease-associated variants are not randomly distributed but enriched in some functional categories of the genome such as the DNase I hypersensitive sites (DHSs) , 21. We its Fig. . Interes(gwasMP)  for quern = 3642) we were only able to quantify the mapping precision for rare variants with MAF down to 0.0003. For rarer variants, larger population-based cohorts with WGS data are required. Our conclusions were drawn from simulations based on modern SNP arrays with 100,000s SNPs, which cannot be applied to studies based on low-dense markers. It should also be noted that all our results are from analyses in European populations, these results need to be applied with caution to non-European populations (e.g. Asian and African populations), given the substantial differences in LD structure between Europeans and non-Europeans. We also did not simulate a case-control design because the sample size of UK10K-WGS data is not large enough to simulate an ascertained case-control study of sufficiently large sample size for a disease of reasonable prevalence. However, the general conclusions about mapping precision should be applicable to case-control studies because mapping precision is essentially determined by the strength of the association signal, LD structure and imputation precision, rather than the scale of the phenotype. Nevertheless, this needs to be confirmed in the future by simulations of case-control design using large WGS datasets.There are certainly more complicated scenarios  that have not been investigated in our simulations. However, these scenarios are unlikely to be the norm and thus are unlikely to bias our results substantially. With limited sample size of the WGS data  < 3  using PLINK [y = g + e, with g = wu and x is the indicator variable for the genotypes of causal variant , f is the frequency of the coded allele, and u is the effect size per standardized genotype sampled from N. The residual e was generated from N(1/q2 − 1)) with q2 being the proportion of variance in phenotype explained by the causal variant. We performed a GWAS analysis for the simulated trait using the variants from different genotyping strategies (see below for details about the genotyping strategies) and selected the top associated variant that passed a genome-wide significance level . We repeated the simulation to quantify the power at different levels of q2 . Note that the simulations at q2 = 0 quantify the false positive rate. We then repeated the simulation 50,000 times at q2 = 2% to quantify the mapping precision  for common and rare variants, respectively. We further repeated analysis to quantify the mapping precision by sampling causal variants from the DNase I hypersensitive sites (DHSs) to mimic the observation that genetic variants associated with complex traits are enriched in DHSs [We used WGS data from the UK10K project (UK10K-WGS)  for simung PLINK . We chosng PLINK  using al in DHSs .n = 500 and 1000) as the reference panel.We performed simulations to quantify the mapping precision using three different genotyping strategies, i.e. WGS, SNP-array data imputed to HapMap 2 reference panel (HapMap2) , and SNPhttps://imputation.sanger.ac.uk/).To investigate the influence of reference sample size on the mapping precision of GWAS using imputed data, we performed additional analyses using genotyped data from HRS and imputed the genotyped data to HRC. There were 8479 unrelated individuals in HRS genotyped on ~1.7 million SNPs  after QC. We left out 50,000 common and 50,000 rare SNPs as a pool to sample causal variants for simulations and imputed the genotypes of the remaining SNPs to the 1KGP3 and HRC reference panel  respectiAdditional file 1:Figures S1–S19, Tables S1–S4, and Text S1. (PDF 5824 kb)This PDF file contains


P=1 × 10−4) with schizophrenia polygenic risk scores explaining up to 0.12% of the variance in ALS (P=8.4 × 10−7). A modest increase in comorbidity of ALS and schizophrenia is expected given these findings (odds ratio 1.08–1.26) but this would require very large studies to observe epidemiologically. We identify five potential novel ALS-associated loci using conditional false discovery rate analysis. It is likely that shared neurobiological mechanisms between these two disorders will engender novel hypotheses in future preclinical and clinical studies.We have previously shown higher-than-expected rates of schizophrenia in relatives of patients with amyotrophic lateral sclerosis (ALS), suggesting an aetiological relationship between the diseases. Here, we investigate the genetic relationship between ALS and schizophrenia using genome-wide association study data from over 100,000 unique individuals. Using linkage disequilibrium score regression, we estimate the genetic correlation between ALS and schizophrenia to be 14.3% (7.05–21.6;  Relatives of patients with amyotrophic lateral sclerosis have an unexpectedly high incidence of schizophrenia. Here, the authors show a genetic link between the two conditions, suggesting shared neurobiological mechanisms. C9orf72 hexanucleotide repeat expansionAmyotrophic lateral sclerosis (ALS) is a late-onset neurodegenerative condition characterized by progressive loss of upper and lower motor neurons, leading to death from respiratory failure in 70% of patients within 3 years of symptom onset. Although ALS is often described as a primarily motor-system disease, extramotor involvement occurs in up to 50% of cases, with prominent executive and behavioural impairment, and behavioural variant frontotemporal dementia (FTD) in up to 14% of casesALS and schizophrenia both have high heritability estimates 3Recently, methods to investigate overlap between polygenic traits using GWAS data have been developed89hS2) for single traitsρg) for pairs of traits, from which genetic correlation (rg) is estimatedχ2=1.13; all ranges reported below indicate 95% confidence intervals), replicating previous estimates based on alternative methodsTo investigate the polygenic overlap between ALS and schizophrenia, we used individual-level and summary data from GWAS for ALSP=1 × 10−4). Results were similar for a smaller schizophrenia cohort of European ancestry LD score regression estimated the genetic correlation between ALS and schizophrenia to be 14.3%  explained up to 0.12%  of the phenotypic variance in a subset of the individual-level ALS genotype data that had all individuals removed that were known or suspected to be present in the schizophrenia cohort  are per-individual scores based on the sum of alleles associated with one phenotype, weighted by their effect size, measured in an independent target sample of the same or a different phenotypea cohort . ALS casr cohort . Permutar cohort .P=0.94). Assuming a true genetic correlation of 0%, we estimated the required rate of misdiagnosis of ALS as schizophrenia to be 4.86% (2.47–7.13) to obtain the genetic correlation estimate of 14.3%  along with five potential novel loci at cFDR<0.01 . No gene set was significantly enriched (after Bonferroni correction) in genome-wide cFDR values when analysed using MAGENTA.We leveraged the genetic correlation between ALS and schizophrenia to discover novel ALS-associated genomic loci by conditional false discovery rate (cFDR) analysis9C9orf72 hexanucleotide repeat expansion, which is associated with ALS and FTD, and with psychosis in relatives of ALS patientshS2=8.2%) and schizophrenia (hS2=23%) and these estimates do not represent all heritability for both diseases, the accuracy of using schizophrenia-based PRS to predict ALS status in any patient is expected to be low (Nagelkerke's R2=0.12% for PT=0.2), although statistically significant (P=8.4 × 10−7). Nevertheless, the positive genetic correlation of 14.3% indicates that the direction of effect of risk-increasing and protective alleles is consistently aligned between ALS and schizophrenia, suggesting convergent biological mechanisms between the two diseases.There is evolving clinical, epidemiological and biological evidence for an association between ALS and psychotic illness, particularly schizophrenia. Genetic evidence of overlap to date has been based primarily on individual genes showing Mendelian inheritance, in particular the CNTN6 Although phenotypically heterogeneous, both ALS and schizophrenia are clinically recognizable as syndromes23MOBP, C9orf72, TBK1, SARM1 and UNC13A have been described previously in ALS and were associated by cFDR analysis in this study owing to their strong association with ALS through GWASTNIP1, PPP2R2D, NCKAP5L and ZNF295-AS1) are novel associations and may represent pleiotropic disease loci. TNIP1 encodes TNFAIP3 interacting protein 1 and is involved in autoimmunity and tissue homoeostasisPPP2R2D is a regulatory subunit of protein phosphatase 2 and has a role in PI3K-Akt signalling and mitosisNCKAP5L is a homologue of NCKAP5, encoding NAP5, a proline-rich protein that has previously been implicated in schizophrenia, bipolar disorder and autism29ZNF295-AS1 is a noncoding RNANo significantly enriched biological pathway or ontological term was identified within genome-wide cFDR values using MAGENTA. Low inflation in ALS GWAS statistics, coupled with a rare variant genetic architectureOur data suggest that other neuropsychiatric conditions  do not share polygenic risk with ALS. This finding contrasts with our recent observations from family aggregation studies and may be unexpected given the extensive genetic correlation between neuropsychiatric conditionsP=0.94) and we estimated that a misdiagnosis of 4.86% of ALS cases would be required to spuriously observe a genetic correlation of 14.3%, which is not likely to occur in clinical practice. We are therefore confident that this genetic correlation estimate reflects a genuine polygenic overlap between the two diseases and is not a feature of cohort ascertainment, but the possibility of some misdiagnosis in either cohort cannot be entirely excluded based on available data.A potential criticism of this study is that the polygenic overlap between ALS and schizophrenia could be driven by misdiagnosis, particularly in cases of ALS–FTD, which can present in later life as a psychotic illness and could be misdiagnosed as schizophrenia. This is unlikely, as strict diagnostic criteria are required for inclusion of samples in the schizophrenia GWAS datasetA positive genetic correlation between ALS and schizophrenia predicts an excess of patients presenting with both diseases. Most neurologists and psychiatrists, however, will not readily acknowledge that these conditions co-occur frequently. Our genetic correlation estimate confers an odds ratio of 1.17 (1.08–1.26) for harbouring above-threshold liability for ALS given schizophrenia (or vice versa) and a lifetime risk of 1:34,336 for both phenotypes together. Thus, a very large incident cohort of 16,448 ALS patients , with detailed phenotype information, would be required to have sufficient power to detect an excess of schizophrenia within an ALS cohort. Coupled with reduced life expectancy in patients with schizophreniaC9orf72-driven overlapIn conclusion, we have estimated the genetic correlation between ALS and schizophrenia to be 14.3% 7.05–21.6), providing molecular genetic support for our epidemiological observation of psychiatric endophenotypes within ALS kindreds. To our knowledge, this is the first study to show genetic correlation derived from polygenic overlap between neurodegenerative and neuropsychiatric phenotypes. The presence of both apparent monogenic 1.6, provr2>0.25) SNPs in both datasets , with SNPs in high-LD regions removed  in the phase 1 integrated release of the 1,000 Genomes Projectgression .R2) of>0.5 in the first round and a distance of 5,000 kb and LD threshold of >0.2 in the second round) using PLINK v1.90b3y, removing high-LD regions : 5 × 10−8, 5 × 10−7, 5 × 10−6, 5 × 10−5, 5 × 10−4, 5 × 10−3, 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5. A total of 100 principal components (PCs) were generated for the ALS sample using GCTA version 1.24.4. Using R version 3.2.2, a generalized linear model was applied to model the phenotype of individuals in the ALS dataset. PCs that had a significant effect on the phenotype  were selected .We calculated PRS for 10,032 cases and 16,627 healthy controls in the ALS dataset (duplicate and suspected or confirmed related samples with the schizophrenia dataset removed), based on schizophrenia-associated alleles and effect sizes reported in the GWAS summary statistics for 6,843,674 SNPs included in both studies and in the phase 1 integrated release of the 1,000 Genomes Project regions , resultiTo estimate explained variance of PRS on the phenotype, a baseline linear relationship including only sex and significant PCs as variables was modelled first:y is the phenotype in the ALS dataset, α is the intercept of the model with a slope β for each variable x.where PT was calculated:Subsequently, a linear model including polygenic scores for each schizophrenia R2 value was obtained for every model and the baseline Nagelkerke R2 value was subtracted, resulting in a Δ explained variance that describes the contribution of schizophrenia-based PRS to the phenotype in the ALS dataset. PRS analysis was also performed in permuted case–control data  to assess whether the increased Δ explained variance was a true signal associated with phenotype. Δ explained variances and P-values were averaged across permutation analyses.A Nagelkerke To ensure we did not over- or under-correct for population effects in our model, we tested the inclusion of up to a total of 30 PCs in the model, starting with the PC with the most significant effect on the ALS phenotype . IncreasPT for which we obtained the highest Δ explained variance (0.2), we subdivided observed schizophrenia-based PRS in the ALS cohort into deciles and calculated the odds ratio for being an ALS case in each decile compared to the first decile using a similar generalized linear model:For the schizophrenia Odds ratios and 95% confidence intervals for ALS were derived by calculating the exponential function of the beta estimate of the model for each of the deciles 2–10.M of FTD–ALS as schizophrenia that would lead to the observed genetic correlation estimate as C/(C+1), where C=ρgNSCZ/NALS and NSCZ and NALS are the number of cases in the schizophrenia and ALS datasets, respectivelyTo distinguish the contribution of misdiagnosis from true genetic pleiotropy we used BUHMBOXTo investigate the expected comorbidity of ALS and schizophrenia given the observed genetic correlation, we modelled the distribution in liability for ALS and schizophrenia as a bivariate normal distribution with the liability-scale covariance determined by LD score regression . LifetimP-values for ALS mixed linear model summary statistics calculated in a dataset excluding Finnish and German cohorts (in which suspected control overlap could not be determined), but including all other overlapping samples . To correct for the relationship between LD and GWAS test statistics, schizophrenia summary statistics were residualized on LD score by subtracting the product of each SNP's LD score and the univariate LD score regression coefficient for schizophrenia. cFDR values conditioned on these residualized schizophrenia GWAS P-values were calculated for mixed linear model association statistics calculated at 6,843,670 SNPs genotyped in 10,147 ALS cases and 22,094 controls. Pleiotropic genomic loci were considered statistically significant if cFDR<0.01  in the complete ALS dataset. Associated cFDR genomic regions were then mapped to the locations of known RefSeq transcripts in human genome build GRCh37. Genome-wide cFDR values were also tested for enrichment in 9,711 gene sets included in the MAGENTA software package  and derived from databases such as Gene Ontology , Kyoto Encyclopedia of Genes and Genomes , Protein ANalysis THrough Evolutionary Relationships  and INGENUITY (http://www.ingenuity.com/). SNPs were mapped to genes including 20 kb up- and downstream regions to include regulatory elements. The enrichment cutoff applied in our analysis was based on the 95th percentile of gene scores for all genes in the genome. The null distribution of gene scores for each gene set was based on 10,000 randomly sampled gene sets with equal size. MAGENTA uses a Mann–Whitney rank-sum test to assess gene-set enrichmentUsing an adapted cFDR methodAll data used in this study are publically available and can be accessed via the studies cited in the text. Other data are available from the authors upon reasonable request.How to cite this article: McLaughlin, R. L. et al. Genetic correlation between amyotrophic lateral sclerosis and schizophrenia. Nat. Commun. 8, 14774 doi: 10.1038/ncomms14774 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figures, Supplementary Tables, Supplementary Notes, Supplementary Methods, and Supplementary References


Both strategies may be under genetic control and could thus be targeted for genetic improvement. Although there is evidence that supports a genetic basis for resistance to porcine reproductive and respiratory syndrome (PRRS), it is not known whether pigs also differ genetically in tolerance. We determined to what extent pigs that have been shown to vary genetically in resistance to PRRS also exhibit genetic variation in tolerance. Multi-trait linear mixed models and random regression sire models were fitted to PRRS Host Genetics Consortium data from 1320 weaned pigs (offspring of 54 sires) that were experimentally infected with a virulent strain of PRRS virus to obtain genetic parameter estimates for resistance and tolerance. Resistance was defined as the inverse of within-host viral load (VL) from 0 to 21  helped resolve this statistical confounding and indicated that genetic variation in tolerance to PRRS may exist if genetic correlations between ADG0 and ADG21 or ADG42 are low to moderate.Multi-trait analysis of ADG associated with either low or high VL was not indicative of genetic variation in tolerance. Similarly, random regression models for ADGEvidence for genetic variation in tolerance of pigs to PRRS was weak when based on data from infected piglets only. However, simulations indicated that genetic variance in tolerance may exist and could be detected if comparable data on uninfected relatives were available. In conclusion, of the two defense strategies, genetics of tolerance is more difficult to elucidate than genetics of resistance.The online version of this article (doi:10.1186/s12711-017-0312-7) contains supplementary material, which is available to authorized users. Infectious challenges in domestic livestock do not only raise health and welfare concerns, but also have detrimental effects on livestock production. The impact of infections on an animal’s productive performance is controlled by two alternative  host traits that may be amenable to genetic improvement: resistance and tolerance. Resistance is defined as the ability of a host to prevent pathogen entry or inhibit replication of the pathogen, whereas tolerance refers to the ability of a host to limit the impact of infection on health or performance without interfering with the pathogen life-cycle per se . Thus, aPorcine reproductive and respiratory syndrome (PRRS) is an endemic virus, which causes one of the most devastating swine diseases worldwide. PRRS causes considerable reduction in the growth rate of piglets, with estimates ranging from 10 to 20%, depending on pig breed and virus strain , and resResistance can be measured as the inverse of within-host pathogen load, whereas tolerance is related to the degree to which performance is reduced by infectious pathogens. Tolerance is mathematically defined as a reaction-norm of performance with respect to pathogen load , 14. AssThe main aim of this study was to determine whether pigs that were previously found to differ genetically in resistance to a virulent strain of PRRSV also differ genetically in tolerance. Furthermore, by augmenting the data with simulated data, novel insights into data requirements to accurately estimate genetic variance in tolerance using random regression models were obtained.Data were provided by the PRRS Host Genetics Consortium (PHGC) from nine different PRRSV challenge trials with an identical infection protocol , 10, whiMycoplasma hyopneumoniae, and swine influenza virus. Pigs were randomly placed in pens of 10 to 15 individuals. Following a 7-day acclimation period, pigs between 17 and 32 days of age were experimentally infected both intramuscularly and intranasally with 105 (TCID50) of NVSL-97-7985, a highly virulent PRRSV isolate [All experimental protocols for these trials were approved by the Kansas State University Institutional Animal Care and Use Committee. In each trial, approximately 200 commercial crossbred piglets were transferred from high health farms at weaning age  to a research facility at Kansas State University. The source farms were controlled and found to be free of PRRSV,  isolate . Body we10-transformed qPCR viremia, as described in Boddicker et al. [10-transformed viremia measures to smooth the data and to obtain continuous viremia estimates over the 42-day observation period [Serum viremia, which was measured by using a semi-quantitative TaqMan PCR assay for PRRSV RNA, provided repeated  measures for logr et al. , 13, 20.n period . As outln period , the uniAcross all trials, 198 pigs died before 42 dpi. PRRS was identified as the primary cause of mortality, except for trial 6, for which mortality was higher (46% by 42 dpi) and was potentially caused by secondary bacterial infections . These pOnly offspring from sires with more than 10 progeny with phenotypes were considered in this study to reduce the risk of bias in tolerance estimates . As suchPedigree information and genomic information using genotypes from Illumina’s Porcine SNP60 Beadchip v.1 , was avaReml 3.0  using thn method , and incn method . The \do42 represents the cumulative log-transformed viral load from 0 to 42 dpi from the Wood’s curve. Since viremia had decreased to undetectable levels within 21 to 28 dpi for a large proportion of pigs, cumulative viral load (and thus resistance) was not only calculated for the entire observation period from 0 to 42 dpi, but also for the period from 0 to 21 dpi. This represents the acute phase of infection and yields two indicator traits for resistance (VL21 and VL42).Resistance is often quantified by a measure of within-host pathogen load, whereby lower pathogen load reflects higher host resistance , 5, 16. 21 or ADG42 on the y-axis) on pathogen load . The regression of ADG42 on VL21 was also evaluated to account for the possibility of a time-lag in growth response with respect to changes in pathogen load.In this study, tolerance was assessed by regressing performance measures , commonly denoted in the tolerance literature as vigor , constit0) was included as a fixed covariate in the corresponding statistical models to partially account for differences in vigor. (2) To gain better insight into data requirements for accurately estimating genetic parameters for tolerance, and about how these estimates depend on the genetic relationship between growth in absence or presence of infection, growth records of infected pigs were augmented with simulated growth records of non-infected half-siblings, as outlined in step 4 below.Two approaches were adopted to overcome this lack of performance measures without infection. 1) In line with the standard approach of quantitative genetic studies of reaction-norms, the origin of the explanatory variable VL was shifted to the mean VL; this ‘shifted intercept’ for ADG is referred to as the ‘level’, in contrast to vigor , 26, 27  In line 210 or ADG420), with increasing simulated genetic correlation from weak to strong between ADG210 and ADG21 or ADG420 and ADG42, respectively. The random regression models from Step 3 were adapted to include variation in ADG210 or ADG420.All statistical analyses were carried out using ASReml 3.0 . Random 0) , respectively. The fixed and random effects of this model were identical to those used in model (1), with exception of The trivariate model (1) from step 1 does not show how growth changes with respect to viral load, and, therefore, does not account for genetic variance in tolerance. A multi-trait sire model for ADG of progeny with categorized VL was used to assess sire-by-VL interactions to get a first indication of whether sires varied genetically in tolerance to infection. If these genetic correlations are less than 1, this is indicative of sire rank changes when offspring are faced with low and high VL respectively, and provides evidence for genetic variation in tolerance slope. Hence, individuals were sorted according to their VL from 0 to 21 dpi or 0 to 42 dpi, and partitioned into VL groups, where the low and high VL groups (n = 330 each) consisted of individuals with VL values in the lower and upper quartiles, respectively, and the mid-range group consisted of the middle half of the data (n = 660). A trivariate sire model was then fitted to measures of ADG associated with low, mid and high VL from 0 to 21/0 to 42 dpi  rather than vigor (ADG at zero VL). The following linear random regression sire model (RRM) for ADG on centered values of VL, which will be referred to as the level-slope model  , 33.210 or ADG420) was simulated for one hypothetical paternal half-sib for each individual with ADG21 and ADG42 records, respectively, thus doubling the size of the dataset. Data were simulated assuming a heritability of 0.4 for both ADG210 and ADG420 [g between the traits would imply less genetic variance in tolerance, low (0.05), moderate (0.30), strong (0.60) or high (0.90) genetic correlations (rg) between ADG210 and ADG21, or ADG420 and ADG42, respectively, were simulated , except that no fixed effects or random pen or litter effects were fitted for the simulated half-sibs. Thus, by including simulated data of non-infected pigs, model (2) was replaced by an intercept-slope model, with genetic variance estimated for growth in the absence of infection, and for tolerance slope.The random regression models (2) were then applied to the extended datasets for each replicate, where the response vector As in Step 3, hierarchical models were fitted (a) without any additive genetic effects for intercept or slope , and with low growth rate in spite of low VL (ADG−VL−) may be indicative of phenotypic variation in tolerance.Figure Growth rate under infection and resistance were moderately heritable and had large standard errors Table . Heritabp < 0.001, based on the LRT that compares models with and without genetic correlations fixed to 1), indicating that not all genetic variation of growth under infection was explained by genetic differences in resistance (inverse of VL)  Table . Furtherns Table . Phenoty21 and ADG42, respectively. Genetic correlations significantly less than 1 would imply that growth rates associated with different degrees of infection severity, as indicated by low versus high VL, are genetically distinct traits and would thus be indicative of genetic variation in tolerance  and 4.56E−03 (1.81E03) for 0 to 21 dpi, and 3.46E−03 (1.24E−03) and 6.89E−03 (2.18E−03) for 0 to 42 dpi, respectively). Referring to the expectations outlined in Fig. Trivariate models for growth at low, mid and high VL failed to converge for both time periods of infection. Using bivariate models for the upper and lower quartiles for VL, high genetic correlations of 0.94 0.18) and 0.91 (0.13) between growth associated with low to high VL were identified for ADG8 and 0.9p < 0.0001), with a population average tolerance slope estimate of −2.78E−03 (3.32E−04) and −1.28E−03 (1.51E−04) kg/day per unit of VL increase for ADG21 regressed on VL21 and ADG42 on VL42, respectively. This corresponds to an average growth rate difference of 213 and 190 g/day between pigs with the lowest and highest observed VL for the 21- and 42-day observation period, respectively, or differences in body weight of 4.5 and 8.0 kg over the 21- and 42-day observation periods, respectively. Similarly, body weight prior to infection had a significant association with ADG post infection (BW0p < 0.0001), with a positive regression coefficient of 0.025 (0.002) at 21 dpi and of 0.029 (0.003) at 42 dpi.Univariate random regression models without genetic effects, but including VL as a fixed linear  covariate were used to test the average association between growth and VL (null model in Table p < 0.0001) (Table p > 0.60) and resulted in negligibly small slope variance estimates.The log-likelihood of the model improved significantly when genetic effects (random sire effects) were included in the model (level model) 1) Table . This in Table . p < 0.0001). However, the level-slope model did not provide a significantly better fit than the level-only model for either 0 to 21 and 42 dpi  , regardless of the simulated genetic correlation between ADG210 and ADG21 or ADG420 and ADG42. However, the intercept-slope model consistently provided a significantly superior fit over the intercept-only model only when the simulated genetic correlation between growth in absence of infection and growth under infection was low to moderate (Table p < 0.05)  and its ability to limit the impact of infection (tolerance). The extensive PHGC dataset has identified substantial genetic variation in resistance of growing pigs to PRRS and led to the discovery of a major quantitative trait locus associated with both resistance and growth of pigs under infection , 13, 20.Focusing on data from infected pigs alone, genetic correlations between body weight prior to infection, resistance (inverse of VL) and growth under infection were found to be moderately strong and positive, in line with previous studies , 20. ThiHowever, closer inspection of the underlying data structure raised suspicion that genetic variance in the reaction norm level absorbed genetic variance in tolerance due to confounding between level and slope in these data . To disentangle the genetic variance in reaction-norm intercepts (i.e. growth rate in the absence of infection) and slopes (i.e. tolerance), the experimental data were augmented with simulated growth rates of non-infected relatives. Thus, the resulting data structure mimicked that of ‘sib challenge tests’ that are common practice in aquaculture and other livestock species –37. The Here, the conventional reaction-norm approach was adopted to model genetic variation in tolerance to infections , 38. Usip = 0.981 and 0.081 for the 0 to 21 and 0 to 42 dpi time periods, respectively).As is common practice for quantitative genetics models using REML, the likelihood ratio test (LRT) was used to test the significance of random effects such as the sire tolerance slope estimates, and whether genetic correlations differed significantly from 1 . For var42 values ranged between 88 and 236 AUC in our study), with no values close to 0. To better accommodate the distribution of the data in the models, the VL was centered at the mean VL value, in line with common practice in the animal breeding literature [Perhaps most importantly, reaction-norms require considerable variation in the independent variable to generate unbiased tolerance slope estimates . Howeverterature , 27, 30.Considering all these effects combined, the weak evidence for significant genetic variation in tolerance to PRRS from the random regression models in this study may simply reflect a lack of statistical power to disentangle sire effects on regression slope and level. The complementary simulation studies presented here, which assumed that additional performance measures of related uninfected individuals were available, demonstrated one way of increasing statistical power. Similarly, it might be possible to increase statistical power by harnessing information from repeated measures of growth and pathogen load for each individual over the course of infection in the statistical models. By increasing the range of distribution of VL for each individual, a more robust slope may be fitted through the centre of the data, alluding to an “overall” picture of tolerance across multiple time-points in infection.Genetic improvement of tolerance may have several advantages over improving resistance. Firstly, host resistance limits pathogen replication within the host and, as a consequence, selection for host resistance may impose selection advantages on pathogen strains that can overcome host resistance mechanisms and eventually result in a loss of selection advantage of the host , 41. GivSecondly, it has been suggested that improving host tolerance may offer cross-protection against other strains of the virus, or other prevalent infectious agents, as tolerance mechanisms primarily target host-intrinsic damage prevention or repair mechanisms, compared to resistance mechanisms, which interfere directly with the pathogen life-cycle , 5, 43. Obtaining reliable tolerance estimates from natural disease outbreaks is extremely difficult due to the myriad of confounding factors , which can severely bias tolerance estimates and mask the underlying genetic signal , 18. ForCollecting equivalent performance records of non-infected relatives of the challenged individuals would be extremely valuable to establish the relationship between tolerance and performance in the absence of infection, and identify shared or distinct genomic regions associated with these traits. A strong genetic correlation between these traits would imply that one could select for high performance at the nucleus to improve tolerance and performance in the more infectious commercial farms. In the current pig breeding structure, a direct data pipeline of performance measures between pigs in commercial farms experiencing disease outbreaks and those of related selection candidates in the almost pathogen free nucleus may be useful. Obtaining unbiased and comparable measures of within-host pathogen load from natural disease outbreaks constitutes the main challenge for producing reliable tolerance estimates from natural disease outbreaks . A pract21), also confers greater tolerance. Valuable insights about these interactions could be harnessed from the available longitudinal measures of pathogen burden and growth, e.g. by following the infection trajectories of individuals and target entire trajectories rather than resistance or tolerance for genetic improvement [Based on resource-allocation theory and earlier findings, resistance and tolerance are conventionally considered as alternative host defense mechanisms to infections, leading to the notion of a trade-off between improving resistance and tolerance. Indeed, a companion genome-wide association study on the same PHGC data found different regions that were associated with tolerance and with resistance . Emerginrovement , 56.In order to target both resistance and tolerance in a sustainable breeding program, the epidemiological and evolutionary consequences of genetic selection in either or both traits combined must be studied in more detail. In particular, it needs to be determined whether evolutionary theory predicts a lower risk of pathogen evolution from selection for improved host tolerance rather than resistance hold in the case of PRRS; and to what extent genetically more resistant or tolerant pigs are also less infectious , 57, 58.Using evidence from the available data alone suggests that growing piglets differ genetically in resistance but does not explicitly show evidence for genetic differences in tolerance to PRRSV infection. However, statistical constraints may have masked genetic variation in tolerance. Currently, unknown genetic correlations between performance under and in absence of PRRSV infection could reveal significant genetic variance in tolerance. Future studies are warranted to validate the results in this study for infections with the same and different strains of the PRRS virus, including vaccine strains. This study shows that genetics of tolerance is more difficult to analyze than genetics of resistance, and is therefore more difficult to target in genetic improvement.


Large-scale sequencing studies often measure many related phenotypes in addition to the genetic variants. Joint analysis of multiple phenotypes in genetic association studies may increase power to detect disease-associated loci.We apply a recently developed multivariate rare-variant association test to the Genetic Analysis Workshop 19 data in order to test associations between genetic variants and multiple blood pressure phenotypes simultaneously. We also compare this multivariate test with a widely used univariate test that analyzes phenotypes separately.p values than the univariate test.The multivariate test identified 2 genetic variants that have been previously reported as associated with hypertension or coronary artery disease. In addition, our region-based analyses also show that the multivariate test tends to give smaller Hence, the multivariate test has potential to improve test power, especially when multiple phenotypes are correlated. In many clinical or epidemiological studies, multiple measures of related traits, that is, a multivariate phenotype, are collected. For example, in the Genetic Analysis Workshop 19 (GAW19) data , 3—or byVarious methods for assessing associations between a single genetic variant and multiple traits jointly have been developed (summarized in Yang and Wang ). HoweveRecently, Sun et al.  proposedi, K correlated phenotypes, v SNPs, m covariates, Here we briefly summarize the MURAT method, which is described in more detail in Sun et al. . SupposeK phenotypes are associated with genotype and covariates jointly by using a multivariate linear model, β, in the above multivariate model is assumed to be normally distributed, j, but the effects of different variants are uncorrelated, so that j and variant j’. A score type statistic is derived for MURAT to test whether β equals zero. With a data-adaptive procedure to manage unknown correlations among variant effects, p values analytically, and hence is fast enough to be used for a genome-wide analysis.For MURAT, however, In this study, we focused on the 1943 unrelated Mexican American samples provided by GAW19, and considered 2 phenotypes, systolic blood pressure (SBP) and diastolic blood pressure (DBP). Age and sex were used as covariates. After removing subjects who have one or both missing phenotypes, a total of 1851 individuals were considered in the analysis. We applied a log transformation to SBP and DBP so as to eliminate skewness; the correlation between log SBP and log DBP was 0.542.Although MURAT and SKAT were designed for region-based rare-variant association studies, they can also be used for single-variant tests. Hence, we selected all exomic variants of the odd-numbered chromosomes provided by GAW19. However, because a lot of these variants are very rare, possibly observed only once or twice, we restricted analysis to only the variants that had 4 or more carriers. As a consequence, a total of 152,337 single-nucleotide polymorphisms (SNPs) were included. Missing genotype values were imputed by the corresponding variant MAFs so that the MAFs didn’t change after imputation.hg19 reference as the annotation file (see https://www.cog-genomics.org/static/bin/plink/glist-hg19) to obtain gene start and gene end positions to define gene-based regions, and then implemented MURAT and SKAT for each gene. In total, 10,886 genes that contain variants in the unrelated GAW19 genotype data were included in the analysis. We also analyzed the GAW19 data using a series of non-overlapping windows of 30 kb, spanning all provided SNPs, which yielded 13,094 windows, and applied MURAT and SKAT to these mutually exclusive regions. Moreover, we performed a focused comparison of MURAT with SKAT for 15 genes that have been reported as associated with hypertension at p < 1.0 −5 according to the National Institutes of Health (NIH) Genome-Wide Association Studies (GWAS) catalog [To explore the performance of MURAT as a region-based test, we also applied it to various predefined variant sets. We first used the mentclasspt{minimap<0.05/152,337=3.28 −7 would be needed. There were 4 SNPs where MURAT’s p value met this level of significance. However, this threshold is likely to be conservative as it assumes independence of all tests. Therefore, Table p values less than 10−6 obtained by either SKAT or MURAT. The MURAT p values are smaller than either of the two SKAT p values at 7 of the 8 SNPs in Table For single-variant tests, to adjust for multiple testing, a Bonferroni-corrected threshold, p values obtained from applying MURAT and SKAT to 10,866 genes are plotted in Fig. p values are shown. Figure p values tend to be smaller than the adjusted SKAT p values. In addition, in Fig. p values obtained from both MURAT and SKAT follow the expected distribution under the null, we can draw the conclusion from Fig. p<4.6 −6 but no genes met this threshold. Using a more liberal threshold of p<10−4, Table −6, or a more liberal threshold of p<10−5.The region-based entclass1pt{minimaFigure In this study, we investigated the performance of a joint analysis of multiple phenotypes for genetic association studies by applying MURAT, a novel region-based multivariate test for rare variants, to the GAW19 unrelated samples. The results show that when multiple phenotypes are correlated, the multivariate test can be more powerful than the univariate test.For the most significant SNPs listed in Table CYP4A22, which was previously reported to be associated with essential hypertension [APOC4, which is associated with coronary artery disease [Some of the SNPs in Table rtension , 14. Sim disease . Compari disease , 17, andHence, power for region-based tests should be best when there are many causal variants. To investigate power of this multivariate test in a situation where associations are likely to be real, we focused on 15 known hypertension associated genes (occurring on odd-numbered chromosomes). Figure We have shown  that comThe new multivariate rare variant test MURAT demonstrated interesting results in joint analysis of systolic and diastolic blood pressure phenotypes in GAW19 unrelated individuals, and identified some loci that are plausible candidates for association with hypertension.