Gallus gallus) genomes and to the assessment of inter-dependencies between gene expression, methylation, and copy-number-variants in data from breast cancer tumors from humans (Homo sapiens). Our analyses reveal that in chicken breeding populations ~50,000 evenly-spaced SNPs are enough to fully capture the span of whole-genome-sequencing genomes. In the study of multi-omic breast cancer data, we found that the span of copy-number-variants can be fully explained using either methylation or gene expression data and that roughly 74% of the variance in gene expression can be predicted from methylation data.Modern genomic data sets often involve multiple data-layers , each of which itself can be high-dimensional. The biological processes underlying these data-layers can lead to intricate multivariate association patterns. We propose and evaluate two methods to determine the proportion of variance of an output data set that can be explained by an input data set when both data panels are high dimensional. Our approach uses random-effects models to estimate the proportion of variance of vectors in the linear span of the output set that can be explained by regression on the input set. We consider a method based on an orthogonal basis (Eigen-ANOVA) and one that uses random vectors  in the linear span of the output set. Using simulations, we show that the MC-ANOVA method gave nearly unbiased estimates. Estimates produced by Eigen-ANOVA were also nearly unbiased, except when the shared variance was very high . We demonstrate the potential insight that can be obtained from the use of MC-ANOVA and Eigen-ANOVA by applying these two methods to the study of multi-locus linkage disequilibrium in chicken ( Modern genomic data often combine information from multiple data-layers, each of which itself can be high-dimensional. Examples of this include data sets comprising of information from several omics, or those combining genomic information with high-throughput phenotyping . The biological processes underlying each of the data-layers can induce complex dependencies between features within each layer  as well as between layers . The main goal of this study is to develop and to evaluate methods to quantify multivariate-associations in settings in which both the input and output sets are high dimensional.The methods proposed in this study can be used to answer ubiquitous questions such as: How much of the inter-individual differences in whole-genome sequence genotypes can be predicted using a low-density SNP array? What proportion of variance in GE can be explained by differences in DNA methylation (ME)? How much of the variance in image-derived phenotypes can be predicted from DNA genotypes?Canonical Correlation Analysis , MultivX) that is explained by another set (W) is not equal to the reciprocal . Many multi-layered data sets are not expected to have a symmetric variance-decomposition .Canonical Correlation Analysis extends the concept of the correlation between two random variables to a multivariate context. However, correlation is symmetric by nature. Therefore, CCA cannot address questions regarding the proportion of variance explained when the proportion of variance of one set  is often) and model complexity . Thus, in cases where p>>n, optimal prediction accuracy may be achieved with a highly parsimonious model  that can produce severely biased estimates of effects. Therefore, to overcome the limitations of existing methods, in this study, we developed and evaluated approaches for estimating the proportion of variance explained when both the input and output sets are high-dimensional.Reduced-rank regressions  and penaWe developed two methods that use random-effects models to estimate the proportion of variance of independent vectors in the linear span of an output layer that can be explained by regression on an input layer. We considered two approaches for generating a sequence of independent vectors in the linear span of the output layer: A Monte Carlo method (MC-ANOVA) which uses random vectors, and one based on eigenvectors (Eigen-ANOVA).Xn×p and Wn×q, holding data for n individuals (rows) and p (X) and q (W) features in columns, respectively. For instance, X may be a matrix with genotype codes at p SNPs and W may be a matrix providing GE levels assessed at q genes. The columns of X = {x1,x2,…,xp} and of W = {w1,w2,…,wq} can be viewed as axes spanning two linear spaces . The linear spans (extensions to nonlinear settings will be addressed in the discussion) of X and W consist of all the vectors that can be obtained by forming linear combinations of the columns of each of these sets, that is αs = {αs1,…,αsp} and δs = {δs1,…,δsq}. In the following, we will use W as the input set and X as the output set; however, the methods proposed are not symmetric and additional knowledge can be gained by switching the roles of X and W.Consider a data set consisting of two numeric matrices, xs∈LX, one can estimate the proportion of variance that can be explained by linear regression on LW using a model of the formFor each vector q is large, the proportion of variance of xs that can be explained by regression on LXβ and ε as Gaussian independent random variables, X , as sucLX (xs) that can be explained by regression on W. Next, we generalize the idea to all vectors in LX. However, LX contains an infinite number of vectors; therefore, some approximation is needed. Perhaps the most natural approach for estimating the proportion of variance of vectors in LX that can be explained by regression on LW is to regress each of the columns of X on W. Such an analysis would produce a sequence of R2 estimates 2, X that could be explained by regression on W. However, one limitation of this approach is that the columns of X are not necessarily independent. Many features may cluster  leading to groups of highly unbalanced sizes. When some features are highly-correlated, the simple average of individual R2-values may be driven by a few clusters of the columns of X. Furthermore, when X is ultra-high dimensional  estimating s = 1,…,p) one-feature-at-a-time will be computationally challenging. Therefore, to address these problems, we propose two methods that use independent vectors from the span of the output set; each of these methods are explained next.In the preceding paragraph we describe how one can estimate the proportion of variance of a vector in LX is infinite, one cannot estimate LX. However, one can ‘explore’ the linear span of the output set by generating random vectors in LX of the form xs = Xαs, where αs is sampled from some distribution. This can be repeated for a large number of vectors in LX to produce a sequence of estimates αs and αs′ are independent, so are xs and xs′. Indeed, noting that X is not random and assuming that αs and αs′ are sampled independently, we have that xs and xs′ are independent.Since αs from a proper multivariate distribution.Draw a random vector xs = Xαs.Form the linear combination xsEstimate the proportion of variance of pression ) with vaB times .Repeat 1–3 Use the sequence of estimated R-squared αs are generated; for this aspect of the algorihtm there are countless possibilities: weights can be sampled from distributions with continuous support  or from mixture models with a point of mass at zero. The weights may be independent or correlated, and the distributions may be symmetric or skewed. We will show later on (using data from chicken genomes) that the process used to generate the weights may affect some features of the distribution of the R2 values, albeit not necessarily the mean or the median R2. The possibility of using different processes for generating random vectors in LX gives the MC-ANOVA a great deal of flexibility. For example, this method could be used to assess how the distribution of the proportion of variance explained may change for different trait architectures–we will further explore that flexibility in greater detail in one of the case studies presented below.In X can be obtained from the singular-value decomposition of UX and VX are the left- and right-singular vectors of X respectively, and DX is a diagonal matrix with the singular values of X in the diagonal. Both UX and VX are orthonormal, thus LX can be represented as a linear combination of the left-singular vectors of X. Therefore, our second method estimates the proportion of variance of each of the left-singular vectors of X that can be explained by regression on W, and produces a global R2 estimate using a weighted sum of the R2 estimated for each singular vector .An orthogonal basis for the row-space of LX; for instance, compute the singular-value decomposition of X respectively, and DX = Diag{di} is a diagonal matrix with the singular values of X in its diagonal .Generate an orthogonal basis for LW using a linear model such as that in expression [ui = xs, and estimate the proportion of variance of each vector that can be explained by regression on LW, Regress each of the left-singular vectors on pression  with ui LX that can be explained by regression on LW using Estimate the global proportion of variance of vectors in Triticum) genotype data set generated by the International Maize and Wheat Improvement Center (CIMMYT) which contains genotypes at 1,279 DNA-markers assessed in 599 wheat inbred lines –a methon. The vectors in the linear span of the genotypes can be thought as ‘breeding values’ formed as linear combinations of genotypes.We note here that while a genotype matrix contains strictly discrete values  the linear span of it includes vectors in Rfirst simulation setting, W599×1,279 was the genotype matrix and X599×1,279 was obtained by adding iid  Gaussian noise to the genotype matrix. We tuned the variance of the noise to generate scenarios of the proportion of variance of X explained by W ranging from 0 (X was pure noise) to 1 (X = W). For each simulated data set we then estimated the proportion of variance of X explained by regression of W using random-effects models, with variance parameters estimated using REML [In our X explained by W without any noticeable bias (Table 1). However, the regression of the left-singular vectors of X on W in Eigen-ANOVA produced estimates that were downwardly biased in case the true proportion of variance of X explained by W was large . Further inspection of the results for individual MC replicates suggested that the bias of the Eigen-ANOVA method was likely due to a relatively large number of ‘corner’ solutions (zero estimated proportion of variance) which were common for high-order eigenvectors –we illustrate this in an analysis of multi-omic cancer data further below. The use of PLS led to a downwardly bias estimates in cases where the proportion of variance of X explained by W was low  and an upwardly biased estimates when proportion of variance explained was high .The Monte Carlo method estimated the proportion of variance of second simulation setting to contemplate cases involving asymmetric proportion of variance explained. To achieve this, we formed X using a subset of the wheat marker genotypes  and formed W by binding the columns of X with additional columns filled with iid Gaussian noise (Z), that is W599×1,279 = [Xp599×, Zp)599×. The columns of X and W were centered and scaled to unit variance; therefore the share of the variance of W explained by X (X explained by W (X is included in W.We then considered a Table 2). However, the Eigen-ANOVA method and the PLS produced noticeable biases, with Eigen-ANOVA method again generating downwardly biased estimates in cases where the true proportion of variance explained was high, and the PLS generating downwardly (upwardly) biased estimates whenever the true proportion of variance was low (high).In our second simulation study, the MC-ANOVA method rendered nearly unbiased estimates of the proportion of variance of one set explained by the other  genomes derived from a combination of whole-genome sequencing (WGS) and imputation. We used this data set to assess the proportion of variance of UHD genotypes that can be captured and predicted using low-density SNP sets. The second data set involved three omic-layers  of human (Homo sapiens) female breast cancer patients. We used this data set to assess the proportion of variance at one omic that can be explained by another omic.We used the MC-ANOVA and Eigen-ANOVA to quantify the proportion of variance explained in two experimental data sets. The first one contains a set of ultra-high-density (UHD) SNPs from chicken  the information contained in UHD SNP genotypes? We used the MC- and Eigen-ANOVA methods to address precisely this question.The continued reduction of genotyping and sequencing costs has led to a sustained increase in the number of loci that can be genotyped. In plant and animal breeding four typical genotyping options include customized low-density arrays with hundreds to a few thousand SNPs , commercData consisted of 1.79 million SNP-genotypes for 892  chickens from six generations of a purebred commercial brown layer line of Lohmann Tierzucht GmbH. These genotypes originated from a combination of whole-genome sequencing of 25 layers and imputation to UHD of the genomes of 867 that were genotyped a high density  Affymetrix Axiom Chicken Genotyping Array . FurtherLX) spanned by the UHD SNP genotypes. The input set, (LW), consisted of low-density genotypes obtained by selecting p  evenly-spaced (in variant counts) SNPs. We estimated the proportion of variance captured by low-density panels using the MC- and Eigen-ANOVA methods. For the MC method we sampled weights from iid standard normal distribution, LX using xs = Xαs, where X is the matrix of UHD SNP-genotypes. These random vectors were then regressed on the lower-density SNP sets, and the proportion of variance explained was estimated using REML. This was repeated 1,000 times to estimate the distribution of the proportion of variance of vectors in LX explained by each of the low-density SNP-sets. For the Eigen-ANOVA method, we regressed each of the left-singular vectors of the UHD SNP genotypes on the low-density panels.In a first analysis, the output space was the linear space . The proportion of variance of the UHD SNPs explained by low-density panels increased with the number of SNPs in the low-density panels reaching 100% with p> = 10K SNPs. The variance in the proportion of variance captured by low-density panels also decreased with the number of SNPs in the array . Small sample size and small effective population size are further factors that may make 10K SNPs to be sufficient to achieve a very high R-sq.According to the MC-ANOVA method, the panel containing 500 evenly-spaced SNPs captured about two-thirds of the variance spanned by the UHD SNP genotypes  of R2, the Eigen-ANOVA only yields the point-estimates which are shown in Fig 1.)The Eigen-ANOVA yielded a very similar estimate of the proportion of variance explained as the MC-ANOVA for X contains whole-genome sequence genomes, one can think of the random vectors in LX (xs = Xαs) as additive-genetic traits and of the MC method as exploring many possible of such traits. However, for any trait, the vast majority of variants in the genome are expected to have no effect. The number of variants affecting any trait could vary from very few (simple traits) to hundreds or thousands (complex traits). Therefore, to explore the effect of the trait architecture on the distribution of the proportion of genetic variance of those traits that could be captured by low-density SNP panels, we repeated the previous analyses using random vectors that had 5,10,50,500 non-zero weights–the set of SNPs with non-zero weight were randomly sampled from the UHD-genotypes, and the weights of those SNPs were iid normal  on all the SNPs of the UHD set. When Fig 2). However, the dispersion of the estimated means was, as expected, much larger for simple traits . For "complex traits" with 500 "causal variants," the proportion of variance explained by regression on 10K or more SNPs was greater than 95% for all MC replicates. However, for simpler traits we had some random vectors with a proportion of variance explained smaller than 0.8. This suggests that, while for highly complex traits low-density SNP arrays of 10K-50K SNPs may be enough to span the variance of the whole genome, for some simple traits, such arrays may not contain enough SNPs in high LD with the causal variants.The estimated proportion of variance explained by regression on lower-density SNP panels was, on average, the same across “trait-architectures”  from The Cancer Genome Atlas (TCGA) to study multivariate associations between those three omics. Details of the technologies used to generate these data, as well as the data quality controls (QC) and editions are described in the Materials and Methods. After QC and editions data consisted of the (log-transformed) expression of 20,319 genes, counts at 11,552 CVN-sites, and ME intensity at 28,241 ME CpG islands. We used the MC- and the Eigen-ANOVA methods to estimate the proportion of variance of one omic that can be explained by regression on another omic; we did this for all pairwise omics combinations .We used GE, ME and CNV data from breast cancer tumors (Table 3). About 70% of the variance spanned by ME was explained by GE and vice versa. Finally, CNV explained a relatively small fraction of the variance spanned by either GE or ME. These results suggest that most CNVs have effects in both ME and GE and therefore, variation in CNV can be predicted by ME and GE. However, although there is an association between CNV and both ME and GE, many other factors  seem to intervene, thus making the proportion of GE or ME explained by CNV relatively small (~20%). Overall the MC- and Eigen-ANOVA methods yielded similar results. However, in cases involving high R2  the Eigen-ANOVA method gave R2 estimates that were lower than those of the MC method. This pattern is consistent with what we observed in the simulation and in the analyses of chicken genomes.Our results with the MC-ANOVA method indicate that the CNV data were completely explained by both GE and ME  showed that the R2 values were, in most cases (except GE~CNV and ME~CNV) very high (and in many cases very close to one) for the top-eigenvectors , and very small for eigenvectors associated with low eigenvalues. The transition in the R2 profile of individual eigenvectors showed a relatively sharp phase transition from R2 values near one to near-zero values. Overall, our results suggest a relatively good agreement in the patterns captured by the top-eigenvectors across omics.Eigen-vector-specific RX) that can be explained by regression on an input set (W). The resulting R2 estimate is a weighted average of the R2 values obtained from independent vectors. To generate independent vectors, we considered two approaches: The first one (MC-ANOVA) is a Monte Carlo method that uses randomly generated vectors in the linear span of the output set. The second one (Eigen-ANOVA) uses an orthogonal basis for the linear span of X.Modern genomic data sets often combine information from multiple non-independent data-layers. Quantifying multivariate associations between data layers can shed light on many important aspects of the data. In this study, we developed two procedures to estimate the proportion of variance explained in settings where both the input and output sets are high-dimensional. The proposed approach uses random effects Gaussian models to estimate the proportion of variance of (independent) vectors in the linear span of an output set .The proposed methods share four important features. First, both methods can be used to perform analysis of variance when both explanatory and dependent data are high-dimensional. Second, estimates are entirely based on the likelihood function and there is no need to make regularization decisions . Third, for any pair of information sets, the analysis of variance is not necessarily symmetric; therefore, the approach accommodates cases where the proportion of variance of Our simulations suggest that MC-ANOVA renders nearly unbiased estimates of the proportion of the variance of one set that can be explained by another. However, the Eigen-ANOVA exhibited systematic biases in scenarios in which the true proportion of variance was high. We also evaluated the PLS regression method, and our simulations suggest that PLS lead to upwardly (downwardly) biased estimates whenever the true proportion of variance is high (low). Therefore, for estimation of the proportion of variance explained we recommend using MC-ANOVA. The Eigen-ANOVA method seems to be a valid alternative, provided that the proportion of variance of one set explained by the other is not too high.X) and then estimating proportion of variance of each of the eigenvectors explained by the explanatory matrix . The computational complexity of standard algorithms for singular-value decomposition is O(n3) (assuming n~p). On the other hand, the MC-ANOVA requires forming B random vectors fo the form xs = Xαs; ignoring the cost of sampling the weights, the computational complexity of forming each of this vectors is O(n2), again assuming n~p; thus, in general the MC-ANOVA will be computationally less involved as long as the number of vectors required for accurate estimation is smaller than n. In our experience, a few hundred random vectors (say 300) are enough to estimate the average, median, and SD of the R2. Therefore, whenever the rank of the response matrix is high, the MC-ANOVA has clear computational advantages. These advantages would be particularly clear for very large rank matrices. Finally, we note that the estimation process of both Eigen-ANOVA and MC-ANOVA is 'embarrassingly' parallel since the R2 of each of the vectors (either eigenvectors or random vectors) can be computed independently of each other.The Eigen-ANOVA requires computing all the eigenvectors of the response matrix . Inspection of the results of the Eigen-ANOVA for individual eigenvectors suggests that the downward bias of the method may originate from ‘corner’ solutions (zero-estimates of R2) for eigenvectors associated with small eigenvalues. Therefore, if the only goal is to estimate the proportion of variance of one set explained by another set, we recommend using the MC-ANOVA method.Consistent with our simulation results, the analyses of experimental data showed that in problems involving a high R2-values for each of the eigenvectors of the output set. This information can help elucidate whether global patterns  in one information set can be predicted from information contained in another information set. For instance, our analysis of the multi-omic breast cancer revealed that the patterns described in the top-eigenvectors derived from GE and ME are very similar; therefore, one should not expect big differences in tumor classifications that are based on the top-eigenvectors derived from either set. Interestingly, we found that in the analyses of omic data the R2 of individual eigenvectors showed a very sharp phase transition, suggesting that eigenvectors associated with intermediate and small eigenvalues may describe omic-specific patterns, or perhaps measurement error associated to each of the techniques.The Eigen-ANOVA method yields R2 estimates across vectors in the linear span of the output set. We used this feature to study the effect of the trait-architecture on the distribution of the R2 estimates. Our results indicate that while the average R2 does not seem to be affected by the sparsity of the coefficients used to form random vectors , the dispersion and the shape of the distribution highly depend on the process used to generate the weights  was skewed  the proposed estimation methods (in particular the MC-ANOVA) can detect the lack of symmetry very well (see Table 2). Interestingly, our analysis of multi-omic data from breast cancer patients exhibited cases where R2 was rather symmetric  and others that were highly asymmetric . The asymmetric cases suggest that almost all the variability in CNV can be predicted from GE (and ME as well); however, only a fraction of the GE variance can be explained by differences in CNV patterns. This result is consistent with the hypothesis that most CNV have an impact on GE, but GE is also affected by factors other than CNV .An important feature of the methods proposed in this study is that the RIn this study, we focused on the application of the Eigen- and MC-ANOVA for problems involving two input sets  evaluated on the same set of individuals. However, with slight modifications, the MC-ANOVA method will be useful for evaluating the proportion of variance of vectors in the span of a training set  that could be captured/predicted by regression on a subset of it, e.g., founders, or “proven” individuals, e.g., , 20.X or W by transforming one or both sets using a non-linear mapping f(.) . Then, the methods presented here could be applied using The methods discussed in this study are entirely based on linear models. However, both MC-ANOVA and Eigen-ANOVA can easily be extended to consider non-linear relationships by embedding each set using a non-linear mapping. For instance, in the case of SNPs, one could generate a linear space that accounts for additive and non-additive effects by considering contrasts for additive, dominance, and epistatic interactions . More ges e.g., , 23)..X or W b2 [In our applications, we considered one dependent and one explanatory set; however, the methodology presented in this study could be easily adapted to accommodate cases with one output set  and multiple explanatory sets . This can be done by expanding the model used to estimate R2  by incluIn conclusion, we developed two methods for estimating the proportion of variance explained in problems in which both the input and output sets are high-dimensional. The MC-ANOVA method provided nearly unbiased estimates across a range of simulation scenarios. In addition to providing estimates of the proportion of variance explained, the two methods can yield useful insight into the association patterns underlying multi-layered high-dimensional data.wheat data set used in Simulations 1 and 2 was generated by the International Maize and Wheat Improvement Center (CIMMYT). This data set provides genotypes at 1,279 molecular markers (Diversity Array Technology DNA markers) assessed in 599 wheat inbred lines. Further details about this data set can be found in [The found in . The datfound in .chicken data set used in Case Study 1 consisted of UHD SNP genotypes of 892 female and male chickens from six generations of a purebred commercial brown layer line of Lohmann Tierzucht GmbH. The genomes of 25 layers were sequenced at 8x read-depth. A total of 4.92M (M = million) SNPs were derived from these 25 genome sequences. The remaining layers (n = 867) were genotyped using the Affymetrix Axiom Chicken Genotyping Array [2 ≥0.99). A total of 1.79M SNPs passed these last two filters.The ng Array  which cong Array  imputed ng Array  for phasng Array  for impung Array . This prbreast cancer data set used in Case Study 2 was from the Cancer Genome Atlas (TCGA https://www.cancer.gov/tcga) and consisted of gene expression (GE), methylation (ME), and copy-number-variants (CNV) data from (n = 593) breast cancer tumors from female breast cancer patients.The Gene expression data (RNA-Sequencing counts) were generated using the Illumina HiSeq RNA V2 platform and DNA methylation profiles were determined using the Illumina HM450 platform. RNA-sequencing data were transformed using the natural logarithm and individual CpG site β-values were summarized at the CpG island level, using the maximum connectivity approach implemented in the WGCNA R package . The CpGFrom each of the three omics we removed features with a coefficient of variation smaller than 1% and those with a proportion of missing values greater than 20%. The missing values that remained were imputed using the clustering algorithm described in . After iMC-ANOVA and EIGEN-ANOVA methods, the proportion of variance of one set  explained by the other set (W) was estimated using a random-effects model of the formz was either a random linear combination of the columns of X .We estimated the variance components of the above model using Restricted Maximum likelihood (REML ) which w-package . The scrX explained by W  by regressing X on W using the pls R-package [We also estimated the proportion of variance of -package .X depends on the number of components used. To determine the number of components, we first fitted the PLS regressions with 1, 2, …, 100 components in 10-fold cross-validation and evaluated the cross-validation prediction mean-square error of each of the resulting models. We then selected the number of components that led to the smallest mean-squared prediction error and fitted a PLS regression with that number of components to the entire data set. The R2 of the fitted model in the training data was used as an estimate of the proportion of variance of X that could be explained by W. The fitPLS function provided in the script provides a wrapper to the plsr function which implements the procedure described above.The ability of the pls regression to fit Both simulations were implemented using genotypes from the wheat data set.W599×1,279 = {w1,…,w1,279}, and X = {x1,…,x1,279} was a noisy version of W obtained by adding Gaussian iid noise, xi = wi+δi where i = 1,…, 1,279. The columns of W were standardized to unit variance, and the noise variance .In the first simulation setting the input set was the wheat genotypes W) did not change across MC samples; however, the output set (X) varied across MC replicates due to the noise term), and, for each simulated data set, estimated the proportion of variance of X explained by regression on W using MC-ANOVA, Eigen-ANOVA, and the PLS method.We conducted 1,000 MC simulations (the input set (X) was included in the other set (W). In this setting Xp599× was generated by including p  of the 1,279 DNA-markers; we used values of p that led to the inclusion of 5%, 10%, 30%, 50%, 80%, 90%, and 95% of all the available DNA markers. Subsequently, W was formed by combining X with  columns filled with iid Gaussian random variables (Z): W599×1,279 = [Xp599×,Zp−1,279)599×Click here for additional data file.


Genome-wide association studies (GWAS) have identified pervasive sharing of genetic architectures across multiple immune-mediated diseases (IMD). By learning the genetic basis of IMD risk from common diseases, this sharing can be exploited to enable analysis of less frequent IMD where, due to limited sample size, traditional GWAS techniques are challenging.Exploiting ideas from Bayesian genetic fine-mapping, we developed a disease-focused shrinkage approach to allow us to distill genetic risk components from GWAS summary statistics for a set of related diseases. We applied this technique to 13 larger GWAS of common IMD, deriving a reduced dimension “basis” that summarised the multidimensional components of genetic risk. We used independent datasets including the UK Biobank to assess the performance of the basis and characterise individual axes. Finally, we projected summary GWAS data for smaller IMD studies, with less than 1000 cases, to assess whether the approach was able to provide additional insights into genetic architecture of less common IMD or IMD subtypes, where cohort collection is challenging.We identified 13 IMD genetic risk components. The projection of independent UK Biobank data demonstrated the IMD specificity and accuracy of the basis even for traits with very limited case-size . Projection of additional IMD-relevant studies allowed us to add biological interpretation to specific components, e.g. related to raised eosinophil counts in blood and serum concentration of the chemokine CXCL10 (IP-10). On application to 22 rare IMD and IMD subtypes, we were able to not only highlight subtype-discriminating axes (e.g. for juvenile idiopathic arthritis) but also suggest eight novel genetic associations.Requiring only summary-level data, our unsupervised approach allows the genetic architectures across any range of clinically related traits to be characterised in fewer dimensions. This facilitates the analysis of studies with modest sample size by matching shared axes of both genetic and biological risk across a wider disease domain, and provides an evidence base for possible therapeutic repurposing opportunities. The collected summary data of genome-wide association studies (GWAS) represent, in a compressed form, assays of thousands of phenotypes across millions of common genetic variants. Analysed individually, GWAS have elucidated the polygenic component of common human diseases , and comThe GWAS approach explicitly accounts for the number of tests (SNPs) by requiring successively larger samples (tens of thousands). Large samples present an insurmountable barrier for rare diseases, where efforts have instead focused on searching for rare variants of high penetrance through whole exome  or wholeWe propose summarising the multifactorial genetic risks of related diseases in an informed dimension-reduction approach. Matrix decomposition, for example via principal component analysis (PCA), expresses a matrix as the product of two smaller matrices and has been used extensively as a dimension-reduction tool in genetics to summarise population structure and address its confounding effects in association studies . It has Here, we propose augmenting PCA of GWAS summary statistics by a Bayesian shrinkage approach that mitigates overfitting. Our central aim is to define a reduced dimension space, with components that describe different patterns of genetic susceptibility corresponding to underlying biological risk factors. In a transfer learning paradigm, we can project independent datasets into this space, allowing us to study the distinct and shared genetic contributions to related diseases, and use standard statistical techniques to test for genetic association of rare diseases or genetic differences between disease subtypes. We use immune-mediated diseases (IMD) as an example of a set of traits with established aetiological overlap  to highlWe aimed to decompose common components underlying susceptibility to a set of related diseases using PCA. There are three particular challenges with performing PCA on GWAS summary statistics. First, the SNP effect estimates  and SNPs . After mean centring columns, we used the R command prcomp to carry out PCA of both M and M′ to generate naive and “shrunk” IMD bases. It is likely that the trailing components of any PCA represent noise, so to assess the maximal subset of informative components, we examined the mean squared reconstruction error and found that the fewest components needed to minimise this error were m = n − 1 = 13  = Qk x I (|Qk|>α) where I  is an indicator function and “x” represents element-wise multiplication. We quantify the distance between projection with Qk and Qk(α) by:We noted that the majority of entries in the MC is the centred matrix of shrunk effect sizes M′, defined above. We chose the threshold for each component, αk, as the largest value α such that Dk (α) < 0.001. Finally, we defined the sparse basis rotation matrix as the matrix constructed from the column vectors Qk, k = 1,...,m. This identified both driver SNPs which define the support for each component, and enabled computationally efficient examination of many traits in the reduced dimension space defined.where http://www.nealelab.is/uk-biobank, http://geneatlas.roslin.ed.ac.uk/—Additional File We constructed a compendium of publicly available GWAS summary statistics across a wide range of traits including UK Biobank (UKBB) self-reported traits (w/σMAF), and projected into basis space by multiplying by the sparse basis rotation matrix Q. We report projected results as δ, differs from control. We calculated variance of Prior to projection, effect alleles were aligned to the 1000 Genomes reference genotype panel. For traits sensitive to missing data (studies of neuromyelitis optica (NMO)  see Addiβ = 0 to identify disease-associated SNPs. This approach has been extended to test genetic correlation through cross-trait polygenic score tests. A SNP set and weights are learnt to optimise genetic prediction of a trait of interest, and the weighted sums of β are constructed in a second dataset, and tested for association with a second trait of interest , and used hierarchical clustering to examine whether expected patterns of similarities between diseases are captured in each reduced dimension space. The first was a naive approach without any shrinkage. Here, the UKBB SRD clustered with each other rather than their GWAS comparator, suggesting that the structure identified related to between-study differences other than disease  from UK BioBank (UKBB)  using suase Fig. . In contase Fig. , suggestZ scores, and set Z = 0 when the associated p > 0.001. As Z scores are standardised or disease frequencies are low, which means information from more common diseases will dominate. We generated hard-thresholded, LD-thinned bases using either Z scores or To illustrate the importance of using continuous shrinkage, we compared it to hard-thresholding, as used in the single-dataset decomposition approach, DeGAs , which rWe projected data from three classes of study onto the basis with shrinkage. First, we used all self-reported disease and cancer traits from UKBB to characterise the basis components, to examine specificity to IMD, and to assess power as a function of sample size: case numbers for UKBB self-reported IMD range from 41,000 (asthma) to 105 (vitiligo). Second, we used IMD GWAS with smaller sample sizes than used in basis construction, including diseases studied in multiple ancestral backgrounds to explore robustness to ancestry differences. Third, we used the basis to analyse studies of IMD that are too rare or clinically heterogeneous to build large GWAS cohorts.Across all 312 projected UKBB traits  IMD GWAS, including JIA, NMO, vasculitis, and their clinical subtypes, 16 were significant  disease affecting the optic nerve and spinal cord for which HLA association is established [JIA is a heterogeneous paediatric disease, with an overall childhood prevalence in Europe of 20/10,000 , and witGiven that most of the IMD and subtypes with small GWAS have few established genetic associations, we sought to exploit the component-level associations above to detect new disease associations. Our basis has only 13 dimensions. If genetic susceptibility to rare IMD and IMD subtypes overlaps that of common IMD, we can increase power by focusing on these dimensions. Of 22 diseases or disease subtypes with < 1000 cases, 12 were significant (FDR < 1%), even with as few as 132 cases (NMO IgG+).p values at driver SNPs on trait-significant components  either in this study (4 associations) or in other published data (8 associations), and a further five were significant in other published analysis that levered external data. These included, for example, the non-synonymous PTPN22 SNP rs2476601 which was associated with myasthenia gravis  by subset-selected FDR < 0.01. This SNP was previously associated with myasthenia gravis in a different study [p = 6 × 10−5) was attributed to differences in population structure. Eight associations (five variants) were not previously reported to our knowledge, including associations near IRF1/IL5 for myasthenia gravis, near TNFSF11 for RF− JIA, and near CD2/CD28 for EGPA.Although not a specific goal, the basis generated is naturally sparse inflammatory axis [ory axis , also chory axis . Weaker ory axis . On the ory axis , 39. On ory axis .Fig. 5FTo help characterise the biology captured by individual components, we projected additional datasets: blood counts , immune PC13 was striking for the general association of many diseases across all four main clusters in a concordant direction and was the only component for which any projected trait was more extreme than any original basis trait , suggesting that this component describes eosinophilic involvement in IMD. This is consistent with the extreme projection of EGPA which is classified as an eosinophilic form of AAV with both asthma and raised eosinophil count included in its diagnostic criteria.ait Fig. . The mosEosinophils are pro-inflammatory leukocytes with an established role in atopic diseases such as asthma , inflammPC3 inflammatory axis in IMD represented by PC1 is well documented, with the gradient along PC1 corresponding to a shift from autoantibody seronegative to seropositive diseases. Significant IMD on the MIG/IP-10-associated PC3 included both “seropositive” and “seronegative” diseases, although not atopy, while all three groups were represented on the eosinophil-associated PC13. While these observations support a link between certain IMD and serum cytokine levels or blood cell counts, our results do not directly implicate these as causal. Both cytokines and blood count data were measured in unselected population cohorts which will include individuals with IMD, such that the association with IMD may be causal or consequential. For example, we can conclude only that PC3 represents an IMD-related process that contributes to serum cytokine levels. Nonetheless, clinical efficacy of MDX1100, a monoclonal antibody to IP-10, has been demonstrated in RA  and a doOur proposed approach may be considered a form of feature engineering. We represent genetic associations for aetiologically related traits using radically fewer features, with attached estimates of uncertainty. This enabled us to identify clusters of IMD and nominate involvement of IP-10 and eosinophil counts as involved in a wider range of IMD than previously suggested. Such observations provide a rationale for potential therapeutic repurposing opportunities. Beyond these uses, we expect that reduced dimensional representation of multiple genetic association datasets will offer a foundation for other novel cross-disease analyses within and beyond the immune-mediated focus here.Additional file 1: Supplementary Note. Mathematical exposition of basis construction.Additional file 2: Tables S1-S8. Summary of input datasets, sources, and sample sizes.Additional file 3: Fig. S1-S21. Distribution of SNPs across the basis components, reconstruction plot error, hierarchical clustering of basis diseases and their basis counterparts using different thresholds, delta plots for the 13 principal components in the IMD basis, test for consistency across trait groups, comparison of projections across different ancestries, distribution of entries in the rotation matrix for each component in the basis, and QQ plots of p-values for driver SNPs on trait-significant components.Additional file 4. Methods for GWAS analysis of individual level datasets: vasculitis, JIA and PsA.Additional file 5: Table S9. Input summary statistics for SNPs needed for basis projection for JIA and PsA. Beta refers to the effect of allele a2 compared to a1. se.beta is the standard error of beta. SNPs are identified by chromosome, position, reference and alternative alleles. (CSV 346 kb)Additional file 6: Table S10. Projection results for each studied trait, giving the delta value for each PC, its variance, and the Benjamini-Hochberg adjusted p value (“fdr.delta”) together with an overall test of significance, both raw  and Benjamini-Hochberg adjusted . (CSV 1552 kb)


Such studies must rely on a small, curated set of variants from the studied region; using all variants in the region requires inverting an ill‐conditioned genetic correlation matrix and results in numerically unstable causal effect estimates. We review methods for variable selection and estimation in cis‐MR with summary‐level data, ranging from stepwise pruning and conditional analysis to principal components analysis, factor analysis, and Bayesian variable selection. In a simulation study, we show that the various methods have comparable performance in analyses with large sample sizes and strong genetic instruments. However, when weak instrument bias is suspected, factor analysis and Bayesian variable selection produce more reliable inferences than simple pruning approaches, which are often used in practice. We conclude by examining two case studies, assessing the effects of low‐density lipoprotein‐cholesterol and serum testosterone on coronary heart disease risk using variants in the HMGCR and SHBG gene regions, respectively.Mendelian randomization (MR) is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. Here, we focus on two‐sample summary‐data MR analyses with many correlated variants from a single gene region, particularly on  Under these three assumptions, MR offers a framework for assessing whether the risk factor is causally related to the outcome; under additional modeling assumptions, one can also estimate the magnitude of the risk factor‐outcome causal effect Figure .p value, or a small number of weakly correlated variants with small p values are selected. Variants from different regions are then combined to create a genome‐wide set of instruments for MR, thus increasing the power of the analysis to detect a causal relationship.Traditionally, MR studies are implemented using independent genetic variants from across the whole genome. This is especially the case when studying complex polygenic traits such as body mass index, cholesterol or blood pressure. Such genome‐wide analyses rely on published results from large‐scale Genome‐wide association studies (GWAS) studies to identify large numbers of genetic regions associated with the risk factor studied. Genetic variants in each region are pruned for independence and only the variant with the smallest cis‐MR studies, because they use cis‐variants (variants in close proximity to the gene of interest) as instrumental variables. The rise in popularity of cis‐MR studies has been driven by the increasing appreciation of the fact that such studies can be used to inform drug target discovery and validation  as a risk factor, since each coding gene region encodes one protein and since proteins are the drug targets of most medicines. By studying the associations of variants in the region with a disease outcome of interest, cis‐MR studies can thus provide information on whether the encoded protein can be used as a drug target for the outcome. Their scope is therefore different to that of genome‐wide MR analyses, which aim to assess causal relationships between phenotypic traits, and more similar to that of transcriptome‐wide and proteome‐wide association studies, as we discuss later.In parallel to the traditional genome‐wide MR studies described above, recent years have seen an increased number of MR studies based on a single gene region , factor analysis and stochastic‐search variable selection. The use of PCA  can be used to address it. However, care must be taken when extrapolating the assumptions made by such algorithms to the framework of many correlated genetic variants. For example, suppose that a region contains a single pleiotropic variant, but that variant is strongly correlated with half of the other variants in the region. This will induce bias in the marginal causal effect estimates of the correlated variants, and hence pleiotropy‐robust methods requiring that a majority or plurality of genetic variants in the region are valid instruments will be biased.33.1cis‐MR studies. Let X denote the risk factor of interest, Y denote the outcome, G1,…,GP denote a set of P putative genetic instruments from a single gene region, and let U represent confounders of the risk factor‐outcome association. Also, let θ denote the causal effect of the risk factor on the outcome. Our task is to obtain a subset of the genetic variants to use as instruments, an estimator θˆ of the causal effect parameter and an associated standard error se(θˆ).We now present various approaches for selecting genetic variants and computing causal effect estimates in βˆXj, βˆYj to denote the marginal associations between genetic variant Gj and the two traits, and σˆXj2, σˆYj2 for the corresponding standard errors. In addition, pXj denotes the p value of association between variant Gj and the risk factor. Finally, we assume that we have access to a reference data set, such as 1000 genomes or the UK Biobank, from which to estimate correlations between genetic variants.We work under the framework of two‐sample summary‐data MR and assume the availability of two sets of summary statistics, one for SNP‐risk factor and one for SNP‐outcome associations, obtained from different data sets. We use 3.2cis‐MR literature have used only the variant with the smallest univariate p value in a region as an instrument , and is usually estimated from a reference data set. The estimator  estimate. If the correlation threshold stimator  because stimator , 2017.Ω to be computed and inverted, a process which can become numerically unstable if highly correlated variants are used  algorithm of Yang et al.  and add it to the set of selected variants.Identify the variant with the smallest conditional p values for each selected variant.Regress the risk factor on all selected variants and compute the joint‐model p values is larger than the significance threshold τ, drop the variant with the largest p value from the set of selected variants.If any of the joint‐model The algorithm is run until it can no longer add or remove any variants. Using conditional  p values for variable selection can improve the algorithm's ability to identify variants with independent signals compared to LD‐pruning. Upon finishing, the algorithm provides a set of genetic variants which can subsequently be used to conduct MR. A causal effect estimate based on the selected variants is then obtained using correlated‐instruments IVW ..p valuesp values can be computed using marginal summary statistics , due to numerical instabilities.In practice, conditional analysis often has a similar performance to LD‐pruning . The matrix Ψ is practically a transformed version of the genetic correlation matrix R=(ρij). It is preferred over the untransformed matrix because its entries depend on the precisions σˆYj−1 of univariate estimates and thus, if two genetic variants are almost perfectly correlated, the variant with the highest precision will be prioritized.PCA is applied to a matrix Ψ and identifies the diagonal matrix of eigenvalues Λ=(λii) and the corresponding matrix of eigenvectors W so that Ψ=WTΛW. By transforming the summary statisticsθˆcor by using only the first k principal components. If W˜ is the sub‐matrix of W containing only the first k columns and β˜X=W˜TβˆX, β˜Y=W˜TβˆY, Ω˜=W˜TΩW˜, then the causal effect estimate based on the first k principal components isk of principal components to use is a tuning parameter for the method. In practice, it is often specified so that the selected principal components explain a specific proportion of variation in the genetic data set. The criterion used for MR :b denotes the vector of joint effects of the genetic variants on the trait . To fit this regression model using summary statistics, JAM employs a transformation z=GTX, for which  the genetic covariance matrix, which can be estimated from reference data. Hence, equation . A similar likelihood is used by the conditional and joint method  to facilitate Bayesian inference for the genetic associations with the trait.The algorithm assumes a linear regression model for the trait ,…,GP):X~N for the model coefficient to obtain the posteriorγ(0) containing only the variant with the smallest p value. Then in each iteration, given a current set of genetic variants γ(k), JAM randomly proposes a new set γ(k+1) by eitherγ(k).Adding a new variant to the current set γ(k).Removing a variant from γ(k) for a variant not in γ(k).Swapping a variant in The algorithm then decides whether to accept the new set by evaluating how well it fits the trait, according to the posterior  and no significance threshold. As an alternative, JAM can avoid the need for pruning by using a ridge term for the genetic covariance matrix to make its inversion more stable. The choice of a pruning threshold is then replaced by the tuning of the ridge term parameter. Here we focus on implementations using pruning as a first step and do not explore the use of a ridge term.Since it jointly models all available genetic variants and can account for genetic correlations, JAM is naturally suited for cis‐MR, JAM has been extended to handle violations of the no‐pleiotropy assumption when working with multiple independent genetic variants, by augmenting its variable selection with a heterogeneity loss function to penalize and downweight pleiotropic variants  genetic covariance matrix GTG. This covariance matrix and its eigendecomposition can be approximated if one has access to a reference data set. The number k of latent factors can be selected either empirically, as is common in factor analysis, or in a more disciplined way, for example using the factor penalization method of Bai and Ng , minimizing the criterionΛˆ is the estimated matrix of factor loadings and DˆX,DˆY are the diagonal matrices whose diagonal terms are the sample variances of each genetic instrument; these can be approximated from the reference data set. Minimization of (a weighted version of) gˆ(θ) yields the factor LIML (F‐LIML) estimate.The factors are then used as genetic instruments in a standard MR model:Under certain conditions, the F‐LIML estimator has been shown to be consistent and asymptotically normal  with the estimation method proposed by its authors. For top‐SNP analysis, causal effect estimation is performed using a Wald ratio estimate. For pruning, conditional analysis, PCA, and JAM, we have used the popular IVW formula. For the factor‐based approach, Patel et al.  explicitIn principle, different methods for variable selection and estimation can be combined. For example, the SNPs selected in each iteration of the JAM algorithm could be combined into an allele score, or used for causal effect estimation via the LIML method. Another idea, as hinted in our previous section, would be to combine the variable selection algorithms presented here with pleiotropy‐robust MR methods. Although these ideas would be interesting, our goal in this manuscript was to present the current state of the literature, therefore we did not pursue them further.44.1cis‐MR approaches, we implemented a simulation study. We generated data under the following simulation model:SHBG region, which encodes the protein sex‐hormone binding globulin and is known to be associated with sex hormone traits, and the HMGCR region, which encodes the protein HMG coenzyme‐A reductase, plays an important role in the metabolic pathway that produces cholesterol and is the drug target of statins. We refer to the real‐data applications for more information about these regions. SHBG and HMGCR represent two distinctly different genetic correlation structures; correlation heat‐maps for the two regions are provided in Figures To compare the various 1%. This resulted in P1=717 genetic variants for the SHBG region and P2=590 variants for the HMGCR region. We extracted individual‐level genetic observations for the selected variants from the UK Biobank, using a sample of Nref=367,643 nonrelated individuals of European origin. Aiming to replicate a two‐sample MR analysis, we then bootstrapped the UK Biobank data and obtained two genetic matrices G1,G2 of sizes N1,N2, respectively. Using the genetic matrix G1, we simulated risk factor measurements according to , we , we 1%. SHBG region, we assumed that six independent genetic effects were present in the region. This was inspired by Coviello et al. ∣+0.1. This created a pattern of univariate SNP‐exposure associations similar to that we observed in our real‐data application.To generate risk factor measurements, we used information from our real‐data applications and the literature. For the o et al.  who inveHMGCR region, we also assumed the existence of six variants independently associated with the risk factor. The six causal signals were placed at genetic variants used in a recent paper ∣+0.03 for the risk‐increasing allele; again, this closely resembled the univariate summary statistics obtained in our real‐data application.For the θ=0,0.05,0.1. We set the G‐X sample size to be N1=10,000, which is fairly small for modern MR standards but may be reasonable for a cis‐MR study using protein expression data for the risk factor. In Supporting Information material, we report simulation results using a larger sample size of N1=100,000. The sample size for SNP‐outcome associations was set equal to N2=180,000, similar to that of the CARDIoGRAMplusC4D data set  test.The performance of the conditional method is often quite similar to that of stepwise pruning  in simulations with “strong instruments”; with “weak instruments” there were simulations in which no variants passed the GWAS significance threshold, so we used a lower value (τ=10−3) instead. For the PCA method, we used principal components that explained k=0.99 or k=0.999 of the variation in the genetic data. For JAM, we implemented a prepruning step with a correlation threshold of ρ=0.6,0.8,0.9,0.95 and no significance threshold—note that JAM does not need a significance threshold for the prepruning step because its variable selection discards variants weakly associated with the risk factor anyway. The algorithm was run for 1 million iterations in each instance. Finally, for the F‐LIML method, we allowed the algorithm to determine the number of latent factors to use.Many of the above methods depend on additional tuning parameters. To assess the sensitivity of each method to the specification of its tuning parameter(s), we used a range of different values. For stepwise pruning, we set a correlation threshold of R. Stepwise pruning and correlated‐instruments IVW were implemented manually. To implement the PCA approach, we used code provided in the appendix of Burgess et al. −1 may lead to spurious increases or decreases in genetic correlations. This form of bias can be detected by computing the condition number of the genetic covariance matrix, but its direction is not straightforward to assess. It is more likely to affect methods using highly correlated variants, such as stepwise pruning with high correlation thresholds.Second, the performance of various methods in our simulations can be affected by numerical issues, in particular related to inverting the genetic covariance matrix 4.3θ=0 we also report the empirical Type I error rates, defined as the proportion of simulations in which the method rejected the null causal hypothesis. For simulations with θ≠0 we also report the empirical coverage of confidence intervals and the empirical power to reject the null causal hypothesis. All methods had very high power in the “strong instruments” scenario with θ=0.1, and very low power in the “weak instruments” scenario with θ=0.05, therefore we do not report power in these two scenarios. Finally, the conditional likelihood ratio test does not provide a causal effect estimate or an associated standard error, hence we only report its coverage, power and Type I error rate.Simulation results are reported in Tables ρ values, exhibiting bias toward the null. The bias was more pronounced for θ=0.1 than for θ=0.05.Table θ=0 suggests that any issues in their performance are due to weak instrument bias, which acts toward the null and hence would only affect simulations with θ≠0. Accordingly, any biases observed for θ≠0 were toward the null.The good performance of all methods for ρ make the inclusion of weak instruments more likely and the numerical computation and inversion of the correlation matrix more challenging. For small values of ρ the method is more robust to the inclusion of weak instruments. On the other hand, when the genetic region studied contains multiple causal signals, using a small correlation threshold may discard some of the causal variants from the analysis. In our simulations, this translated into a fairly small increase in causal standard errors and a decrease in the method's power to detect a causal effect. We also note that in the simulations of Table p values did not reach genome‐wide significance. This is a “best‐case scenario” for the method in terms of avoiding weak instrument bias; in practice, pruning is often implemented using less stringent thresholds  and attempted to adjust for the presence of weak instruments by producing wider confidence intervals; in fact, it was rather conservative in our simulations, with coverage rates above The F‐LIML method had the opposite performance compared to JAM: the algorithm provided quite accurate causal effect estimates, but underestimated standard errors and resulted in confidence intervals with inflated Type I error rates and below nominal coverage. The inefficiency of the algorithm in weak instrument scenarios has been noted by its authors. On the other hand, the conditional likelihood ratio test was the method least affected by weak instruments bias and offered a reliable way of assessing the existence of a causal effect. Its power was worse than the (overprecise) F‐LIML method but better than that of the JAM algorithm. The relation between these results and the estimation algorithms used is worth noting. It has been reported in the literature  from the analysis before implementing the methods, but we have not considered that here.In summary, our simulations suggest that simple methods such as LD‐pruning and single‐variant MR analysis can be reliable in simulations where weak instrument bias is of lesser concern, but should be used with caution in 4.4In Supporting Information material, we report results from a range of additional simulation scenarios. Specifically, we conducted three additional simulations, on which we comment here briefly.N1=100,000 from which to obtain risk factor‐outcome summary statistics. This could be reminiscent of a cis‐MR analysis using a downstream biomarker as a proxy for protein expression, and obtaining G‐X summary data from a large‐scale GWAS. Our results  cholesterol concentration and the risk of CHD using genetic variants from the HMGCR region. The HMGCR region is located in chromosome 5 and encodes the protein HMG coenzyme‐A reductase. The protein plays an important role in the metabolic pathway that produces cholesterol, and its inhibition by statins is a common treatment to reduce LDL‐cholesterol levels.We now compare the various cis‐MR, associations between HMGCR variants and a range of biomarkers have been used to investigate whether statin treatment increases the risk of type 2 diabetes .Since a clear link between HMGCR protein expression and lowering LDL‐cholesterol has been established, we used LDL‐cholesterol as a risk factor instead of protein expression. We estimated genetic associations between variants in the HMGCR gene. In total, 2915 variants were present in both the UK Biobank and the CARDIoGRAMplusC4D data set. Of those 2915 variants, 20 were discarded because they either had missing associations with LDL‐cholesterol in the UK Biobank data set or concerned multiple alleles on the same locus that were not detected in both data sets. We did not discard variants with low effect allele frequencies. Our analysis was therefore based on P=2895 genetic variants. In Figure HMGCR region, and present a Manhattan plot of genetic association with LDL‐cholesterol levels.We used a wider region than in our simulations and extracted information on variants within 500 kb pairs from the cis‐MR using the minimum p value variant, LD‐pruning, principal components analysis, the JAM algorithm, and the factor‐based methods. The various methods were implemented using a range of different parameter specifications, similar to those used for our simulation study. For stepwise pruning, we used the values ρ=0.1,0.3,0.5,0.7,0.9 for the correlation threshold and a GWAS significance threshold of τ=5×10−8. Of the 2895 variants in the region, 1424 had p values below the GWAS threshold. For the PCA method, we used principal components that explained k=99% or k=99.9% of variation in the genetic data. For JAM, we implemented a prepruning step with a correlation threshold of ρ=0.6,0.8,0.9,0.95 and no significance threshold. For F‐LIML, we allowed the algorithm to determine the number of latent factors to use.We then conducted 5.1.395% confidence intervals obtained by each method. The reported estimates represent log‐odds ratios of increase in CHD risk per standard deviation increase in LDL‐cholesterol levels.The results of our analysis are presented in Table HMGCR region is known to be associated with increased risk of CHD ). Interestingly, the principal components method suggested a null effect. The main difference in the implementation of the method compared to our simulation study was the larger number of genetic variants used here. Since the presence of many noncausal variants can exacerbate bias due to weak instruments, we conjecture that this was the issue behind the method's poor performance. To confirm our suspicions, we implemented the PCA method using only the 1424 GWAS‐significant variants in the data set. The method produced much more reasonable results, in line with other methods: the log‐odds ratio estimates were 0.423 for k=99% and 0.448 for k=99.9% and the null causal hypothesis was rejected on both occasions.Genetically elevated LDL‐cholesterol concentration based on variants in the ρ=0.7 but yielded a larger causal effect estimate for ρ=0.9, as a result of numerical errors. Bias due to numerical errors is more likely to be a concern here than in our simulation study, due to the larger number of variants used. For the JAM algorithm, there were small differences between implementations for ρ=0.6 and larger values of the correlation threshold, but overall the algorithm was more robust to the choice of that threshold than LD‐pruning. The algorithm suggested the existence of three–five genetic variants independently associated with LDL‐cholesterol in the region. The F‐LIML method suggested a slightly higher causal effect than the other methods, although differences were within the margin of statistical error. As an additional form of sensitivity analysis, we implemented both JAM and F‐LIML using only GWAS‐significant variants; results were similar to those in Table The remaining methods were more consistent in their results. LD‐pruning exhibited the usual attenuation toward the null for 5.25.2.1SHBG gene region to assess the causal relationship between testosterone levels and CHD risk. The SHBG region is located in chromosome 17 and encodes sex‐hormone binding globulin, a protein that inhibits the function of sex hormones such as testosterone and estradiol. The region has been shown to contain strong genetic associations with testosterone levels, as well as a number of sex hormone traits . Estimates from the PCA method were in the risk‐decreasing direction but did not achieve statistical significance. Overall, both Burgess et al. . In addition, the inference procedure used by TWAS/PWAS methods is effectively a two‐stage least squares algorithm. Regarding variable selection, TWAS/PWAS also face the issue of having to select among a group of correlated genetic variants, but these approaches often assume access to individual‐level data for gene expression, and the corresponding methods are often linked to individual‐level eQTL data sets. This gives TWAS methods greater flexibility to overcome the variable selection issues discussed in the current manuscript.The similarities between cis‐MR studies. For example, cis‐MR is typically conducted with a focus on a specific gene region of interest, while TWAS studies are mode agnostic and are often implemented across the genome. In addition, although cis‐MR studies regularly use protein expression data as an exposure, the methods developed for cis‐MR can be extended to any MR analysis with correlated instruments. However, these differences should not distract from the strong similarities between cis‐MR and TWAS/PWAS studies. Although the methods were developed under different names, they are effectively different implementations of the same approach to investigate causal links between gene regions and downstream outcomes.A few minor differences exist in how TWAS and PWAS studies have been utilized so far in the literature compared to A detailed description of the methods available for TWAS/PWAS studies is beyond the scope of this manuscript. Instead, we refer to the relevant literature for an overview of methods  and the additional note that IVW‐based methods can suffer from bias due to sample overlap in this case. On the other hand, with access to individual‐level data, a range of additional methods such as two‐stage least squares and control function approaches can be implemented. These methods might suffer from similar issues as the summary‐level methods outlined here, because they also rely on inverting the genetic correlation matrix to perform inference, but may be able to avoid some of the secondary challenges discussed in this paper, such as the potential bias induced by inaccurately estimating the genetic correlation matrix in a reference data set. It is also possible to compute summary statistics from one‐sample individual‐level data and then implement the methods presented here, though this may also be biased by sample overlap as mentioned earlier.Another limitation is that our work has focused on Cis‐MR is an active area of research, both methodological and applied. As the field develops further, it is likely that new statistical approaches will be created to aid applied investigators in their work. By providing an overview and evaluation of existing methods, we hope that our current paper will contribute to that direction.Paul J. Newcombe and Stephen Burgess devised the idea for this project. Paul J. Newcombe and Apostolos Gkatzionis reviewed the literature and developed the relevant methodology. Apostolos Gkatzionis implemented the simulation study. Stephen Burgess facilitated access to real data for the applied analyses. Apostolos Gkatzionis conducted the real‐data analyses, and all three authors discussed their results. Apostolos Gkatzionis led the writing of the manuscript. Paul J. Newcombe and Stephen Burgess reviewed the manuscript and provided feedback.The authors declare no conflict of interest.Supplementary InformationClick here for additional data file.


This study evaluated the effect of pedigree errors (PEs) on the accuracy of estimated breeding value (EBV) and genetic gain for carcass traits in Korean Hanwoo cattle.h2) estimates for carcass traits. Correlation of the simulated data under PEs was also estimated using Pearson’s method.The raw data set was based on the pedigree records of Korean Hanwoo cattle. The animals’ information was obtained using Hanwoo registration records from Korean animal improvement association database. The record comprised of 46,704 animals, where the number of the sires used was 1,298 and the dams were 38,366 animals. The traits considered were carcass weight (CWT), eye muscle area (EMA), back fat thickness (BFT), and marbling score (MS). Errors were introduced in the pedigree dataset through randomly assigning sires to all progenies. The error rates substituted were 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80%, respectively. A simulation was performed to produce a population of 1,650 animals from the pedigree data. A restricted maximum likelihood based animal model was applied to estimate the EBV, accuracy of the EBV, expected genetic gain, variance components, and heritability (2, 8.63 mm, and 3.31, respectively. When errors were introduced in the pedigree, the accuracy of EBV, genetic gain and h2 of carcass traits was reduced in this study. In addition, the correlation of the simulation was slightly affected under PEs.The results showed that the carcass traits per slaughter year were not consistent. The average CWT, EMA, BFT, and MS were 342.60 kg, 78.76 cmThis study reveals the effect of PEs on the accuracy of EBV and genetic parameters for carcass traits, which provides valuable information for further study in Korean Hanwoo cattle. Pedigrees are essential tools in the livestock breeding industry, because they provide ancestral information and knowledge for predicting progeny performance. A pedigree record contains the performance records of individuals and their progeny, and each domestic animal species has traits that are of economic value. For examples, meat and milk traits in cattle, sheep and goats . Carmen h2, and genetic gain for meat and milk traits in cattle populations. In addition, biased estimates of EBV and genetic gain for both bulls and cows have been reported [h2) would be useful in the Hanwoo beef industry. Therefore, the aim of this study was to assess the effect of PEs on the accuracy of EBV and genetic gain for carcass traits.Harder et al  describereported ,13–15. AThe raw data set was based on the pedigree records of Korean Hanwoo cattle, which were the offspring of Korean proven bulls with different dam lines. The animals’ records were obtained using Hanwoo registration records from Korean animal improvement association database . The recErrors were introduced in the pedigree dataset through randomly assigning sires to all progenies born between 2000 and 2013. This method of changing sire records resulted in wrong sire information. SampleBy function in doBy package of the R software package was used for making PEs. For each generation, the pedigree dataset was substituted by error rates of 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80% as the true parent previously described in Oliehoek and Bijma .A simulation was performed to produce one replicate population of 1,650 animals using QMSim software package . The numA restricted maximum likelihood (REML) based animal model was applied to estimate variance and covariance components of the studied traits using ASReml 4.0 software package . The modwhere y, b, u, and e, are the vectors of phenotypes (lists of traits), fixed effects, random effects and residual errors, respectively, and X and Z are the design matrices.The similar animal model was also used for estimation of breeding values using Henderson’s BLUP method  as impleThe expected genetic gain from the selection was calculated using the following equation.Gyr = expected genetic gain/yr, i = intensity of selection, rIH = accuracy, GA = genetic standard deviation, L = generation interval.where Δi, L were set as 0.80, 5.5, rIH = estimates in GA = square root of σ2a per each trait. Then, the expected genetic gain per year for each trait was obtained from the studied dataset.In the equation the term h2 estimates for carcass traits were estimated using a single trait animal model in h2 estimates was as follows,The variance components as well as 2a, additive genetic variance; σ2p, phenotypic variance; h2, heritability.where σ2, 1.76 mm, and 0.79, respectively. 2, 8.63 mm, and 3.31, respectively.The average carcass traits per year are presented in 2, 0.34 mm, and 0.17 for CWT, EMA, BFT, and MS with no PE (0%), and that deemed to decline constantly as PEs were increased gradually in the dataset. With a 5% PE, the decline in the traits were 0.34 kg, 0.03 cm2, 0.01 mm, and 0.01 for CWT, EMA, BFT, and MS with respect to that estimate at 0% PE. This result was followed by the highest values of 2.85 kg, 0.73 cm2, 0.26 mm, and 0.17 decline at 80% PE.h2 estimates for carcass traits. For CWT, the estimated h2 with no PE was 0.36 in this study. However, this h2 decreased consistently as more PE introduced in the dataset and reached to as low as 0.03 at 80% of PE. A very similar negative effect of PE on h2 of EMA was observed as well, where h2 with no error was estimated as high as 0.42 and as low as 0.05 at 80% PE. The presence of PE equally affected the h2 of BFT and MS. In this regard, BFT h2 was reduced from 0.48 with no PE to 0.11 with 80% of PE, whereas for MS, such decrease in h2 was from 0.58 to a negligible heritability (0.00).h2 estimates of carcass traits. In general, the carcass traits per year were evaluated from 2000 to 2013 as shown in In this study, we assessed the effect of PE on the accuracy of EBVs, genetic gain, and The overall mean of carcass traits is presented in With a dataset including PE, some parameters were found to be influenced in our study . We obseThe correlations of the simulated data under PE were slightly reduced in our study as shown in We found that the expected genetic gain in animals was also largely reduced due to PEs as presented in h2 estimates for carcass traits are illustrated in h2 estimates were negatively affected as more errors were introduced in the pedigree. The h2 being affected by PE also indicated that such errors could reduce the selection accuracy at the same time. For this reason, h2 is very important to selection for polygenic traits, because selection accounts for those animals with the best breeding values to become the parents of the next generation. In order to increase selection accuracy, we need good information about the candidates for selection because the only information available is the phenotypic records, which is the strength of the relationship between phenotypic values and breeding values . Therefore, when h2 is low, the phenotypic values mostly reveal little about the underlying breeding values, and it is difficult to determine which animals have the best breeding values to become the potential parents [h2 estimates for birth and weaning weights in Herford cattle. Previous studies by Gelderman et al [h2 estimates in milk fat and milk yield in both cattle and buffalo populations under erroneous pedigree.The variance components and  parents . Our stu parents  who obsean et al , and Paran et al  also repThe accuracy of EBV, genetic gain, and heritability estimates for the studied traits were affected by introduction of errors in the pedigree. On the other hand, the result of the correlation estimates of simulated data for carcass trait was slightly decreased as errors were introduced in the pedigree. As a result, PEs had a negative effect on the overall estimates, which could slower the rate of genetic or selection progress in a population.


Cannabis is gaining greater social acceptance for its beneficial medicinal and recreational uses. With this acceptance has come new opportunities for crop management, selective breeding, and the potential for targeted genetic manipulation. However, as an agricultural product Cannabis lags far behind other domesticated plants in knowledge of the genes and genetic variation that influence plant traits of interest such as growth form and chemical composition. Despite this lack of information, there are substantial publicly available resources that document phenotypic traits believed to be associated with particular Cannabis varieties. Such databases could be a valuable resource for developing a greater understanding of genes underlying phenotypic variation if combined with appropriate genetic information. To test this potential, we collated phenotypic data from information available through multiple online databases. We then produced a Cannabis SNP database from 845 strains to examine genome wide associations in conjunction with our assembled phenotypic traits. Our goal was not to locate Cannabis-specific genetic variation that correlates with phenotypic variation as such, but rather to examine the potential utility of these databases more broadly for future, explicit genome wide association studies (GWAS), either in stand-alone analyses or to complement other types of data. For this reason, we examined a very broad array of phenotypic traits. In total, we performed 201 distinct association tests using web-derived phenotype data appended to 290 uniquely named Cannabis strains. Our results indicated that chemical phenotypes, such as tetrahydrocannabinol (THC) and cannabidiol (CBD) content, may have sufficiently high-quality information available through web-based sources to allow for genetic association inferences. In many cases, variation in chemical traits correlated with genetic variation in or near biologically reasonable candidate genes, including several not previously implicated in Cannabis chemical variation. As with chemical phenotypes, we found that publicly available data on growth traits such as height, area of growth, and floral yield may be precise enough for use in future association studies. In contrast, phenotypic information for subjective traits such as taste, physiological affect, neurological affect, and medicinal use appeared less reliable. These results are consistent with the high degree of subjectivity for such trait data found on internet databases, and suggest that future work on these important but less easily quantifiable characteristics of Cannabis may require dedicated, controlled phenotyping.The use of  One of the major goals of plant breeding research in domesticated species is to understand the genetic basis of traits important in their biology or commercial utilization , 2. ThisPlant breeders have focused on a large diversity of domesticated plant species and there are hundreds of studies using association approaches to understand the genetic or genomic basis of crop development and phenotypic traits , 6. One Cannabis (aka ‘marijuana’), there has been rapid acceptance of this plant for medicinal and recreational purposes. Accordingly, it has transitioned from an ‘illegal weed’ to a valuable agricultural product, with predicted retail sales for 2021 estimated to be worth $11.9 to $17.1 billion dollars in the United States alone [Cannabis lags behind other agricultural products in our understanding of its underlying genetic architecture and how genetic variation influences phenotypic variation [Cannabis strains [Starting in the 1970s and 80s with national laws to decriminalize possession of small amounts of Cannabis strains in existence. However, given its history of elicit use, it remains unclear how much overlap among these strains exists [Cannabis [Cannabis in cultivation today, it is clear that among these plants there exists a good deal of phenotypic variation [There are hundreds of distinctly named s exists . FurtherCannabis . Regardlariation . Of mostariation .Cannabis. What little work has been done have focused on chemical compositions, particularly THC, CBD, and CBN quantity [Cannabis strains available online through various commercial and open websites . The information on these websites ranges from THC, CBD, and CBN quantities to the impact of the strain on individual mental state to taste or odor of the strain. This information is available for a wide number of individual strains and can be collated by viewing the websites. It is possible that Cannabis may even have some benefit over traditional crops regarding phenotypic data availability due to the greater spirit of openness and historical sharing of information among Cannabis growers [The likelihood of finding genetic variation that correlates with a phenotype of interest depends on a number of factors, but one of the most important is the quality of the phenotypic data. More specifically, it is essential that described phenotypes of genotyped samples are accurately characterized, if confident genetic associations are to be found . To datequantity –17. Howe growers .Cannabis agricultural production and use. It was not our goal to explicitly perform genetic association studies to locate genetic variation that correlates with specific phenotypic traits. Rather our aim was to employ a GWAS analytical framework to test the feasibility of using available online phenotypic data in future work, possibly in conjunction with other datasets. Our ability to locate statistically robust genetic variants associated with one or more phenotypes was considered as evidence in support of this aim. If and when we did locate significant associations with a phenotype, we secondarily wanted to assess the ‘reasonability’ of these associations. Such reasonability was determined based on physically proximate genes (to the variant of interest) and a review of these genes’ known biological function(s) in Cannabis or other plant species. Finally, we wanted to compare different categories of phenotypic data to determine if some traits are more amenable to GWAS than others, when considering the use of publicly available strain phenotypic information.In this paper we examine the utility of publicly available phenotypic information provided by growers and breeders for understanding the genetic architecture of traits important in Cannabis strains to produce a single nucleotide polymorphism (SNP) database for testing genetic associations in conjunction with our 201 scored phenotype catalogs.To these ends, we produced 201 web-based phenotypic character catalogs, 46 of which were based on quantitative measures of chemical content, specifically THC, CBD and CBN. The other 155 trait catalogs included 29 growth phenotypes , 80 physiological or neurological affect phenotypes , 18 taste phenotypes , eight phenotypes tied to origin of strain (sativa vs. indica), and 30 medicinal uses . We then used publicly available next-generation sequence data from 845 distinct Cannabis websites: ‘I Love Growing Marijuana’ , CannaSOS  and Leafly . We also examined the websites Grow Marijuana (https://grow-marijuana.com/), NCSM (https://www.ncsm.nl/english/), Allbud , Wikileaf (https://www.wikileaf.com/) and Cannabis.info (https://www.cannabis.info/en/), for information on Cannabis strain phenotypes, but settled on the three sites mentioned above because of maximum overlap of strains and complete phenotypic datasets. All of the websites had substantial amounts of data for THC, CBD and CBN content in different strains as well as anecdotal information about medicinal uses, adverse effects and taste. There was also information on the growing conditions and growth traits of many strains. No two websites completely overlapped in the data they provided, and THC, CBD, and CBN levels for a given strain often varied from website to website. Additionally, there was some variability for the data on growth traits as well as anecdotal information.We manually collected phenotypic traits from three popular Cannabis strains for which we had genetic data, there were 290 strains that also had consistent and extensive phenotype data . Next, we scored and compiled strain-specific phenotypes for these traits  for each website individually. Second, where possible, we averaged values across websites . We examined associations for non-chemical traits from each website individually.Cannabis samples have been made available by Phylos Bioscience (https://phylos.bio/), under BioProject PRJNA347566 . These samples were all sequenced on an Illumina NextSeq 500. We downloaded the raw reads for each sample using the ‘fastq-dump’ function of the SRA Toolkit (v. 2.8.1–3). After downloading, we used Trim Galore  to remove sequencing adaptors and trim bases from read ends with quality scores (Q score) less than 20. Next, we removed reads that were less than 30 bases long, in addition to any resulting unpaired reads.Paired reads from targeted amplicon sequencing of genomic DNA from 845 Cannabis sativa reference genome ASM341772v2 . This was followed by indel realignment using IndelRealigner from the Genome Analysis Toolkit (‘GATK’) v. 3.8 [To produce our variant dataset for association analyses, we first mapped the trimmed reads to the 17725.2, ) using t17725.2, . We then) v. 3.8 . Indepen2) greater than 50% within sliding windows of 50 SNPs at 10 SNP increments between windows [After the samples were combined, we removed any variant that was not a bi-allelic, single nucleotide polymorphism (SNP). This left us with 61,393 variants. We then removed SNPs that had a quality by depth less than 20 (QD < 20.0), Fisher strand bias greater than 60 (FS > 60.0), mapping quality less than 45 (MQ < 45.0), mapping quality rank sum less than -0.2 (MQRankSum < -0.2), read position rank sum less than -1 (ReadPosRankSum < -1.0), and a strand odds ratio greater than 2 (SOR > 2.0). All filtering options were based on the developer’s recommended cutoffs, with more stringent adjustments for FS, MQ, MQRankSum and ReadPosRankSum based on the observed distributions for these parameters. Finally, we used PLINK v. 1.90b6.6  to remov windows . The remOur phenotype trait matrix was combined with our SNP data for analysis with Plink v. 1.90b6.6 . We thenFor this study, we considered two major factors that could contribute to the false detection of associations, or conversely failure to detect an association. First, the phenotype as presented might be too complex or ambiguous for consistent results across strains  appearing in three or more tests for a particular phenotypic subcategory  were considered significant (‘Method 2’). Subcategories are listed in −9) for any test associated with a phenotype either within the chemical or non-chemical categories were considered (‘Method 3’). A comparison of SNPs found to be significant via Method 3 also allowed us to consider SNPs with potential pleiotropic effects . To do this, for each SNP found to be significant via Method 3, we determined whether it appeared in more than one phenotypic test subcategory , in at least 95% of the runs were considered further (‘Method 4’).It is well established that imbalances in the numbers of case and control samples may affect association study results , 28. To Cannabis reference genome  to locate all genes within 25 Kb both upstream and downstream of the variant . In some cases, there were no annotated genes within this span, while in other cases there were as many as seven genes. When one or more genes were present, we conducted a literature survey to assess the likelihood that the gene(s) could have an effect on our phenotype of interest.For any SNPs with a phenotypic association that met or exceeded our significance threshold, we next used information from the annotated Cannabis [sativa:indica hybrid ratio.The causative gene or genes for a specific trait can be as distant as two million base pairs from the associated SNP . TherefoCannabis , 32. Forhttps://www.uniprot.org/), and then fed into the Panther gene list analyzer (http://www.pantherdb.org/). We examined the gene categories and GO annotations for the categories using Panther by generating histograms of the nearest child terms (i.e. more narrowly defined categories) in four parent GO categories: ‘molecular function’, ‘cellular component’, ‘biological process’, and ‘protein class’. We also examined GO terms that were over-represented to determine if any categories of genes showed strong genetic associations with phenotypes. This was done in Panther, with Fisher’s exact test and Bonferonni correction.To further examine how phenotypes may be impacted by the genetic variation identified, we utilized all genes found to be within 25Kb of a significantly associated SNP (Method 1). This gene list was compiled using UNIPROT , were most amenable to performing association studies in a genome-wide context with information from available online databases.The goals of this study were threefold. First, we wanted to establish if online databases providing Cannabis phenotypic variation with genetic variation in a ‘case’ vs. ‘control’ framework. We performed 201 distinct trait association tests, 155 of which were for non-chemical traits  and 46 of which were for chemical traits  across all tests, with about half of the tests yielding significant SNP associations. The number of SNPs associated with chemical and non-chemical traits was roughly proportional to the number of tests performed suggesting randomness in these results. Furthermore, within the non-chemical traits we could subdivide these into growth, affect, medicinal, and taste traits. The number of significant associations in each of these subcategories of non-chemical traits was again proportional to the number of tests within this category, further suggesting an element of randomness.In many of our Method 1 analyses, either the case or control sample sizes were relatively small. Comparisons between the number of significant associations and sample sizes  Figs shoAssessing the presence of significantly associated SNPs across multiple tests within a subcategory Method 2), allowed us to reduce our list of ~900 SNPs considerably , the number of phenotype-associated SNPs found diminished substantially . We alsoOur second, complementary approach to reducing the large number of significantly correlated SNPs was to repeatedly subsample the overrepresented category and normalize sample sizes between ‘cases’ and ‘controls’ (Method 4). Combining this with a bootstrapping approach allowed us to focus on another conservatively determined subset of SNPs , Table 4Cannabis genome. Four of the significant SNPs detected by Method 4 are in genes that have roles in plant physiology peripherally or are directly connected to plant secondary compound production  synthase, which encodes the enzyme responsible for catalyzing the conversion of cannabigerolic acid (CBGA) to THC . EquallyCannabis has recently been established [As indicated above, non-chemical traits appeared less stable with respect to attempts to discover associations except possibly for growth traits such as height, time to flowering, yield and growth area. As a consequence, we will discuss here the SNP associations with growth traits Tables  and 4. Tablished , 47, 48,Brodie and colleagues  demonstrCannabis genome on Chromosome 6 [Three chromosomes , harbored the majority of the chemical SNPs. This result is interesting because of the co-location of known THC and CBD synthesis genes on these chromosomes. The THCA synthase and CBDA synthase genes (genes coding for enzymes involved in the last step of THC and CBD respectively), are located on Chromosome 6 and indeed there is also considerable duplication of these genes in the mosome 6 , 49. Chrmosome 6 , and Welmosome 6 , suggestUsing the large number of significantly associated SNPs found using Method 1, we combined the genes associated with these SNPs and categorized the related GO terms. The distribution of children GO categories linked to these genes are shown in We also tested the list for over-representation of GO terms in the GO parent categories. The Cellular Component parent category had no significant over-representation, while Molecular Function and Biological Process did at two-fold enrichment. The Biological Process over-representation is for ‘cellular metabolic processes’ and the Molecular Function over-representation is for ‘organellar processes’. These results suggest that regulation of chemical composition (THC and CBD) may be connected to the cellular metabolic processes of the plant cells and also associated with organellar function. It is well known that both THC and CBD have effects on and in organelles, particularly mitochondria where they bind to membranes and disrupt mitochondrial function . It is pCannabis strains for determining genetic associations with some of this plant’s important phenotypic traits. We found that internet sources of strain-specific information that is readily quantifiable such as chemical composition (i.e. THC and CBD content) and growth traits might be potentially useful for association studies. However, phenotypic information that is more qualitative or relies on anecdotal descriptions is likely insufficiently precise for useful association analyses. This result suggests that more precise measurement of traits such as yield, medicinal, or side effects would be needed in order to perform genetic association studies for Cannabis non-chemical traits.This study set out to assess the potential utility of web-based information from a large number of Cannabis plants, or might be involved in more mundane cellular processes like organellar properties or cellular metabolism properties. At the very least, the SNPs we detected for chemical  may be linked to the known cannabinoid synthesis genes on Chromosomes 3, 6 and 8.If the associations we have detected for chemical traits like THC and CBD content using this approach have any biological significance, then we can also conclude that genetic variation influencing these phenotypes occurs outside the genes within the synthetic pathways of THC and CBD. The genes effected by these variants may be involved in the quantity of these chemicals produced by Overall, web based chemical content data appears to have potential utility for gene association studies considering THC and CBD content. In the future, more directed and precise chemical concentration data might enhance detection of other chemical traits such as ratios and CBN content. Such data will additionally provide more precise inferences for the traits successfully examined here. Some such studies of chemical makeup have been reported  and thesS1 FigWe have divided the space into Case Size slivers. A is between 0 and 10, B between 10 and 25, C between 25 and 50, D between 50 and 100 and E between 100 and 150.(TIF)Click here for additional data file.S2 FigThe boxes indicate two ranges over which we are confident of reasonable results. The read box indicates the range of the most stringent approach we took.(TIF)Click here for additional data file.S1 TableThe phenotypic traits examined in this study, classified by category. Also given are the binary (case vs. control) trait scoring definitions used for each phenotype.(XLSX)Click here for additional data file.S2 TableCannabis strains used for trait associations in this study. The strains listed had both phenotypic data available through one or more of the websites listed in the methods, as well as genetic data available. Also given is each strain’s NCBI-SRA BioSample ID (https://www.ncbi.nlm.nih.gov/sra).The list of (XLSX)Click here for additional data file.S3 TableThe websites, traits and phenotypes of the 201 basic association tests performed in this study. The sizes of the case category and the p values of the most significant SNP (‘most sign’) are also given in the table.(XLSX)Click here for additional data file.S4 TableExtended data for all SNPs determined to be significant using Methods 2 and 3.(XLSX)Click here for additional data file.S5 TableSNPs determined to be significantly associated with more than one phenotypic trait (from Method 3).(XLSX)Click here for additional data file.