This study assesses the association of the genetic risk for psychiatric disorders with population traits of these disorders in Sweden. Are genetic risks for psychiatric disorders associated with subclinical population traits of these disorders?Phenotype data were available for 13 923 twin pairs at 9 years of age, 5165 pairs at 15 years of age, and 4273 pairs at 18 years of age, and genetic data were available for 13 412 individuals. Genetic risk factors for psychiatric disorders were associated with risk factors for subclinical traits; polygenic risk scores for psychiatric disorders were also significantly associated with subclinical traits.The findings suggest that psychiatric disorders are associated with continuously distributed genetic risks throughout the general population. Psychiatric traits associated with categorically defined psychiatric disorders are heritable and present to varying degrees in the general population. It is commonly assumed that diagnoses represent the extreme end of continuously distributed traits in the population, but this assumption has yet to be robustly tested for many psychiatric phenotypes.To assess whether genetic risk factors associated with psychiatric disorders are also associated with continuous variation in milder population traits.This study combined a novel twin analytic approach with polygenic risk score (PRS) analyses in a large population-based twin sample.Phenotypic and genetic data were available from the Child and Adolescent Twin Study in Sweden. Inpatient data were available for January 1, 1987, to December 31, 2014, and outpatient data for January 1, 2001, to December 31, 2013. The last day of follow-up was December 31, 2014. Data analysis was performed from January 1, 2017, to September 30, 2017.Questionnaires that assessed traits of autism spectrum disorder (ASD), attention-deficit/hyperactivity disorder (ADHD), learning difficulties, tic disorders (TDs), obsessive-compulsive disorder (OCD), anxiety, major depressive disorder (MDD), mania, and psychotic experiences were administered to a large Swedish twin sample. Individuals with clinical psychiatric diagnoses were identified using the Swedish National Patient Register. Joint categorical/continuous twin modeling was used to estimate genetic correlations between psychiatric diagnoses and continuous traits. The PRSs for psychiatric disorders were calculated based on independent discovery genetic data. The association between PRSs for each disorder and associated continuous traits was tested.Phenotype data were available for 13 923 twin pairs  at 9 years of age, 5165 pairs  at 15 years of age, and 4273 pairs  at 18 years of age. Genetic data were available for 13 412 individuals . Twin genetic correlations between numerous psychiatric diagnoses and corresponding traits ranged from 0.31 to 0.69. Disorder PRSs were associated with related population traits for ASD (β [SE] = 0.04 [0.01] at 9 years of age), ADHD (β [SE] = 0.27 [0.03] at 9 years of age), TDs (β [SE] = 0.02 [0.004] at 9 years of age), OCD (β [SE] = 0.13 [0.05] at 18 years of age), anxiety , MDD , and schizophrenia (β [SE] = 0.02 [0.01] at 18 years of age). Polygenic risk scores for depressive symptoms were associated with MDD diagnoses .These results suggest that genetic factors associated with psychiatric disorders are also associated with milder variation in characteristic traits throughout the general population for many psychiatric phenotypes. This study suggests that many psychiatric disorders are likely to be continuous phenotypes rather than the categorical entities currently defined in diagnostic manuals, which has strong implications for genetic research in particular. To our knowledge, this approach has not been applied to other psychiatric phenotypes, meaning that the degree of genetic correlation between most psychiatric disorders and related traits has been largely understudied using twin methods. Few twin studies have focused on the links between anxiety and major depressive disorder (MDD) with the traits of these disorders despite these being 2 of the most common psychiatric diagnoses.Preliminary support for this theory comes from twin and molecular genetic studies. Twin studies indicate consistent heritability of traits at varying levels of severity4 This approach requires large genome-wide data sets, however, which are lacking for psychiatric traits beyond symptoms of ADHD, MDD, and ASD.7 An alternative approach is to calculate polygenic risk scores (PRSs) based on discovery genome-wide association studies (GWASs) of psychiatric disorders; PRSs capture an individual’s common variant risk for a phenotype.8 A review4 of preliminary studies reported that psychiatric disorder PRSs are associated with corresponding population traits of ASD, ADHD, obsessive-compulsive disorder (OCD), and MDD, with null or mixed findings for schizophrenia and bipolar disorder (BD).Molecular genetic methods also allow estimation of genetic correlations between psychiatric disorders and subclinical traits of these disorders based on additive, common genome-wide variants. Such studies report strong genetic correlations across disorders and traits for ADHD and MDD, with a moderate estimate for ASD.5 to estimate the genetic correlation between psychiatric diagnoses and continuous traits of these disorders. We then calculated PRSs based on recent, large-scale GWASs and tested their associations with continuous variation in related phenotypes.Although some preliminary evidence supports shared genetic risks across disorders and traits for some psychiatric phenotypes, evidence is weak, mixed, or entirely lacking for many phenotypes. We aimed to assess the degree of shared genetic risks between disorders and traits for multiple psychiatric disorders. Leveraging data from a unique twin sample, with comprehensive clinical diagnostic, trait measurement, and genetic data available, enabled us to perform twin modeling and molecular genetic methods in the same sample. We used a novel twin method9 The response rate was 75%. Follow-ups were conducted when the twins were 15 years of age  and 18 years of age . Exclusion criteria were brain injuries (n = 207 pairs), chromosomal syndromes (n = 35 pairs), death (n = 29 pairs), and migration (n = 100 pairs). Phenotypic data were available for 13 923 pairs at 9 years of age , 5165 pairs at 15 years of age , and 4273 pairs at 18 years of age . Zygosity was ascertained using a panel of 48 single-nucleotide polymorphisms (SNPs) or 5 questions concerning twin similarity. The latter method was only used in cases with a 95% probability of correct classification. Zygosity was reconfirmed for pairs with genotype data. All families provided written informed consent before participation, and all data were deidentified. This study received ethical approval from the Karolinska Institutet Ethical Review Board.Families of all twins born in Sweden beginning in 1992 were contacted in connection with the twins’ ninth birthday  and invited to participate in the Child and Adolescent Twin Study in Sweden (CATSS).10 A total of 11 081 samples passed quality control assessment; MZ twins were then imputed, resulting in 13 576 samples and 6 981 993 imputed SNPs that passed all quality control assessments. After individual-level exclusions (described above), 13 412 children  were included in genetic analyses.DNA samples  were obtained from the CATSS participants at study enrollment. A total of 11 551 individuals with available DNA were genotyped using the Illumina PsychChip. Standard quality control and imputation procedures were performed in the sample; for details, see the article by Brikell et al.11 The NPR contains International Statistical Classification of Diseases and Related Health Problems, Tenth Revision (ICD-10) codes for diagnoses from all visits to specialist inpatient and outpatient care in Sweden. Inpatient data were available for January 1, 1987, to December 31, 2014, and outpatient data for January 1, 2001, to December 31, 2013. Diagnoses of ASD, ADHD, intellectual disability (ID), tic disorders (TDs), OCD, anxiety disorders (ADs), and MDD were extracted. Diagnostic codes and the numbers of individuals with each diagnosis are given in The CATSS is linked with the Swedish National Patient Register (NPR).Traits of ASD, ADHD, ID, TDs, OCD, ADs, and MDD were measured using continuous scales at 9 and 12 years of age. Internalizing problems (related to ADs and MDD) were then measured at 15 years of age. Traits of OCD, ADs, MDD, mania, and psychotic-like experiences were assessed at 18 years of age. Details of these measures and sample sizes are provided in 22 The principles of the twin design are described at length elsewhere.23We used joint categorical/continuous twin models to estimate the degree of etiologic overlap between continuous traits and categorical diagnoses. These models assume a normal distribution of continuous liability underlying psychiatric disorders, whereas questionnaires were treated continuously. The model partitions variance in each phenotype into additive genetic (A), nonadditive genetic (D), shared environmental (C), and nonshared environmental  components. The correlations among these components are then estimated between 2 phenotypes. The phenotypic correlations were decomposed into genetic and environmental factors to assess which factors explain the correlation between psychiatric diagnoses and traits. On the basis of twin correlations, we tested ACE or ADE models for each disorder-trait pairing. We included a sibling interaction term in ADE models (ADE-s) because these interactions can mimic the effects of D on the twin correlations.24 Opposite-sex twins were included, but the study was underpowered to test for sex differences. Obsessive-compulsive disorder was omitted from the twin analyses because of the small sample and low heritability.The ACE or ADE-s model was compared with a saturated model of the observed data. If the pattern of twin correlations differed between the continuous trait and the categorical diagnoses, both models were fitted and the best-fitting model was chosen on the basis of the lowest Bayesian Information Criteria value. More parsimonious models were tested by reducing each model by constraining certain components to equal zero and comparing these models to the ACE or ADE-s model using the likelihood ratio test; if the model fit did not deteriorate significantly, the reduced model was favored. Continuous scales were standardized by sex, whereas the association of sex with the thresholds were included in the models. Models were fitted in OpenMx.34 eTable 2 in the P value thresholds used for SNP selection. The primary analyses are based on the threshold P < .50. The PRSs were standardized using z-score transformations; effect sizes can be interpreted as increase in risk of the outcome per SD increase in PRS. Principal component analysis was used to derive covariates to account for population stratification  and 3 continuously distributed psychiatric or cognitive traits  were used to derive PRSs in the CATSS individuals.ICD-10 diagnoses to determine whether effects were driven primarily by individuals with clinically recognized problems. Third, we tested for associations between PRSs for each of the 3 discovery GWASs of continuously distributed population traits and the corresponding psychiatric diagnosis in the target sample. Fourth, all PRS analyses were repeated using PRSs derived on the basis of different P value selection thresholds to assess sensitivity. False discovery rate corrections were applied in R (using the fdr method in the function p.adjust)  to account for multiple testing.Analyses of PRSs were performed using generalized estimating equations using the R package drgee, with robust SEs, based on clustering related individuals to account for twins in the data. The principal components, sex, and age (for measures that were assessed at 9 or 12 years of age) were included as covariates. First, we tested for association between PRSs for each of the 8 discovery GWASs of psychiatric disorders and the corresponding continuously distributed trait(s). Second, these analyses were repeated after excluding individuals diagnosed with the relevant psychiatric disorder based on available information on 36 we reran all twin and PRS analyses for 3 specific DSM-IV ASD dimensions  and 2 DSM-IV ADHD dimensions (hyperactivity/impulsivity and inattention). These domains were assessed by dividing the Autism-Tics, AD/HD, and Other Comorbidities Inventory ASD and ADHD subscales based on prior work.9Because there is some evidence of genetic specificity within ASD and ADHD trait domains,Phenotype data were available for 13 923 twin pairs  at 9 years of age, 5165 pairs  at 15 years of age, and 4273 pairs  at 18 years of age. Genetic data were available for 13 412 individuals . Probandwise concordances for each diagnosis, which represent the probability of co-twins of probands also receiving a given diagnosis, are given in eTable 3 in the For all traits, AE-s or AE models fit best except for ADs at 9 and 12 years of age, where there was a small, significant C estimate  showed modest to strong genetic correlations with related traits. Squaring these correlations gives the proportion of genetic variance shared between 2 traits; thus, our findings suggest that at least a modest proportion of genetic factors associated with clinical psychiatric disorders are associated with continuous variation in milder traits of these disorders. This finding replicated the results of an earlier study26 Studies of traits in community-based samples may also be more representative than clinical samples while generating results that, to a degree, generalize to clinical populations.Our study went beyond traditional twin studies by directly estimating the genetic correlation between psychiatric disorders and continuous traits; we also assessed the association between disorder PRSs and continuous traits in the same sample. Dichotomous definitions of psychiatric disorders may not be optimal for all studies of these phenotypes. Our results indicate that moving beyond dichotomous definitions of psychiatric disorders to joint analyses of disorders and traits may increase statistical power and yield insights into the biology of these traits. The value of such an approach was demonstrated by a recent ADHD GWAS.37 and ID.38 Correlations between environmental factors associated with psychiatric disorders and traits were also lower than the genetic correlations, suggesting that environmental factors associated with psychiatric disorders may be more unique to psychiatric disorders than genetic factors. Future work identifying risk factors that are not shared between psychiatric traits and disorders may thus help elucidate why some individuals present with mild traits, whereas others manifest clinically severe problems.However, genetic correlations in the twin analyses were less than 1. Associations between PRSs and traits had small effect sizes . Thus, only a proportion of genetic risks were shared across disorders and traits. Although twin methods capture all sources of inherited genetic risk, PRSs are limited to additive common effects. Rare genetic variants may have a more deleterious effect than common variants; however, several studies have demonstrated genetic overlap from rare variants across disorders and continuous measures of ASDA unique strength of our study was that we were able to perform both twin and molecular genetic analyses in 1 cohort. Linkage with nationwide patient records enabled us to focus on clinical diagnoses of psychiatric disorders as opposed to percentile-based cutoffs or screening diagnoses. This study design allowed the exclusion of individuals diagnosed with psychiatric disorders from PRS analyses, thus ruling out the possibility that observed effects were driven by individuals with clinically recognized problems. Assessments from multiple ages and raters led to a wealth of information on psychiatric phenotypes.Nonetheless, the sample was young. Although many disorders develop during childhood and adolescence, disorders such as schizophrenia, BD, and severe depression become more common with age. Because few of the participants had passed through the periods of high risk for these disorders, we could not perform twin analyses of schizophrenia or BD or exclude those individuals from PRS analyses. Studies of older individuals are thus needed as a next step. In addition, the NPR covers specialist care; thus, diagnoses ascribed through primary care were likely missed.39 may have decreased the observed effect sizes, particularly at later ages. In addition, the estimates of variance explained were low although typical of PRS analyses  because PRSs capture only the most strongly associated common variants and rely on discovery GWAS power to accurately estimate SNP effects. Although the PRS results showed the presence of associations between genetic risk for disorders and traits consistent with the twin analyses, the degree to which common genetic risks are shared is unclear from our study. Future studies that use larger GWAS data sets and other methods are needed to estimate genetic correlations from molecular genetic data.Specific limitations of the genetic analyses include modest sample sizes and associated low power of several of the discovery GWAS analyses used to derive PRSs; for certain phenotypes, these limitations may have led to less robust results . Nonrandom attrition, previously reported to affect genetic studies,40 In addition, all the continuous measures used in this study were designed to assess potentially problematic behaviors. As such, we cannot extrapolate our results to the very low positive end of each trait distribution. Studies that use measures that are sensitive to lower scores are needed.41We did not have the statistical power to divide the cases by severity or diagnostic subtype. Thus, we cannot conclude that all levels of disorder severity share genetic risks with milder traits. This topic will be an important focus in future research because there is some evidence that severe ID is genetically independent from cognitive abilities and milder ID.Although our results do not rule out the possibility that some genetic factors are not shared between psychiatric disorders and milder traits of these disorders, they suggest that a proportion of genetic risks associated with psychiatric disorders are also associated with milder traits of these disorders. Future studies are needed to replicate our findings in older individuals and to test whether more severe forms of psychiatric disorders also share genetic risks with milder traits.


The mainstream of research in genetics, epigenetics, and imaging data analysis focuses on statistical association or exploring statistical dependence between variables. Despite their significant progresses in genetic research, understanding the etiology and mechanism of complex phenotypes remains elusive. Using association analysis as a major analytical platform for the complex data analysis is a key issue that hampers the theoretic development of genomic science and its application in practice. Causal inference is an essential component for the discovery of mechanical relationships among complex phenotypes. Many researchers suggest making the transition from association to causation. Despite its fundamental role in science, engineering, and biomedicine, the traditional methods for causal inference require at least three variables. However, quantitative genetic analysis such as QTL, eQTL, mQTL, and genomic-imaging data analysis requires exploring the causal relationships between two variables. This paper will focus on bivariate causal discovery with continuous variables. We will introduce independence of cause and mechanism (ICM) as a basic principle for causal inference, algorithmic information theory and additive noise model (ANM) as major tools for bivariate causal discovery. Large-scale simulations will be performed to evaluate the feasibility of the ANM for bivariate causal discovery. To further evaluate their performance for causal inference, the ANM will be applied to the construction of gene regulatory networks. Also, the ANM will be applied to trait-imaging data analysis to illustrate three scenarios: presence of both causation and association, presence of association while absence of causation, and presence of causation, while lack of association between two variables. Telling cause from effect between two continuous variables from observational data is one of the fundamental and challenging problems in omics and imaging data analysis. Our preliminary simulations and real data analysis will show that the ANMs will be one of choice for bivariate causal discovery in genomic and imaging data analysis. Despite significant progress in dissecting the genetic architecture of complex diseases by association analysis, understanding the etiology, and mechanism of complex diseases remains elusive. Using association analysis and machine learning systems that operate, almost exclusively, in a statistical, or model-free modes as a major analytic platform for genetic studies of complex diseases is a key issue that hampers the discovery of mechanisms underlying complex traits Pearl, .X, Y are two random variables with joint distribution P. If an external intervention that is from outside the system under consideration forces the variable X to have the value x and keeps the rest of the system unchanged, after Y is measured, the resulting distribution of Y, P(Y|do (x)) is defined as the causal effect of X on Y. Power of causal inference is its ability to predict effects of actions on the system  with continuous variables , association of continuous variables  with continuous variables , association of discrete variables (DNA variation) with binary trait (disease status), and association of continuous variables  with binary trait (disease status). All these four types of associations can be extended to four types of causations. This paper focuses on studying causal relationships between two continuous variables.https://sph.uth.edu/research/centers/hgc/xiong/software.htm.Many causal inference algorithms using observational data require that two variables being considered as cause-effect relationships are part of a larger set of observational variables  and the conditional distribution P(Y|X) of Y given X are independent. Statistics provides definition of independence between two random variables, but provides no tools for defining independence between two distributions  as a major tool for bivariate causal discovery. Assume no confounding, no selection bias and no feedback. Consider a bivariate additive noise model X and EY are independent. Then, the density PX, Y is said to be induced by the additive noise model (ANM) from X to Y  are independent ], then the linear model is identifiable. Otherwise, the linear model is not identifiable  to measure the degree of dependence between the residuals and potential causal variable  and kx. In practice, we often use the Gaussian kernel function. Compute the Kernel matrices:Step 3: Select two kernel functions Step 4: Compute the HSCI for measuring dependence between the residuals and potential causal variable.where In summary, the general procedure for bivariate causal discovery is given as follows  + EY andRegress X on Y: X = fX(X) + EX.Regress Dtrain = {Yn, Xn} to predict residuals:Step 3: Use the test data set and estimated non-parametric regression model that fits the training data set Step 4: Calculate the dependence measures Step 5: Infer causal direction:If P-values of the independence tests. To overcome these limitations, the permutation/bootstrap approach can be used to calculate the P-values of the causal test statistics. The null hypothesis isWe do not have closed analytical forms for the asymptotic null distribution of the HSIC and hence it is difficult to calculate the H0: no causations X → Y and Y → X .Calculate the test statistic:np. For each permutation, we fix xi, i = 1, …, m and randomly permutate yi, i = 1, …, m. Then, fit the ANMs and calculate the residuals EX(i), EY(i), i = 1, …, m and test statistic TC. Repeat np times. The P-values are defined as the proportions of the statistic DTE). After cause is identified, we then use Equations (4) and (5) to infer causal directions X → Y or Y → X.Assume that the total number of permutations is In everyday language, correlation and association are used interchangeably. However, correlation and association are different terminologies. Pear correlation coefficient is defined as where β≠0.X → Y is identified by the ANM:The causation X and ε follow a normal distribution, then cov = 0 if and only if X and ε are independent. If X and ε are not normal variables, this statement will not hold. For general distribution, we extend the concept of covariance to cross covariance operator X and ε, X and Y are independent  causation X → Y, but no linear correlation, and (c) linear correlation, but no causation X → Y.Now we give examples of a pair of random variables to illustrate existence of three cases: (a) both linear correlation and causation a) Both linear correlation and causation X → Y.Y = f(X). When Y = f(X), Equation (9) holds, which implies X → Y. If we assume that h(X) = X and g(Y − f(X)) = Y − f(X), then Equation (9) holds and implies thatWe consider a special case: f(X) = βX, then Equation (10) impliesIf we further assume This is estimation of linear regression coefficient.b) CausationX → Y, but no linear correlationConsider the model:X follows a uniform distribution between −2 and 2 and ε follows a uniform distribution between −1 and 1.where Y = 5X2 + ε. Assume that 2,000 subjects were sampled. Permutation was used to calculate P-value for testing causation. We found that the Pearson correlation was −0.00070 and P-value for testing causation X → Y was 10−5. This example showed the presence of causation, but lack of linear correlation (Pearson correlation was near zero).Figure c) Linear correlation, but no causationX → Y.Consider the model Figure :Z ~ N, ε1 ~ N, ε2 ~ N, Z, ϵ1, ε2 are independent.and The model can be rewritten asY and X exists.First we show that linear correlation between In fact,Y and X exists.Thus, the Pearson linear correlation coefficient is equal to X and ε2 − ε1 are not independent.Next we show that cov = −var(ε1) = −1 and X, ε2 − ε1 follow normal distribution. Since the covariance between X and ε2 − ε1 is not equal to zero, this implies that X and ε2 − ε1 are not independent. The conditional distribution PY|X is the distribution of ε2 − ε1. But, we show that the normal variables X and ε2 − ε1 are not independent. This implies that the distribution P(X) and PY|X are not independent. Therefore, we finally show that there is no causation X → Y.Note that Y → X.Similar conclusions hold for t distribution. We assumed that the cause X follows a normal distribution N.To investigate their feasibility for causal inference, the ANMs were applied to simulation data. Similar to Nowzohour and Bühlmann , we consN and t distribution with 5 degrees of freedom:First we consider two models with a quadratic function and two types of random noise variables, normal Model 1:b ranges from −10 to 10 and ε1 is distributed as N .where the parameter Model 2:b is defined as before and ε2 is distributed as t distribution with 5 degrees of freedom.where the parameter b ∈  was discretized. For each grid point, 1,000 simulations were repeated. For each simulation, 500 samples were generated. The ANMs were applied to the generated data. Smoothing spline is used to fit the functional model. The true causal direction is the forward model: X → Y. The false decision rate was defined as the proportion of times when the backward model Y → X is wrongly chosen by the ANMs. Figures b for the models 1 and 2, respectively. We observed from Figures b = 0. This showed that when the model is close to linear, the ANMs could not identify the true causal direction. However, when b moved away from 0, the false decision rates approached 0 quickly. This showed that when the data were generated by non-linear models, with high probability, we can accurately identify the true causal directions.The parameter space To further confirm these observations, we consider another two non-linear functions.Model 3:Model 4:Model 5:Model 6:b and the noise variables ε1 and ε2 were defined previously.where the parameter X → Y for the models 3, 4, 5, and 6 were presented in Figures The false decision rates of the ANMs for detecting the true causal direction To evaluate the performance of the ANMs for bivariate cause discovery, we calculate the type 1 error rates. We consider two scenarios: (a) no association, (b) presence of association.No associationX ~ N, Y ~ N and X, Y are independent. Number of permutations was 500. Number of replication of tests was 1,000. The sampled subjects from the generated population for type 1 error rate calculations were 500, 1,000 and 2,000 respectively. The test statistic Tc and permutations were used to test for causation between two variables X and Y. Table We first generated the data with 100,000 subjects from the model: Presence of associationX ~ N, Y ~ N, X and Y were associated, but without causation. Number of permutations was 500. Number of replication of tests was 1,000. The sampled subjects from the generated population for type 1 error rate calculations were 500, 1,000 and 2,000 respectively. The test statistic Tc and permutations were used to test for causation between two variables X and Y. Table Then, we generated the data with 100,000 subjects from the model: In summary, Tables S1, S2 showed that type 1 error rates of the ANM based on permutation even in the presence of association were not significantly deviated from nominal levels.To further evaluate the performance of the ANMs for bivariate cause discovery, we used simulated data to estimate their power to detect causation. We generated data with 100,000 subjects from the causal model:xj ~ N, X ~ Nand N ~ N. X and N are independent, and Tc and permutations were used to test for causation between two variables X and Y. Table where X causes changes in expression of gene Y or vise verse changes in expression of gene Y causes changes in expression of gene X.Regulation of gene expression is a complex biological process. Large-scale regulatory network inference provides a general framework for comprehensively learning regulatory interactions, understanding the biological activity, devising effective therapeutics, identifying drug targets of complex diseases and discovering the novel pathways. Uncovering and modeling gene regulatory networks are one of the long-standing challenges in genomics and computational biology. Various statistical methods and computational algorithms for network inference have been developed. The ANMs can also be applied to inferring gene regulatory networks using gene expression data. Similar to co-gene expression networks where correlations are often used to measure dependence between two gene expressions, the ANMs can be used to infer regulation direction, i.e., whether changes in expression of gene The ANMs were applied to Wnt signaling pathway with RNA-Seq of 79 genes measured in 447 tissue samples in the ROSMAP dataset  data with 91 individuals with Diffusion Tensor Imaging (DTI) and cholesterol phenotypes measured at four time points: baseline, 6, 12, and 24 months. After normalization and image registration, the dimension of a single DTI image is 91 × 109 × 91. Three dimensional functional principal component analysis (3D-FPC) was used to summarize imaging signals in the brain region  and association of cholesterol with images of 19 brain regions where the canonical correlation method was used to test association  and temporal R hippocampus regions , and only association of cholesterol with imaging signal variation at 12 months in the temporal L region . Figures P-value < 0.0003 at 12 months, P-value < 0.00004 at 24 months), but no causation . Figure After image imputation, DTI images at all four points and cholesterol and working memory of 91 individuals were available. The DTI images were segmented into 19 brain regions using the Super-voxel method  (image → working memory), but identified no association of working memory with imaging signal variation in the temporal R (hippocampus) region   at 24 months with 4) Table . Figure 4) Table  and was 4) Table . Abnorma4) Table .X be altitude and Y be temperature. Meteorology assumes that places with higher altitude tend to be colder than those with lower altitude (roughly 1 centigrade per 100 meter). There is no doubt that altitude is the cause and temperature the effect, so ground truth is X → Y. P-value of using the ANMs and permutation test for detecting the causation was 0.001.Next we investigate two examples from the gold-standard data set in . In other words, causal generating processes of a system's variables are independent. If we consider two variables, the ICM states that distribution of cause and conditional distribution of effect given the cause are independent.The second issue is how to measure independence (or dependence) between two distributions. Statistics only provides tools for measuring independence between two random variables. There are no measures or statistics to test independence between two distributions. Therefore, we introduce algorithmic information theory that can offer notion and mathematical formulation of independence between two distributions or independence of mechanisms. We use algorithmic mutual information to measure independence between two distributions which can be used to assess causal relationships between two variables. Algorithmically independent conditional implies that the joint distribution has a shorter description in causal direction than in non-causal direction.X and conditional distribution PY|X of effect given the cause is equivalent to the independence of two random variables X and EY in the ANM.The third issue is to develop causal models that can easily assess algorithmic independent conditions. The algorithmic independent condition states that the direction with the lowest Kolmogorov complexity can be identified to be the most likely causal direction between two random variables. However, it is well-known that the Kolmogorov complexity is not computable . Some theoretical analysis and real trait-imaging data analysis showed that there were three scenarios: (1) presence of both association and causation between two variables, (2) presence of association, while absence of causation, and (3) presence of causation, while lack of association in causal analysis.Finally, in real imaging data analysis, we showed that causal traits change the imaging signal variation in the brain regions. However, the traits that were associated with the imaging signal in the brain regions did not change imaging signals in the region at all.The experiences in association analysis in the past several decades strongly demonstrate that association analysis is lack of power to discover the mechanisms of the diseases and provide powerful tools for medicine. It is time to shift the current paradigm of genetic analysis from shallow association analysis to more profound causal inference. Transition of analysis from association to causation raises great challenges. The results in this paper are considered preliminary. A large proportion of geneticists and epidemiologists have serious doubt about the feasibility of causal inference in genomic and epigenomic research. Causal genetic analysis is in its infantry. The novel concepts and methods for causal analysis in genomics, epigenomics, and imaging data analysis should be developed in the genetic community. Large-scale simulations and real data analysis for causal inference should be performed. We hope that our results will greatly increase the confidence in genetic causal analysis and stimulate discussion about whether the paradigm of genetic analysis should be changed from association to causation or not.RJ: Perform data analysis and write paper; NL and ZH: Perform data analysis; DB: Provide data and result interpretation; LJ: Design project; MX: Design project and write paper.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


There is evidence that lower height is associated with a higher risk of coronary artery disease (CAD) and increased risk of type 2 diabetes (T2D). It is not clear though whether these associations are causal, direct or mediated by other factors. Here we show that one standard deviation higher genetically determined height (~6.5 cm) is causally associated with a 16% decrease in CAD risk . This causal association remains after performing sensitivity analyses relaxing pleiotropy assumptions. The causal effect of height on CAD risk is reduced by 1–3% after adjustment for potential mediators . In contrast, our data suggest that lung function  is a mediator of the effect of height on CAD. We observe no direct causal effect of height on the risk of T2D. Eirini Marouli et al. use Mendelian randomisation analyses to investigate the causal relationship between adult height, coronary artery disease (CAD) and type 2 diabetes (T2D) in the UK Biobank. They find that height has a causal effect on CAD, which is mediated by lung function, while there is no direct effect on the risk of T2D. Other studies have tried to elucidate this inverse association by using a twin design5 or Mendelian randomisation approaches7. A decrease of one standard deviation in genetically determined height (~6.5 cm) has been associated with a 13% higher risk of coronary artery disease (CAD)4. Health is sometimes compromised in favour of immediate survival or reproduction8. Subtle trade-offs are both predicted and observed in growth, health and reproduction9. Another trade-off is between reproduction and longevity, with many studies indicating that parental survival declined in proportion to the number of children produced10. There is also controversial evidence suggesting taller populations are not always in lower risk of CAD11.Evidence from observational studies suggests that height is associated with different disease outcomes12, can therefore be applied to investigate any causal effect that adult height may have on cardiometabolic outcomes, and provide some insight about potential mechanisms. Mendelian randomisation offers major advantages; for example, germ-line genetic variants are assorted during formation of gametes prior to conception and are not confounded by lifestyle or environmental factors in ethnically homogeneous samples of unrelated individuals. Thus, it becomes possible to investigate how height variants may affect cardiometabolic risk and whether this effect is direct or mediated through other biological pathways.In situations where randomised trials are inappropriate or impossible, Mendelian randomisation provides a good alternative to study the causal relationship between a trait and a disease outcome. Mendelian randomisation which is an instrumental variable-based method to infer causality in observational studies14 harbouring over 960 independent associations. In our latest study, height-increasing alleles at all 606 height-associated variants (Exome Chip data) were enriched for nominally significant protective effect on several cardiometabolic traits: total cholesterol , triglyceride  and coronary artery disease .Mendelian randomisation relies on the availability of genetic variants robustly associated with height. So far, large-scale meta-analyses of genome-wide association studies (GWAS) have identified circa 600 loci associated with adult height15. Adult stature is the result of bone elongation. Bone serves as a scaffold for other organs and is an endocrine organ involved in the regulation of glucose and energy metabolism. Consequently, hormones implicated in bone remodelling may affect risk of cardiometabolic disease16. Adult height has also been associated with cardiorespiratory mortality17. Epidemiological studies have reported that much of this association can be attributed to lung function17 and there is evidence suggesting that measures of lung development can serve as biomarkers for childhood exposures that may modify an individual’s risk of developing CAD18. Previous efforts have reported that taller individuals have a lower risk of CAD giving as potential explanations that taller people have a better lung function7, but it is still unclear whether and to which extent lung function mediates this effect.Besides CAD, greater adult stature has also been reported to be associated with lower risk of type 2 diabetes (T2D)19. Height has been also reported to have a strong positive effect on educational attainment, with 2.5 additional centimetres in height yielding one additional month of schooling20. There is also support for low education as a causal risk factor in the development of CAD21. Previous studies have tried to clarify the associations between height and its association with CAD risk factors7, but it is still unclear which risk factors, mediate the inverse association between height and CAD.In general, height has an important partial role in determining several aspects of an individual’s socioeconomic status, including education, income and job class22 by using a comprehensive set of height associated variants. We perform instrumental variable analysis using individual data and 828 of the previously established height-associated SNPs, which explain around 30% of height variation14. In this context we investigate glycaemic measures , 2 h postprandial glucose-2hGlu); blood pressure measures (systolic blood pressure (SBP), diastolic blood pressure (DBP), pulse pressure); obesity traits ; lipid measures , high density lipoprotein (HDL), triglycerides); and lung function measures (forced expiratory volume in 1 s (FEV1) and forced vital capacity (FVC)). We also take into account socio-economic status variables including: age in years at completion of full time education, education coded as college or University degree, income variable representing annual household income before tax and downsend deprivation index . Our results show that increased height reduces the risk of CAD by 16% and traditional risk factors attenuate this effect by only 1–3% suggesting different mediating pathways. Adjustment for the genetic effect of lung function (measured by FEV1 and FVC) completely abolishes the effect of height on CAD. We do not observe any direct effect of height on T2D risk.Here, we test whether height is causally related to cardiometabolic disease (CAD and T2D), including traditional risk factors in the first instance. We undertake Mendelian randomisation analyses in UK Biobank (UKBB)To test whether genetically determined height is related to cardiometabolic disease phenotypes, independently of traditional risk factors, we undertook Mendelian randomisation analyses in UKBB including 449,094 unrelated British participants with both phenotypic and genetic data     in order to estimate the causal effect for height that is independent of each cardiometabolic factor. Our results suggest that the effect of height on CAD is independent of each risk factor tested whereas its effect on T2D was completely abolished after adjustment for BMI . In each case the remaining variants constitute valid instruments and their causal effect estimates will therefore be immune to confounding. After excluding the variants associated with BMI, a 1 standard deviation increase in height, measured by the genetic score (weighted genetic score gave very similar results), was associated with 22% lower risk of CAD , the same as the observed effect without instrument exclusions. Similar results were obtained also after excluding variants associated with any lipid trait, a 1 standard deviation higher height was associated with a 13% decrease in the odds of CAD , whereas exclusion of variants associated with BP resulted in an 15% lower risk  of CAD  or lipids  resulted in an attenuation of the height effect after removing BMI, lipid or BP associated variants from the two-stage analysis ; weighted median, mode-based estimate (MBE)24, generalised summary-data-based Mendelian randomisation (GSMR)25 and MR-PRESSO26 approaches.We accessed summary statistics from the largest genetic studies publically available for height , CAD , and T2D . Two-sample Mendelian randomisation analyses were performed using the inverse-variance weighted (IVW) methodConsistency in results across methods builds confidence in the obtained estimates, as they rely in different assumptions and models of horizontal pleiotropy. Funnel plots were also assessed for any deviations which can be suggestive of pleiotropy. We note that the plots appear generally symmetrical, suggesting no evidence for horizontal pleiotropy . The slope from the Egger regression was consistent with these findings , and no evidence of directional pleiotropy   assumption (see Methods) (Supplementary Data p = 2.91 × 10−21) ; 1 standard deviation increase in height 6.4 cm) was associated with a 14% (OR = 0.86) lower risk of CAD with no evidence for directional pleiotropy (Egger method) , but not when we excluded variants associated with lipids (p = 0.14) or BP (p = 0.08) (Supplementary Data p = 0.95)  slightly increased the signal, a 1 standard deviation higher height (cm) was associated with a 19% (-BMI variants), 14% (-BP) or 19% (-lipids) lower risk of CAD (Supplementary Data P p = 0.0 (Supplemp = 7.32 × 10−13). However, for T2D no causal effect was observed in the multiple stage least square approach after adjustment for BMI    was fulfilled. Therefore, we explored the role of BMI in the relation between height and CAD or T2D. Valid instruments for height and BMI were included. We applied a multiple-stage approach (see Methods) in UKBB to assess the direct genetic effect of height on CAD and T2D  to 0.86 (95% CI 0.83–0.89) with adjustment for LDL (Supplementary Data p = 0.95)  using summary statistics data, in order to interrogate whether the exposure is causally associated with the outcome given the risk factors. Using this approach, we estimated the effect of height on CAD and T2D risk adjusting for the effect of each instrument with genetic BMI28, T2D29 and lung function on adult height by two-sample Mendelian randomisation using summary statistics data.As a negative control, we investigated the effect of the known CAD associated variantsp = 0.57) on height  and no evidence or directional pleiotropy (p = 0.62) from the MR-Egger regression  but also the extent to which traditional risk factors , lung function and socio-economic status may mediate such effects.30, our Mendelian randomisation results provided strong evidence for a protective causal effect of adult height on CAD risk, 1 standard deviation higher height (~6.5 cm) was causally associated with a 16% lower risk of CAD  using summary statistics data.Consistent with previous studies31. Shorter individuals have increased heart rate, increased augmentation of the systolic pulse, which may increase ventricular systolic work32. Furthermore, shorter individuals have smaller vessel calibre, so their arteries can become more easily occluded and subsequently increase CAD risk35. However, exclusion of variants that are nominally associated with BP only marginally attenuated the causal association between height and CAD. Lipids appeared to have an even more modest effect in comparison to BP as possible mediators of the causal effect of adult height on CAD risk. There is also evidence suggesting that increased height is associated with increased risk of cancer and among mechanisms linking height with CAD and cancer are insulin and insulin-like growth factor signalling pathways36.Our results suggest that the effect of height on CAD is not mediated via socio-economic status variables. Furthermore, this effect is not completely mediated by traditional cardiometabolic risk factors and may involve alternative biological pathways. For example, it has been postulated that the inverse association between height and CAD may be due to shorter individuals having higher BPIn contrast to the modest effects of BP and lipids as possible mediators of the effect of height on CAD, we found that lung function (as measured by FVC and FEV1) is a mediator. Mediation analyses accounting for the genetic effect of FEV1 or FVC abolished the association between height and CAD.We did not find any evidence supportive of a direct causal effect of height on T2D, despite the modest association we observed based on observational data. Our results suggest that while there is an indirect effect on T2D, this effect is not direct and may be mediated by multiple factors .37. Such participants tend to be slightly healthier than the underlying population participants selected from. While UK Biobank participants are not representative of the general population , valid assessment of exposure-disease relationships are nonetheless widely generalisable and do not require participants to be representative of the population at large. In the two-sample Mendelian randomisation, where independent samples were used, weak instrument bias may result in bias towards the null. Similarly, in mediation analyses weak instrument bias could result in underestimation of the mediating effects. However, we assumed that estimates come from two different homogenous population studies without overlapping samples. The use of large sample sizes and instruments with large F statistics in our analyses is likely to have minimised any effect on the obtained results. Also, the IVW method has been shown to lead to slightly biased estimates (10% in either direction) in the presence of binary outcome and to a natural correlation between causal estimates and standard errors that could contribute to the presence of heterogeneity misinterpretable as pleiotropy38.A potential limitation of our study is that we have assumed no interaction between height and the mediators. However, we were unable to test for this as we used aggregated genome-wide data for glycaemic and lipid traits . Also, selection bias is an issue when using any general population cohort, including the UK Biobank30. Although we considered several socio-economic factors, it remains possible that we are not fully accounting for all confounding by other socio-economic status parameters in our Mendelian randomisation analyses20.Adult height is known to be associated to different socio-economic factorsIn summary, we show that the main mediator of causal effect of height on CAD is lung function whereas traditional CAD risk factors have only marginal effects. We also show that there is no evidence of a direct causal effect between height and T2D.22. Data underwent central quality control (see (http://biobank.ctsu.ox.ac.uk). UKBB samples were excluded due to sample relatedness determined as kinship coefficient greater than 0.0884.The UKBB recruited more than 500,000 individuals aged 37–73 between 2006 and 2010 across Great Britain. All participants provided information with questionnaires and interviews regarding health status, anthropometric characteristics as well as blood, urine and saliva samplesa ± 5 standard deviation away from the mean of the sampled population.Height (cm) was measured using a Seca 202 device in all participants of UKBB. We excluded individuals who exceeded BMI was constructed from height and weight measured during the initial Assessment Centre visit. Value is not present if either of these readings were omitted. Continuous traits were adjusted for demographics, genetic structure and converted to a normal distribution to limit the influence of any population stratification and provide standard deviation effect sizes. Residuals of the exposure from standard linear regression were taken by using as covariates: age, sex, five principal components and batch. The residuals were then inverse normalised in order to improve comparability with summary data Mendelian randomisation analysis.CAD definitions: UKBB self-reported data: ‘Vascular/heart problems diagnosed by doctor' or ‘Non-cancer illnesses that self-reported as angina or heart attack’. Self-reported surgery defined as either PTCA, CABG or triple heart bypass. HESIN hospital episodes data and death registry data using diagnosis and operation—primary and secondary cause: MI defined as hospital admission or cause of death due to ICD9 410–412, ICD10 I21-I24, I25.2; PTCA is defined as hospital admission for PTCA ; CABG is defined as hospital admission for CABG (OPCS-4 K40–K46); Angina or chronic IHD defined as hospital admission or death due to ICD9 413, 414.0, 414.8, 414.9, ICD10 I20, I25.1, I25.5–I25.9.Type 2 diabetes definitions: UKBB self-reported data: ‘Diabetes by Doctor’ or “Non-cancer illnesses that self-reported as T2D’. HESIN hospital episodes data and death registry data using diagnosis and operation—primary and secondary cause: T2D defined as hospital admission or cause of death due to ICD10 E11.Hypercholesterolaemia definitions: UKBB self-reported data: ‘Non-cancer illnesses that self-reported as Hypercholesterolaemia. HESIN hospital episodes data and death registry data using diagnosis and operation—primary and secondary cause: Hypercholesterolaemia defined as hospital admission or cause of death due to ICD10 E780, E7800, E7801.Whether observational associations between height and cardiometabolic disease have been documented, for consistency purposes we performed conventional regression analysis of each cardiometabolic disease (CAD and T2D) against height by using logistic regression. Height was the independent variable for each trait of interest by using linear and logistic regression for continuous and binary traits, respectively. These associations were adjusted for age, sex, first 40 PCs and batch. This information was compared with the estimates derived from instrumental variable analyses.r2 ≤ 0.05) and GWA significant (p < 5 × 10−8) SNPs were selected from the large GWA studies for height14.Genotypes were extracted from UKBB imputation dataset  14. In the derived weighted genetic score, β represents the association between an additional weighted height-associated allele at each single nucleotide polymorphisms (SNP) and height from large GWA meta-analyses14: weighted score = β1 × SNP1 + β2 × SNP2 + …βn × SNPn. We present the range of the possible number of weighted height-increasing alleles, by dividing the score by the average effect size of the variants for each individual39. This is a transformation of the wGRS so that the range equalled that of the unweighted score. Linear regression for each score with height and logistic regression for each score with disease status were performed.The unweighted genetic scores for each individual were created by summing the number of height increasing alleles for the 828 SNPs they are carrying. Weighted genetic scores were also modelled. The weighted genetic score was calculated as the sum of the number of height-associated alleles, weighted by the relative effect size (β-coefficient) reported from the discovery meta-analysisp-value and standard errors were extracted. In order to test the statistical significance of the association of the instrument with height, an F statistic was calculated using the formula: (β exposure × β exposure)/(se exposure × se exposure)40.SNPs from large GWAS study of height to date were identified by the 2015 and 2017 summary statistics files from the GIANT (Genetic Investigation of Anthropometric Traits) consortium. Data on effect and other alleles for each of the 828 LD pruned variants in up to 700,000 individuals of European descent, along with allele frequencies, beta coefficients for allele dose, and a 6.4 cm change in height, 3. For this purpose LD between all variants was estimated in European samples from 1000 Genomes using Plink software version 1.941. When two or more SNPs were in LD (r2 > 0.05) only the most strongly associated variant with height, based on p-value, was kept.One condition of Mendelian randomisation is that exposure-related SNPs  must not be in LD with each other, as that can result in confoundingF statistic and the R2 value. It is substantial to have large studies, especially in instances where the instrumental variable explains a small amount of the variance in the exposure (R2). Genome wide association studies for height have yielded a large number of genetic variants that account for around 30% of height heritability. That allows the use of strong instruments to be developed. The instrumental variable has to be independent of any confounder45. When using individual level data, known confounders can be checked. In two-sample Mendelian randomisation, confounders can obstruct testing of this assumption due to lack of summary data results on the association between the candidate genetic instruments and the confounders. The instrumental variable is independent of the outcome, given the exposure and any possible confounders. The instrumental variable should not influence the outcome on an alternative path, other than through the exposure. This assumption is violated by horizontal pleiotropy, in which there are alternative pathways that the instrumental variable can affect the outcome.Mendelian randomisation relies on certain assumptions , T2D (DIAGRAM)29 using two-sample Mendelian randomisation methods. To investigate potential mediators, genetic associations with fasting insulin, fasting glucose, 2hGlu and HbA1c were obtained from MAGIC, http://www.magicinvestigators.org/); HDL-cholesterol, LDL-cholesterol, total cholesterol and triglycerides were obtained from GLGC (http://csg.sph.umich.edu/abecasis/public/lipids2013/); anthropometric traits for GIANT ; and BP from ICBP46. Associations for lung function (FEV1 and FVC), socio-economic status variables and body fat percentage summary data were extracted from http://www.nealelab.is/uk-biobank. Summary statistics are provided in Supplementary Data We first performed an instrumental variable analysis  in UKBB, where we had access to individual level data, and then expanded this analysis to the largest summary statistics data sets currently available, assuming homogeneity among the studies. We used summary data from genetic studies of the associations of height associated variants with height from GIANT meta-analysesThe Mendelian randomisation approach used in this study was based on the following assumptions: the height genetic scores had a strong association with measured height; the height genetic scores were not associated with confounding factors that could bias the observational association between height and cardiometabolic disease; the height score was related to the outcome only through its effect on the exposure, assuming a linear relationship between height and the logit-transformed outcome.49. The analysis was performed in two stages. First, the association between height genetic score and height was assessed. These predicted values were then used as the independent variable and disease status as the dependent variable in a logistic regression model. Analyses were adjusted for age, sex, 40 principal components and batch effect.In order to estimate the causal effect of height on disease status we performed instrumental variable analysis by using height genetic score as instrument. For the binary traits, we used the two-stage estimator (logistic control function estimator)Two-sample Mendelian randomisation was undertaken using genome-wide association summary data from separate samples, where data of the genotypes and the exposure of interest are available in one sample, and data on genotype and the outcome of interest are available in the other. For this part no ethical approval was sought as all data were derived from summary statistics of published GWAS studies, with no individual-level data used.Coronary artery disease genotyping data were derived from the most recent meta-analysis of Cardiogram+C4D, which investigated the association of 7 M variants after imputation in up to 30,000 cases. The per-allele log-OR of CAD was extracted together with its standard error for each of the independent genome-wide significant height variants. Effect sizes were aligned to the height increasing allele.50. Wald ratios were estimated for each SNP by dividing the per allele log-OR for CAD (beta_gy) by the per-allele effect on height for each SNP (beta_gx). Standard error for each Wald ratio was derived from the standard error of the variant-outcome association divided by the variant-exposure association for each instrument. We calculated the Wald ratio estimate where outcome ~ genetic score and exposure ~ genetic score estimates were obtained using the previous regression models with the genetic score.The two-sample Mendelian randomisation was undertaken using previously described methodsQ and quantified with the I2 index51. We also used the Mendelian Randomization package to perform IVW analysis assuming random effects52.Conventional linear regression analysis of the variant-exposure association and variant-outcome association for each instrument was undertaken and weighted by inverse variance. The point estimate is equal to that derived from fixed-effect meta-analysis. The IVW method assumes that all variants are valid instrumental variables. An IVW corrected for the standard errors of each instrument method was also applied. In this approach we corrected for the correlation between the associations of the instrument with the exposure and the association of the instrument with the outcome. When the IVW method shows substantial heterogeneity, this means that there may exist alternative pathways through which the SNPs affect the outcome . Heterogeneity for the Wald ratios was tested with the Cochran’s 50.MR-Egger method is more robust to potential violations of the standard instrumental variable assumptions. This method was used to address the issue of the aggregate unbalanced horizontal pleiotropy, which could violate the third assumption of instrumental variable analysis. MR-Egger is similar to the IVW method except that the intercept is not constrained to pass through the originMR-Egger method uses a weighted regression with an unconstrained intercept to regress the effect sizes of the variant-outcome associations against effect sizes of variant-exposure associations. The unconstrained intercept removes the assumption that all genetic variants are valid instruments. This method is less prone to confounding from possibly pleiotropic variants which could have stronger effects on outcomes compared to the effect on the exposure.Q statistic graphically.When a non-zero intercept from the MR-Egger is observed, that would suggest that there are pleiotropic effects; this could result in bias of the IVW estimates, which are in the direction indicated by the intercept term. The estimate for the effect of the exposure on the outcome, is provided by the slope of the MR-Egger. It is important to mention that this estimate is correct, taking into account an additional assumption, the InSIDE (instrument strength independent of direct effect) assumption, which means that the associations between the genetic variants and the exposure are independent of the effect that he variants have directly on the outcome. Funnel plots can be used to demonstrate the individual variant effects on the exposure and the outcome against the inverse of their standard error. When no pleiotropy is present, the instrumental variable estimates for each variant are symmetrically distributed around the point estimate. However, it is possible to understand the contribution of each instrumental variable on the overall 2 statistic in order to quantify the strength of NOME violation for MR-Egger. This measure is called IGX2 and lies between 0 and 1. A high value of IGX2 and close to 1, indicates that dilution does not affect the standard MR-Egger analyses performed53. For the main analyses we used the first order weights, which correspond to the first term of the Taylor series expansion, which approximate the standard error of the Wald ratio estimate53. The IVW and the MR-Egger regression analyses were repeated using the second order weights, which correspond to the first two terms of the Taylor series expansion54.IVW and Egger methods use weights that consider the SNP-exposure associations to be known rather than estimated. This is called as the NO measurement error assumption (NOME). We use an adaptation of the I55. In this method, the Mendelian randomisation estimates are ordered and weighted by the inverse of their variance. When more than 50% of the total weight comes from SNPs without pleiotropic effects, the median Mendelian randomisation estimate should remain unbiased. This method improves precision and is more robust to violations of the InSIDE assumption. If InSIDE holds, then MR-Egger is consistent, while the weighted median will be only if 50% of the total weight comes from SNPs without pleiotropic effects.The weighted median method was used to investigate pleiotropy24.The MBE method has presented less bias and type-I error rates in simulations than other methods under the null in many situations. The MBE relaxes the instrumental variable assumptions and is less prone to bias due to violations of the InSIDE assumption23, we also applied the method Generalised Summary-data-based Mendelian randomisation (GSMR) that performs a multi-SNP Mendelian randomisation analysis using GWAS summary-level data accounting for the sampling variance in the estimated SNP effects and remaining LD between SNPs. The GSMR R-package implements the GSMR method to test for putative causal association between a risk factor and a disease. We used 1000 Genomes (European population) imputed data to create the LD correlation matrix25.Given that the correlations between the SNP instruments could lead to biased  Mendelian randomisation standard errors26.MR-PRESSO   is a method that allows for the evaluation for horizontal pleiotropy in multi-instrument Mendelian randomisation analyses using genome-wide summary association data56 implemented in the publically available tool mRnd (http://cnsgenomics.com/). Power calculations are provided in Supplementary Fig. Calculations were performed using a non-centrality parameter-based approachTo further investigate the presence of pleiotropy and narrow down the set of height variants which may have a causal effect on the risk of CAD and T2D, we performed sensitivity analyses.Q statistic for each instrument. We then used some different thresholds (5th (L1), 1st (L2), 0.19th (L3) percentile of a chi-squared with 1 degree of freedom) and excluded variants which had a Q > L3, Q > L2 and Q > L1.First, we assessed which variants may contribute to the total heterogeneity, by estimating the Second, we assessed which variants are associated with any potential mediators including BMI, BP  and lipids . We excluded any height associated variant which showed evidence for association with these traits.57. We evaluated the proportion of the effect that is mediated by any of the potential mediators by the changes in the total effect of the genetically determined height and on the outcomes, assuming that the mediators are continuously measured variables (multivariable Mendelian randomisation). We estimated the total, direct and indirect effects of the risk factor on the outcome by using summary data27. It is recommended to provide estimates of the total and direct effects, but not the indirect effect, as calculation of the indirect effect relies on the linearity of the relationship that cannot occur with a binary outcome27.To estimate the effect of height on T2D and CAD taking into account the role of potential mediators, we performed multivariable Mendelian randomisation analyses, by using the IVW Mendelian randomisation method with summary statistics data, after adjusting for the effect of each instrument with the potential mediator58. The weighted regression method for calculating the direct effect is also equivalent to a two-stage regression method, except that the first stage also regresses the mediator on the genetic variants, and the second stage regresses the outcome on fitted values of the exposure and fitted values of the mediator. This two-stage approach can be undertaken to estimate the direct effect when individual-level data are available49.Using individual level data we also applied a three stage approach where we first estimated the fitted values of the height genetic risk score with height, second the fitted values of a BMI genetic risk score with BMI and finally we used these fitted values to estimate the direct effect of height on the outcomes28. We used a similar approach for the bidirectional Mendelian randomisation analyses with T2D. We used genome-wide associated with T2D in the DIAGRAM consortium29. We also performed bidirectional Mendelian randomisation analysis by using 268 lung function associated variants  as exposure to interrogate the effect of lung function on height. Our results suggest that there is no evidence of a causal effect between lung function and height with the Egger regression. Two-sample Mendelian randomisation analyses were conducted as described above for height and coronary artery disease.We performed bidirectional Mendelian randomisation analyses of the association of Coronary artery disease and height. To construct a genetic instrument for CAD, we used variants which reached genome-wide significance in the CARDIOGRAM+C4D consortium. For the SNP-exposure we used the effect estimates and standard error of the associations of each variant with CAD derived from the meta-analysisStatistical analysis was performed using R  software.Further information on experimental design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary DataReporting Summary


Heterobasidion annosum species complex is the most economically important disease of conifer trees in boreal forests. Wood decay in the infected trees dramatically decreases their value and causes considerable losses to forest owners. Trees vary in their susceptibility to Heterobasidion infection, but the genetic determinants underlying the variation in the susceptibility are not well-understood. We performed the identification of Norway spruce genes associated with the resistance to Heterobasidion parviporum infection using genome-wide exon-capture approach. Sixty-four clonal Norway spruce lines were phenotyped, and their responses to H. parviporum inoculation were determined by lesion length measurements. Afterwards, the spruce lines were genotyped by targeted resequencing and identification of genetic variants (SNPs). Genome-wide association analysis identified 10 SNPs located within 8 genes as significantly associated with the larger necrotic lesions in response to H. parviporum inoculation. The genetic variants identified in our analysis are potential marker candidates for future screening programs aiming at the differentiation of disease-susceptible and resistant trees.Root and butt rot caused by members of the  Picea abies (L.) H. Karst.] is one of the dominant species in European boreal forests. As a major source of timber, it is one of the most commercially important species in Nordic countries. However, a combination of biotic and abiotic factors pose a threat to sustainable timber supply from Norway spruce plantations  and living tissues  -catechin, a compound showing a fungistatic effect on H. parviporum   was grown on 2% malt extract agar (MEA) plates supplemented with Norway spruce sawdust. The plates were inoculated with H. parviporum and incubated at 20°C for 4 weeks. For the mock inoculation, the sterile 2% MEA plates with 2% sawdust were used as a control.A H. parviporum, and three saplings of each clone were mock-inoculated to perform as a control. The inoculation method used . For control saplings, holes were inoculated with uncolonized sawdust-containing malt extract agar plugs. Saplings were harvested 2 months after inoculation. Harvested material was stored at −20°C until used. The necrotic lesions in phloem and xylem tissues were measured after removing the periderm tissues using a sterilized knife. The saplings dimensions  were also documented.After the 2-month acclimatization, 4 to 7 saplings of each clone were inoculated with d Figure  was simid Figure . The steYij is the value of ijth observation, μ is the overall mean, ci is the fixed effect of the clone i, and eij is the random residual term associated with the ith clone and jth ramet. Differences between clones were tested with the least significant difference (LSD) test between the means.Data were analyzed using the SPSS version 25.0  and Microsoft Excel 2016. A one-way analysis of variance (ANOVA) was performed to detect differences among the necrosis sizes of each clone and among the inoculation and mock treatments. The normality of the error variances was checked with Levene's test and by skewness and kurtosis values for the data distribution, the values for lesion size were converted to the logarithmic scale  and the lengths of various lesions using the following linear model:j is the fixed effect of the jth treatment , and ciTj is the random interaction effect between ith clone and jth treatment. This enabled us to separate the clone and clone by environment (treatment) interaction components of variance in the estimation of broad-sense heritability:cT) was calculated as a simple ratio:Secondly, to analyze the magnitude of clone by treatment interaction in the lesion traits we used the mixed effect model:P. abies v1.0 genome  method with modifications described in Terhonen et al. . DNA conP. abies v1.0 genome using Mosaik version 2.1 as described before . Since the spruce genome is not ordered and fragmented, the p-values plotted on the Manhattan plot do not represent any physical or genetic distance, but rather each SNP was simply considered a coordinate on the x-axis for visualization purposes . The average xylem lesion size for each clone was used as a quantitative phenotype for the GWAS, which was carried out using EMMAX  in both cases  = 96.58, F = 547.82, F = 130.52, and F = 402, respectively at p < 0.001]. Horizontal lesion length in phloem was significantly higher than in xylem (p < 0.001), but there was no significant differences between the tissues in the vertical lesion length.The lesions developed faster in vertical than in horizontal direction, as indicated by significant differences between vertical and horizontal lesion lengths in all treatments . The distribution of lesion length among the analyzed clones was similar to normal , there were significant negative correlations between the growth traits  and the observed lesion sizes. The strongest negative correlation was found in inoculated xylem that differed significantly at 01 Table .The heritability estimates, indicating the proportion of clonal variation of the total phenotypic variation in each treatment, were moderate to large, ranging from 0.18 to 0.80. The levels of heritability were consistently larger for the clones subjected to mock treatment than the respective estimates for inoculated trees. The genetic coefficients of variation displayed the similar tendency Table . The cloWe genotyped 64 clonal lines of Norway spruce by resequencing of predicted exons corresponding to 34 761 gene models. On average, 6.3 million reads were generated per clonal line. Reads were aligned to Norway spruce reference genome, with the median experiment-wide sequencing depth of 40.35×. The efficiency of the sequence enrichment strategy was high, capturing 79 170 out of 80 000 probes. Calling of genetic variants identified 373 384 high-quality biallelic SNPs.Arabidospis thaliana ILITYHIA, which is required for the establishment of systemic acquired resistance  that were significantly associated (at 5% FDR significance level) with the size of necrotic lesions formed in response to fungal inoculation  all the traits studied showed moderate heritability. The relative magnitude of the interaction was high for a single trait, phloem horizontal necrosis, but small to moderate for the rest of the lesion traits and very small for all of the three growth traits. This kind of discrepancy is interesting, yet difficult to explain. The finding needs to be verified in further studies to make sure that it was not just a random occurrence.H. parviporum inoculation. These SNPs correspond to 8 genes. None of the identified genes was previously reported as being implicated in control of resistance of Norway spruce to Heterobasidion infection. At the same time, none of the SNP markers associated with the Norway spruce resistance to H. parviporum in a previous screening program  in our study is particularly noteworthy, as the corresponding protein was demonstrated to play a key role in the induced defense reactions in Arabidopsis  close to the significance threshold (Supplementary File The gene MA_4047g0010 encodes a predicted subtilase (subtilisin-like serine peptidase). This protein family is largely expanded in plant genomes, and their physiological functions include the control of growth and development, regulation of programmed cell death and senescence and plant responses to biotic and abiotic stressors . This observation indicates that more extensive genotyping programs involving several hundreds of individuals might be required to identify the most relevant alleles controlling responses of Norway spruce to H. annosum infection using sequence capture enrichment strategy. Obtained results illustrate the suitability of this approach for genotyping of Norway spruce, a species with a very large genome and a high content of repetitive elements. Some of the identified genes are promising candidates, and further analysis should investigate their role in spruce defense reactions. However, our study also illustrates that even larger efforts might be required to identify genetic variants controlling economically important traits and occurring in low frequency in natural populations.This study is the first attempt to identify genes involved in the control of Norway spruce resistance to Phenotyping of Norway spruce saplings was performed by MM and EJ; total genomic DNA extraction was done by MM and EJ; genetic and genome-wide association analyses were done by LN; heritability analysis was carried out by MH; MM, AK, and LN analyzed the data; MM and AK prepared the manuscript draft; MK and FA conceived the study and contributed to the experiment design. All authors read and approved the final version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Objectives: Orofacial clefting is one of the most prevalent craniofacial malformations. Previous research has demonstrated that unaffected relatives of patients with non-syndromic cleft lip with/without cleft palate (NSCL/P) show distinctive facial features, which can be an expression of underlying NSCL/P susceptibility genes. These results support the hypothesis that genes involved in the occurrence of a cleft also play a role in normal craniofacial development. In this study, we investigated the influence of genetic variants associated with NSCL/P on normal-range variation in facial shape.Methods: A literature review of genome wide association studies (GWAS) investigating the genetic etiology of NSCL/P was performed, resulting in a list of 75 single nucleotide polymorphisms (SNPs) located in 38 genetic loci. Genotype data were available for 65 of these selected SNPs in three datasets with a combined sample size of 7,418 participants of European ancestry, whose 3D facial images were also available. The effect of each SNP was tested using a multivariate canonical correlation analysis (CCA) against 63 hierarchically-constructed facial segments in each of the three datasets and meta-analyzed. This allowed for the investigation of associations between SNPs known to be involved in NSCL/P and normal-range facial shape variations in a global-to-local perspective, without preselecting specific facial shape features or characteristics.Results: Six NSCL/P SNPs showed significant associations with variation in normal-range facial morphology. rs6740960 showed significant effects in the chin area (p = 3.71 × 10−28). This SNP lies in a non-coding area. Another SNP, rs227731 near the NOG gene, showed a significant effect in the philtrum area (p = 1.96 × 10−16). Three SNPs showed significant effects on the shape of the nose. rs742071 (p = 8.71 × 10−14), rs34246903 (p = 6.87 × 10−12), and rs10512248 (p = 8.4 × 10−9). Respectively, these SNPs are annotated to PAX7, MSX1, and PTCH1. Finally, rs7590268, an intron variant of THADA, showed an effect in the shape of the supraorbital ridge (p = 3.84 × 10−7).Conclusions: This study provides additional evidence NSCL/P-associated genetic variants influence normal-range craniofacial morphology, with significant effects observed for the chin, the nose, the supraorbital ridges and the philtrum area. Human facial features are highly variable and mostly genetically determined. Although craniofacial morphology is of interest to many scientists, its genetic architecture remains poorly understood  is one of the most common craniofacial anomalies, causing significant functional and psychological burden to the patient  and genetic PCA outliers (n = 15) were identified and removed. The intersection of individuals with quality-controlled images, covariates and genotype data included 2,297 subjects.Three datasets with 3D images and corresponding genetic data were used in this study. For the Pittsburgh sample, data were obtained from the 3D Facial Norms Database, which is a repository of 3D facial images and measurements , participants were excluded based on missing covariate data (n = 748) and quality control of the images resulted in the elimination of 52 participants. Based on the genotype data, European participants were selected  and related individuals were removed (n = 59) (see Genotyping methods section), resulting in 1,555 participants for analysis. No genetic outliers were identified.The data collected through Penn State consists of participants recruited in State College, PA; New York, NY; Urbana-Champaign, IL; Twinsburg, OH; Dublin, Ireland; Rome, Italy; Warsaw, Poland; and Porto, Portugal. The minimum age in this sample was 18, the maximum age 83 . Data on self-reported ancestry, body characteristics, age and sex as well as genotype data were obtained. Individuals were excluded if they reported a personal or family history of any birth defect or syndrome affecting the head or face, a personal history of any significant trauma, surgery, or any medical condition that might alter the structure of the face. From the entire Penn State dataset  is a longitudinal birth cohort in which pregnant women residing in Avon with an expected delivery date between 1 April 1991 and 31 December 1992 were recruited  was 5, determined by the cross-validation (CV) error for each k value. These results were then used to select samples with < 10% ancestry from all of the non-European admixture components. In the ASPAC sample, population stratification was assessed by multidimensional scaling analysis and compared with Hapmap II (release 22) European descent (CEU), Han Chinese, Japanese and Yoruba reference populations; all individuals with non-European ancestry were removed.To select participants with primarily European ancestry in the Penn State Sample, an ADMIXTURE analysis was done with the 1000 Genomes Phase 3 dataset as the reference  was higher than 0.125. Ancestry axes were determined with principal component analysis (PCA). Outliers (n = 15) were removed based on Z-scores calculated in the first 10 principal components. Z-scores higher than 6 indicated outliers, who were subsequently removed after which PCA was computed again.To assess population structure within the European subsets after removing non-European individuals, the same protocol was followed for the three datasets using PLINK 1.9  were detected and one SNP per pair was eliminated to avoid unnecessary multiple testing. The elimination of SNPs in LD resulted in a set of 75 lead-SNPs from 38 different loci . For the Penn State sample, both 3dMDface camera systems and Vectra H1  camera systems were used. For the ALSPAC sample, a Konica Minolta Vivid 900 laser scanner  was used to take two high-resolution facial images which were subsequently processed, merged and registered using an algorithm implemented as a macro in Rapidform® software; INUS Technology Inc., Seoul, South Korea  is symmetrical relative to the sagittal plane, which allows reflected images to be created by changing the sign of the x-coordinate of the original mapped images. Both the original and the reflected remapped faces were then superimposed following a generalized Procrustes superimposition to eliminate differences in orientation, position and scale  is obtained which is beneficial to obtain a well-defined segmentation of landmark covariations and the determination of significant principal components (PCs) using parallel analysis. Moreover, facial shape data across all three datasets are now in the same shape space, enabling across-dataset analyses including a meta-analysis.To study the effects of NSCL/P candidate variants on facial shape in a detailed manner, a data-driven facial segmentation was performed  and the dependent  variables were corrected for these covariates. Additionally, a partial least squares regression was performed  in the same way as the CCA, to obtain the percentage of variance explained by the SNP in the facial segment that was tested.Each candidate SNP was tested against 63 facial segments each represented by multiple dimensions of variation . To this end we used canonical correlation analysis  to test the effect of the 64 SNPs on facial shape under the reduced model. CCA is a multivariate testing framework which extracts the linear combination of PCs from a facial segment that has maximal correlation with the SNP being tested. The correlation is tested for significance based on Rao's F-test approximation , creating univariate phenotypic variables which are then also tested for genotype-phenotype associations. This step of the meta-analysis will be referred to as the replication. The replication results in univariate phenotypic variables are measured in the replication datasets as a function of the discovered phenotypic trait in the CCA. In doing so, as proposed in Claes et al. , the phep-values ].Analyzing 65 SNPs in 63 separate facial segments introduces a multiple testing burden. The facial segments are overlapping and hierarchically constructed and are thus not completely independent. To determine the number of independent tests, we evaluated the eigenvalues of pairwise multivariate correlations between facial segments and of pairwise genotype correlations and determined 37 independent segments  in at least one segment for one of the three meta-analyses. To decrease the risk of identifying false positives, the Bonferroni threshold was determined by the number of independent segments, the number of independent genetic variants and, although not completely independent, the three meta-analyses.The replication strategy in Claes et al.  was adapn = 1,555), rs7590268, rs34346903, and rs10512248 do not reach significance. Another possible explanation is that the true effects in the different datasets are not the same, for example due to small population differences between the datasets. This idea is analogous to between-study heterogeneity in genetic meta-analyses of quantitative traits  for NSCL/P, and associate these against normal facial variation in an open-ended phenotyping approach. The PRS capture an individual's genetic propensity toward a trait and thus combines the effect sizes discovered in a GWAS into a univariate score capturing a risk for NSCL/P. Combining the information of multiple markers in one score analogous to this study would result in a facial phenotype associated with NSCL/P risk. Additionally, the risk-score could increase power in comparison to the use of individual SNPs. Another approach would be to calculate a quantitative measurement that indicates to what degree the endophenotype is present in each participant and to use this in a genetic mapping effort, using candidate variants, genome-wide SNPs or PRS. The methodology described in this study allows us to study the effects of genes with a known role in a certain condition on facial morphology. In the future, genes responsible for syndromes with a distinct facial phenotype can also be tested in this framework to see if variations in these genes are responsible for morphological changes in the face.Many genetic syndromes and malformations are characterized by a distinctive facial phenotype  at accession phs000949.v1.p1. The 3D facial images are available through the FaceBase Consortium (https://www.facebase.org/data/record/#1/isa:dataset/RID=14283) The participants making up the Penn State University dataset were not collected with broad data sharing consent. Given the highly identifiable nature of both facial and genomic information and unresolved issues regarding risk to participants, we opted for a more conservative approach to participant recruitment. Broad data sharing of these collections would thus be in legal and ethical violation of the informed consent obtained from the participants. This restriction is not because of any personal or commercial interests. Additional details can be requested from M.D.S. The ALSPAC data will be made available to bona fide researchers on application to the ASLAPC Executive Committee.The datasets analyzed for this study are available through various sources. For the Pittsburgh dataset, the genotypic markers are available through the dbGaP controlled-access repository  approval was obtained at each recruitment site, and all participants gave their written informed consent before participation; for children, written consent was obtained from a parent or legal guardian. For the Pittsburgh sample, the following local ethics approvals were obtained: University of Pittsburgh IRB PRO09060553 and RB0405013; UT Health Committee for the Protection of Human Subjects HSC-DB-09-0508; Seattle Children's IRB 12107; University of Iowa Human Subjects Office/IRB 200912764 and 200710721. For the Penn State sample, the following local ethics approvals were obtained: State College, PA (IRB 44929 and 4320); New York, NY (IRB 45727); Urbana-Champaign, IL (IRB 13103); Dublin, Ireland; Rome, Italy; Warsaw, Poland; and Porto, Portugal (IRB 32341); Twinsburg, OH (IRB 2503). For the ALSPAC sample, ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees.KI performed all analyses and wrote the first draft of the manuscript under supervision of PC, GH, and HP. PC, JR, EF, JS, SW, MM, JW, and MS conceptualized the design of the study. JR, EF, JS, SW, and MM organized the PITT cohort. JW and MS organized the PSU cohort and imputed the PSU genetic data. SR coordinated the collection of the ALSPAC images. JR, HH, and JW provided input throughout the analyses and the writing process. All authors contributed to manuscript revision, read and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The strong heritability of extreme human longevity supports the hypothesis that this is a genetically-regulated trait. However, association studies focused on common genetic variants have discovered a limited number of longevity-associated genes. We conducted a genome-wide association study of 4,216 individuals including 1317 centenarians from the New England Centenarian Study (median age = 104 years) using >9M genetic variants imputed to the HRC panel of ~65,000 haplotypes. The set included approximately 5M uncommon variants. The associations were tested using a mixed effect logistic regression model with genotype-based kinship covariance of the random effects to adjust for cryptic relations using the package GENESIS. The analysis discovered 45 genome-wide significant SNPs (p< 5E-08) including 8 new loci in chromosomes 3, 6, 7, 9, 10, 14 and 15 in addition to the APOE locus. The list includes new pQTLs in serum that suggest a new biological mechanism involved in extreme human longevity.