Genetic correlations estimated from GWAS reveal pervasive pleiotropy across a wide variety of phenotypes. We introduce genomic structural equation modeling (Genomic SEM), a multivariate method for analyzing the joint genetic architecture of complex traits. Genomic SEM synthesizes genetic correlations and SNP-heritabilities inferred from GWAS summary statistics of individual traits from samples with varying and unknown degrees of overlap. Genomic SEM can be used to model multivariate genetic associations among phenotypes, identify variants with effects on general dimensions of cross-trait liability, calculate more predictive polygenic scores, and identify loci that cause divergence between traits. We demonstrate several applications of Genomic SEM, including a joint analysis of summary statistics from five psychiatric traits. We identify 27 independent SNPs not previously identified in the contributing univariate GWASs. Polygenic scores from Genomic SEM consistently outperform those from univariate GWAS. Genomic SEM is flexible, open ended, and allows for continuous innovation in multivariate genetic analysis.

Cannabis use is a heritable trait that has been associated with adverse mental health outcomes. In the largest genome-wide association study (GWAS) for lifetime cannabis use to date (N = 184,765), we identified eight genome-wide significant independent single nucleotide polymorphisms in six regions. All measured genetic variants combined explained 11% of the variance. Gene-based tests revealed 35 significant genes in 16 regions, and S-PrediXcan analyses showed that 21 genes had different expression levels for cannabis users versus nonusers. The strongest finding across the different analyses was CADM2, which has been associated with substance use and risk-taking. Significant genetic correlations were found with 14 of 25 tested substance use and mental health-related traits, including smoking, alcohol use, schizophrenia and risk-taking. Mendelian randomization analysis showed evidence for a causal positive influence of schizophrenia risk on cannabis use. Overall, our study provides new insights into the etiology of cannabis use and its relation with mental health.

We introduce two novel methods for multivariate genome-wide association meta-analysis (GWAMA) of related traits that correct for sample overlap. A broad range of simulation scenarios supports the added value of our multivariate methods relative to univariate GWAMA. We applied the novel methods to life satisfaction, positive affect, neuroticism, and depressive symptoms, collectively referred to as the well-being spectrum (N obs = 2,370,390), and found 304 significant independent signals. Our multivariate approaches resulted in a 26% increase in the number of independent signals relative to the four univariate GWAMA, and in a ~ 57% increase in the predictive power of polygenic risk scores. Supporting transcriptome -and methylome-wide analyses (TWAS/MWAS) uncovered an additional 17 and 75 independent loci, respectively. Bioinformatic analyses, based on gene expression in brain tissues and cells, showed that genes differentially expressed in the subiculum and GABAergic interneurons are enriched in their effect on the wellbeing spectrum.In the past decade, genome-wide association studies (GWAS) have provided insights into the genetic basis of quantitative variation in complex traits 1 . With summary statistics of these GWASs becoming public and the development of linkage disequilibrium score regression (LDSC) 2,3 , genetic correlations between traits can be systematically estimated (e.g. Brainstorm consortium 4 ). Levering this widely observed genetic overlap between traits, we introduce two novel methods for multivariate genome-wide association metaanalysis, where we define a multivariate model as a model where the effect of a single SNP is considered for multiple traits: 1) N-weighted multivariate GWAMA (N-GWAMA), with a unitary effect of the SNP on all traits, and 2) model averaging GWAMA (MA-GWAMA), where we relaxed the assumption of a unitary effect of the SNP on all traits. Both methods are well equipped to deal with (unknown) sample overlap. The dependence between effect sizes (error correlation) induced by possible sample overlap is estimated from the univariate GWAMA using LDSC 2,3 . Furthermore, the univariate LDSC intercept is used to correct for population stratification and cryptic relatedness. Both methods have advantages over existing methods. In contrast to MultiPhen 5 , CCA (mv-PLINK) 6 , Combined-PC 7 , and mv-BIMBAM 8 , both our methods can be applied without the need of individual-level genotypic data as only GWAS/GWAMA summary-statistics are required. Additionally, in contrast to S Hom 9 , N -and MA-GWAMA take a more precise estimate of the error correlation into account. In contrast to MTAG 10 , MA-GWAMA , similar to S Het 9 , generates trait specific estimates for each SNP allowing for a certain degree of heterogeneity (see online methods). Finally, in contrast to TATES 11 , both N-GWAMA and MA-GWAMA generate effect sizes for the multivariate effect where TATES only generates a P-value. The absence of a signed statistic in TATES complicates or even prohibits polygenic prediction.

Little is known about the genetic architecture of traits affecting educational attainment other than cognitive ability. We used Genomic Structural Equation Modeling and prior genome-wide association studies (GWAS) of educational attainment ( n = 1,131,881) and cognitive test performance ( n = 257,841) to estimate SNP associations with educational attainment variation that is independent of cognitive ability.We identified 157 genome-wide significant loci and a polygenic architecture accounting for 57% of genetic variance in educational attainment. Non-cognitive genetics were enriched in the same brain tissues and cell types as cognitive performance but showed different associations with gray-matter brain volumes. Non-cognitive genetics were further distinguished by associations with personality traits, less risky behavior,and increased risk for certain psychiatric disorders.For socioeconomic success and longevity, non-cognitive and cognitive-performance genetics demonstrated similar-magnitude associations. By conducting a GWAS of a phenotype that was not directly measured, we offer a first view of genetic architecture of non-cognitive skills influencing educational success.

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