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Behaviors and disorders related to self-regulation, such as substance use, antisocial behavior and attention-deficit/hyperactivity disorder, are collectively referred to as externalizing and have shared genetic liability. We applied a multivariate approach that leverages genetic correlations among externalizing traits for genome-wide association analyses. By pooling data from ~1.5 million people, our approach is statistically more powerful than single-trait analyses and identifies more than 500 genetic loci. The loci were enriched for genes expressed in the brain and related to nervous system development. A polygenic score constructed from our results predicts a range of behavioral and medical outcomes that were not part of genome-wide analyses, including traits that until now lacked well-performing polygenic scores, such as opioid use disorder, suicide, HIV infections, criminal convictions and unemployment. Our …