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Recent and classical work has revealed biologically and medically significant subtypes in complex diseases and traits. However, relevant subtypes are often unknown, unmeasured, or actively debated, making automated statistical approaches to subtype definition valuable. We propose reverse GWAS (RGWAS) to identify and validate subtypes using genetics and multiple traits: while GWAS seeks the genetic basis of a given trait, RGWAS seeks to define trait subtypes with distinct genetic bases. Unlike existing approaches relying on off-the-shelf clustering methods, RGWAS uses a novel decomposition, MFMR, to model covariates, binary traits, and population structure. We use extensive simulations to show that modelling these features can be crucial for power and calibration. We validate RGWAS in practice by recovering a recently discovered stress subtype in major depression. We then show the utility of RGWAS by identifying three novel subtypes of metabolic traits. We biologically validate these metabolic subtypes with SNP-level tests and a novel polygenic test: the former recover known metabolic GxE SNPs; the latter suggests subtypes may explain substantial missing heritability. Crucially, statins, which are widely prescribed and theorized to increase diabetes risk, have opposing effects on blood glucose across metabolic subtypes, suggesting the subtypes have potential translational value. [ABSTRACT FROM AUTHOR]