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Polygenic scores (PGSs) that can predict response to interventions can facilitate precision medicine and are detectable in observational datasets as PGS-by-exposure (PGS×E) interactions. PGSs based on interactions (iPGSs) or variance effects (vPGSs) may be more powerful than standard PGSs for detecting PGS×E, but these have yet to be systematically compared. We describe a generalized pipeline for developing and comparing these PGS types and apply it to detect genetic modification of the relationship between adiposity (measured by BMI) and a broad set of cardiometabolic risk factors. Our applied analysis in the UK Biobank identified significant PGS×BMI for 16/20 risk factors, most consistently for the iPGS approach. Many interactions replicated in All of Us (AoU); for example, we observed a 72% larger BMI-alanine aminotransferase association in the top iPGS decile in AoU. Our study provides a framework for the comparison of PGS×E strategies and informs efforts toward clinically useful response-focused PGSs.