In this study, we extend the SMR approach to a more general form (generalized SMR or GSMR) by leveraging power from multiple genetic variants accounting for linkage disequilibrium (LD) between the variants, and demonstrate by simulation that GSMR is more powerful than existing summary data-based MR methods12,13,18. Separation of signals of causality from pleiotropy (a single locus directly affecting multiple phenotypes, also called type-II pleiotropy19) and further separation of marginal effect from conditional effect (the net effect of a risk factor on the outcome accounting for the effects of other risk factors, e.g., there is no effect of HDL cholesterol on CAD correcting for the other serum cholesterol levels20,21) are recognized issues that require careful interpretation in MR analyses19. We develop a method (HEIDI-outlier) to detect and eliminate genetic instruments that have apparent pleiotropic effects on both risk factor and disease, and another method (multi-trait-based conditional and joint analysis, or mtCOJO) to estimate the effect of a risk factor on disease conditioning on other risk factors. All methods developed in this study only require summary-level data (with LD between genetic
