Fig. 4

Mendelian randomization approach and results. A Formulation of the Mendelian randomization causality test. G represents genotypes, Z is a genetic instrument value constructed from G, X represents ln(MT-CN), Y represents ln(Insulin), and U represents any confounders of the association between X and Y. The arrow from X to Y is dashed to indicate that although an association is known, the relationship is not known to be causal. In this formulation, a significant association between Z and Y would provide evidence that X is casual for Y. B Strategy for choosing variables to adjust for when building Z in order to enforce MR assumptions. A represents those columns of covariate matrix W that are associated with Y (represented by the solid line between A and Y), and B represents those columns of matrix W that are associated with X conditional on A (represented by the solid line between B and X). Dashed lines represent possible, but unproven associations. The penalized regression of X on G used to build Z is adjusted for A and B (with no penalty) in an attempt to prevent any associations between Z and either A or B (represented by the blue X’s). While an association between B and Y is unlikely (represented by the dashed line between B and Y) because B is not contained in A, B is still adjusted for in the penalized regression to be as conservative as possible. C Strategy for choosing covariates to adjust for in the causality test of Y against Z in another attempt to reduce the impact of any remaining associations between Z and assumption-violating variables. Covariate sets I, II, III, and IV are defined by the presence of known first-order associations (represented by black lines) with Z and Y (see Methods). Yellow lines represent relationships where a first-order association is not known, but a higher-order association is possible. Covariate sets II, III, and IV (colored blue) are adjusted for in the causality test because there is at least one first-order association linking them to Z and Y, so they risk violating MR assumptions 2 or 3. D Results of Mendelian randomization test for causality of MT-CN on fasting serum insulin