With a single genetic variant j, the causal effect of the exposure on the outcome can be estimated using the ratio method (or Wald method17) as the coefficient from regression of the outcome on the genetic variant (denoted by Γ^j) divided by the coefficient from regression of the exposure on the variant (denoted γ^j).18 The reduced-form equation relating the outcome to the genetic variant j can be written as: Yi=ΓjGij+ϵ′ijY=(αj+βγj)Gij+ϵ′ijY. If the genetic variant is a valid IV, αj=0 and the ratio method estimand (the quantity that is being estimated, denoted by βj) is Γjγj=βγjγj=β.
