**Figure 1:** Schematic presentation of valid and invalid instrumental variables
X, Y, Z, and U denote the exposure, outcome, IV, and confounders (observed
or unobserved), respectively. a) Z is associated with X and only related to Y
through X (valid IV), b) Z is not associated with X (first IV assumption is violated),
c) Z is not independent of confounders, i.e. Z has an indirect effect on Y (second
IV assumption is violated), d) Z is not independent of Y given X and U, i.e. Z has
a direct effect on Y (third IV assumption violated) |