Fig. 1. Graphical representation of valid instrument causal scenarios, for a variant j.

These causal graphs depict the genetic instrumental variable assumptions on which MR is based, with a genetic variant with genotype $G_j$ causally affecting the exposure $X$ which in turn (potentially) causally affects $Y$, while allowing for the presence of confounders $C$ of the exposure and outcome. In this and subsequent figures, variables are shown as rectangles or ovals, with ovals denoting that the variable is not (necessarily) observed, and causal effects are indicated using one-sided arrows in the direction of the causal effect, with an accompanying effect size parameter shown next to it. Two-sided arrows denote correlations between variables caused by other variables external to the model. For simplicity of notation throughout the paper, all variables are assumed to be standardized, with mean of zero and unit variance. Shown in (A) is the basic valid instrument scenario, with in (B) the same graph emphasizing the causal paths explicitly ruled out by the independence and exclusion restriction assumptions. The graph in (C) shows an alternative valid instrument scenario where the variant $j$ used is not causal, but is in LD with another variant $k$ that is.