Illustrative data on the associations of multiple genetic variants with an exposure variable and with an outcome variable for 15 variants are displayed as a scatter plot in Figure 2. This is similar to a radial plot occasionally used in meta-analysis to display multiple estimates of the same quantity with a range of precisions.26 In this example, all of the IVs are invalid, but the InSIDE condition holds. The true causal effect is shown by the dotted line. The ratio estimates based on each genetic variant are the gradients of the slopes from the origin to the data point for that variant. The IVW estimate (shown by the solid red line) is the slope of the best fitting line through the data points that also passes through the origin. This is equal to the coefficient from a weighted regression of the gene–outcome association estimates (Γ^j) on the gene–exposure association estimates (γ^j) with the intercept constrained to zero, and weighted by the inverse of the precision of the IV–outcome coefficients (σYj−2).27 Here, all of the instruments are invalid, and so the slope of this line differs substantially from the true causal effect.
