It has been also asserted that β^E is a bias-reduced estimate for the true causal effect.14 Under model (1), we have the following equation for the slope coefficient from Egger regression: β^E=cov(Γ^,γ^)var(γ^)=β^+cov(α^,γ^)var(γ^). In the limit as both the sample size and the number of genetic variants increase to infinity, the InSIDE condition ensures that cov(α^,γ^)→N→∞cov(α,γ)→J→∞0 and therefore β^E is a consistent estimate of the causal effect β. This is illustrated by the solid blue line in Figure 2.
