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Chunk #6 — METHODS — Univariable Mendelian randomization

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Extending the MR-Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy.
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With a single genetic variant, G 1 say, the causal estimate is β^Y1/β^X1.14 This is a consistent estimate of the causal effect θ when α 1=0. With multiple genetic variants, the inverse‐variance weighted (IVW) estimate is the weighted average of these causal estimates,15 using the inverse of their approximate variances se(β^Yj)2/β^Xj2 as weights: (2)θ^UI=∑jβ^Yjβ^Xjse(β^Yj)−2∑jβ^Xj2se(β^Yj)−2.