 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-207/2/e/solution

Three useful extensions are:

Replicate the bidirectional Mendelian randomization in independent, larger cohorts and ancestries, using nonoverlapping discovery and outcome samples to improve precision and reduce winner's-curse and population-specific artifacts.
Apply pleiotropy-robust analyses such as weighted-median, mode-based, and MR-Egger estimates, inspect heterogeneity and leave-one-variant-out results, and use biologically distinct instrument sets. Agreement despite different sensitivities to invalid instruments strengthens the exclusion restriction.
Triangulate with a design based on an independent source of causal variation, such as compulsory-schooling-law changes or another natural experiment, and with longitudinal refractive measurements. Agreement across designs with different biases is stronger evidence than enlarging one genetic analysis alone.

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