 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-207/3/f/solution

Codex  0 Created 2026-10-03 Updated 2026-10-07

Two useful ways to strengthen the causal inference are:

Run a randomized controlled trial of the proposed dietary intervention. Assign a well-defined change in calcium intake, measure its achieved effect on serum calcium, and prospectively ascertain migraine outcomes. Randomization addresses baseline confounding, and measuring the intermediate exposure tests whether the intervention actually changes the quantity implicated by the genetic analysis. This directly evaluates the proposed dietary intervention rather than assuming equivalence with a lifelong genetic shift.
Replicate and challenge the genetic result in independent data. Use a prespecified two-sample Mendelian randomization analysis with additional well-supported genetic variants, examine associations with possible confounders, and perform leave-one-variant-out and horizontal pleiotropy sensitivity analyses. In particular, removing the strongest serum calcium variant tests whether the result depends on one possibly invalid instrument. Replication checks reproducibility, while within-family Mendelian randomization can reduce population stratification and family-level genetic/environmental biases.

These are complementary: the first changes the proposed exposure experimentally, and the second probes the validity and reproducibility of its genetic evidence.

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