Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 1 / 1 / 5 / Solution

The overall odds ratio is $0.99$ with 95% interval $(0.95,1.02)$, so there is little evidence for an average effect. The estimate changes sharply across residual-vitamin-D strata: it is $0.69$ $(0.59,0.80)$ in the deficient group, $0.94$ $(0.89,0.99)$ in the insufficient group, and close to one in the two higher groups. The pattern is consistent with effect modification: raising vitamin D may reduce mortality among deficient people but offer little benefit once concentration is adequate. The claim still depends on the Mendelian randomization assumptions and should account for the fact that several subgroup estimates were examined.