Solution (source code)

= 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.