Mendelian randomization

Mendelian randomization uses inherited genetic variants associated with an exposure as instrumental variables. Its causal interpretation requires instrument relevance, instrumental-variable independence, and the exclusion restriction.

Within-family Mendelian randomization uses genetic contrasts within families, such as differences between siblings. Conditioning on shared parental background can reduce population stratification and family-level sources of confounding, although the exclusion restriction and sufficient instrument relevance remain necessary.

MR-Egger regression fits genetic outcome associations to genetic exposure associations with a free intercept. Its slope estimates a causal effect under the InSIDE assumption and appropriate instrument-strength assumptions; its intercept assesses average directional horizontal pleiotropy. A nonsignificant intercept, especially with few genetic variants, does not prove the exclusion restriction for every instrument.

InSIDE stands for instrument strength independent of direct effect. It requires the genetic associations with the exposure to be independent of the direct, pleiotropic effects of those genetic variants on the outcome. It is a key identifying assumption for MR-Egger regression.

This weighted median of genetic variant ratio estimates consistently estimates a common causal effect when more than half of its asymptotic weight comes from valid instrumental variables, subject to the usual sampling regularity conditions. It is a sensitivity analysis for horizontal pleiotropy, not an unconditional guarantee of validity.

Two-sample Mendelian randomization combines genetic variant associations with an exposure estimated in one sample and their associations with an outcome estimated in another. It requires the instrumental variable assumptions and compatible associations across the populations; sample overlap can change the behaviour of weak instruments.

Horizontal pleiotropy occurs when a genetic instrument affects an outcome through a pathway other than the exposure under study. It violates the exclusion restriction in Mendelian randomization.

Residual exposure stratification subtracts the genetically predicted component of an exposure before forming exposure strata. Under a suitable additive first-stage model, this avoids directly conditioning on the component caused by the instrument and can reduce the resulting collider bias.