A Note on the Use of Egger Regression in Mendelian Randomization Studies

A large number of epidemiological studies use genetic variants as instrumental variables to infer causal relationships. For a genetic variant to be a valid instrument in these so-called Mendelian randomization (MR) studies, three assumptions need to hold:
(i) the genetic variant is associated with the exposure of interest (relevance assumption);
(ii) the genetic variants should be independent of all confounders (independence assumption);
(iii) the genetic variants only effect the outcome through the exposure of interest (exclusion restriction).
Without specific knowledge about the biological mechanisms affected by genetic variants, it is virtually impossible to prove that the exclusion restriction holds for a specific genetic variant. For example, genetic variants may have pleiotropic effects on both the exposure and the outcome through different biological pathways. [...]