Synonyms: IV2 assumption, second MR assumption

Known as the second MR assumption (and sometimes also referred to as the “exchangeability” assumption), this states that there are no confounders of the association between the instrumental variables (IVs) and the outcome.

As genetic variants are determined at conception it is not possible for them to be affected by confounders of exposure-outcome associations. When referring to the second MR assumption, factors that could influence the genetic variants and outcome include population stratification or structure, intergenerational (dynastic) effects and assortative mating. Generally, genetic variants can influence confounders of the exposure-outcome association and would be analagous to horizontal pleiotropy. If they do and these confounders are not measured nor accounted for in the MR analysis, then a path from the genetic IV via these factors could bias the causal effect estimate. As noted under "confounding" in both one-sample and two-sample MR, associations of the genetic IV with potential confounders can be undertaken and methods such as multivariable MR used to control for these, where possible.

## References

- Davey Smith G, Lawlor DA, Harbord R, Timpson N, Day I, Ebrahim S. Clustered environments and randomized genes: a fundamental distinction between conventional and genetic epidemiology. PloS Medicine 2008; 4: e352.
- Sheehan NA, Didelez V. Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail. Human Genetics 2019; 139: 121-136.

## Other terms in 'Sources of bias and limitations in MR':

- Assortative mating
- Canalization
- Collider
- Collider bias
- Conditional F-statistic for multiple exposures
- Confounding
- Exclusion restriction assumption
- F-statistic
- Harmonization (in two-sample MR)
- Homogeneity Assumption
- Horizontal Pleiotropy
- INstrument Strength Independent of Direct Effect (InSIDE) assumption
- Intergenerational (or dynastic) effects
- Monotonicity assumption
- MR for testing critical or sensitive periods
- MR for testing developmental origins
- No effect modification assumption
- NO Measurement Error (NOME) assumption
- Non-linear MR
- Non-overlapping samples (in two-sample MR)
- Overfitting
- Pleiotropy
- Population stratification
- R-squared
- Regression dilution bias (attenuation by errors)
- Relevance assumption
- Reverse causality
- Same underlying population (in two-sample MR)
- Statistical power and efficiency
- Vertical pleiotropy
- Weak instrument bias
- Winner's curse