This is one of a set of additional (to the core) MR assumptions that are required for estimating a well-defined causal parameter.

The assumption is that either the 1) the effect of the exposure on the outcome is homogeneous (i.e., is the same for everyone in the population) or 2) the effect of the exposure on the outcome does not depend on the genetic instrumental variable (IV). If this assumption holds, the IV estimate is consistent with the average causal effect (ACE) for the population to which inference is being made. Increasing biological knowledge of genetic variant functionality may provide evidence for some genetic IVs fulfilling this assumption. Weaker assumptions (e.g., the no effect modification and monotonicity assumptions) can alternatively be evoked. However, it is difficult in practice to know how important violation of these additional assumptions are in MR studies. Large genome-wide association study (GWAS) collaborations increasingly combine results from many studies (e.g., those across multiple European samples) and show consistency of association between genetic variants and traits across these studies at genome-wide significance (i.e., those variants used in most MR studies). This therefore suggests that homogeneity in effect estimates may exist for several MR studies in European populations. Non-parametric methods that provide bounds of causal effect estimates requiring only the core MR assumptions to be met may be applicable for some MR studies where violations of any of these additional assumptions is possible.

## References

- Sheehan NA, Didelez V. Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail. Human Genetics 2019; 139: 121-136.
- Swanson SA, Hernán MA. The challenging interpretation of instrumental variable estimates under monotonicity. International Journal of Epidemiology 2017; 47: 1289-1297.
- Small DS, Tan Z, Ramashai RR, Lorch SA, Brookhart MA. Instrumental Variable Estimation with a Stochastic Monotonicity Assumption. Statistical Science 2017; 32: 561-579.

## 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)
- Horizontal Pleiotropy
- Independence assumption
- 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