The traditional definition of a confounder is that: i) it is associated with the exposure; ii) it is associated with the outcome conditional upon the exposure; and iii) it is not on the causal pathway between the exposure and outcome. However, because this set of rules does not generalize to complex modelling structures, the modern interpretation uses Pearl's directional-separation rules. In this context, the modern definition of confounding is the existence of an open “backdoor pathway” between the exposure and outcome - where one or more characteristics influence the exposure and outcome of interest and generate a spurious (confounded) association between the exposure and outcome. Confounding can generate a positive or negative association when there is no causal effect of the exposure on the outcome and can exaggerate or attenuate a true causal effect.

Associations of genetic variants with outcomes are generally less prone than associations of non-genetic characteristics to confounding by many socio-demographic, lifestyle and clinical characteristics from across the lifecourse. The independence assumption states that there are no confounders of the IV and outcome. In MR studies, demonstrating that genetic IVs are not related to observed exposure-outcome confounders within available (likely individual-level) data is one possible mechanism of falsifying invalidations of this assumption (though it is not possible to show they are not related to unobserved confounders). In two-sample MR, it may not be possible to explore associations with such confounders. Instead, using data sources for the two samples that are representative of the same underlying population (i.e., the populations are homogenous) may avoid such confounding. If summary-level data from genome-wide association studies (GWASs) of any known or hypothesised confounders are available, it may be used to explore whether there are associations between the genetic IV and these confounders; however, the MR assumption that is being tested (i.e., the second - independence - or third - exclusion restriction - assumption) should be considered.

## 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.
- Lawlor DA, Richmond R, Warrington N et al. Using Mendelian randomization to determine causal effects of pregnancy (intrauterine) exposures on offspring outcomes: Sources of bias and methods for assessing them. . Wellcome Open Research 2017; 2: 11.

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

- Assortative mating
- Canalization
- Collider
- Collider bias
- Conditional F-statistic for multiple exposures
- Exclusion restriction assumption
- F-statistic
- Harmonization (in two-sample MR)
- Homogeneity Assumption
- 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