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; 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 risk factor and outcome of interest and generate a spurious (confounded) association between risk factor and outcome. Confounding can generate a positive or negative association when there is no causal effect of risk factor on 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 IVs are not associated with confounders of the risk factor-outcome association. In MR studies, demonstrating that genetic IVs are not related to observed risk factor-outcome confounders is important (though we cannot show they are not related to unobserved confounders). In two-sample MR with summary (aggregate) data, it may not be possible to explore associations with observed risk factor-outcome confounders in the outcome sample (sample 2). However, summary-level data from GWAS for any known or hypothesised confounders may be available and if so these should be used to explore whether there are associations with the risk factor-outcome confounders.

## 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-doi:10.1371/journal.pmed.0040352.
- 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
- Dynastic effects
- Exclusion restriction assumption
- Harmonization failure (in two-sample MR)
- Homogeneity Assumption
- Horizontal Pleiotropy
- Independence assumption
- InSIDE assumption (in two-sample MR using aggregate data)
- Monotonicity assumption
- MR for testing critical or sensitive periods
- MR for testing developmental origins
- No effect modification assumption (Additional IV assumption)
- Non-linear effects
- Non-overlapping samples (in two-sample MR)
- Overfitting
- Pleiotropy
- Population stratification
- Regression dilution bias (attenuation by errors)
- Relevance assumption
- Reverse causality
- Same underlying population (in two-sample MR)
- Statistical power/efficiency
- Vertical Pleiotropy
- Weak instrument bias
- Winner's curse