When MR is used to test the effect of a binary exposure, such as hypertension, obesity, or insomnia, results can also be difficult to interpret. At face value, the effect estimate is a ratio of a ratio. Additional considerations regarding violation of IV assumptions may be required in comparison to continuous exposures.

The exclusion restriction assumption may be violated by variation in the underlying or latent continuous trait (e.g., blood pressure or BMI), which will vary within the two categories (e.g., hypertensive versus normotensive). In MR analyses (as with multivariable analyses), one should consider whether dichotomising underlying continuous variables is appropriate. Where binary exposures are used, a cautious interpretation of the ‘genetic liability’ to an exposure might be warranted. Scaling the results, for example describing the effect estimate as a risk ratio (of a binary outcome) of difference in mean (continuous outcome) per doubling of the liability to exposure has been recommended.

## References

- Burgess S, Labrecque JA. Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates. European journal of epidemiology 2018;33:947-952.
- Bowden J, Vansteelandt S. Mendelian randomization analysis of case-control data using structural mean models. Statistics in Medicine 2011;30:678-694.
- Palmer TM, Thompson JR, Tobin MD, Sheehan NA, Burton PR. Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses. International Journal of Epidemiology 2008;37:1161-1168.