The strengths of two-sample MR in terms of weak instrument bias being towards the null and minimising, overfitting of the data assume that the two samples are completely independent of each other (i.e., there is no overlap of participants between the two samples).

In practice, when aggregate data from publicly available data are used, it may not be possible to determine whether there is overlap between samples. This is because many GWASs are conducted on consortia of many studies. Thus, there is potential for overlap between some of the studies that contribute to these consortia (such as the GIANT consortia GWAS of BMI, waist-hip ratio and height, and the DIAGRAM consortia GWAS of diabetes). Careful reading of consortia websites and supplementary material should be undertaken to determine which studies contribute to each of the ‘samples’ used for the genetic IV-risk factor and genetic IV-outcome samples and, if possible, sensitivity analyses undertaken with overlapping studies removed.

## References

- Lawlor DA. Two-sample Mendelian randomization: opportunities and challenges. . International Journal of Epidemiology 2016;doi:10.1093/ije/dyw127.
- Hartwig FP, Davies NM, Hemani G, Davey Smith G. Two-sample Mendelian randomization: avoiding the downsides of a powerful, widely applicable but potentially fallible technique. Int J Epidemiol 2016;45:1717-1726.

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

- Assortative mating
- Canalization
- Collider
- Collider bias
- Confounding
- 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
- 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