Instrument strength is determined by the magnitude and precision of association of the genetic IVs with the risk factor of interest.

The R2 and F-statistic for the association of the genetic IV with the risk factor provide an indication of instrument strength (the higher the value of both, the stronger the instrument and the greater statistical power in MR analyses). For reference, genetic IVs were traditionally considered to be sufficient if the corresponding F-statistic was >10. In one-sample MR, weak instruments tend to bias towards the confounded risk factor-outcome association; whereas, in two-sample MR (with non-overlapping samples) the bias is expected to be towards the null.

## References

- Zheng J, Baird D, Borges MC et al. Recent Developments in Mendelian Randomization Studies. Curr Epidemiol Rep 2017;4:330-345.
- Lawlor DA, Harbord RM, Sterne JAC, Timpson NJ, Davey Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Statistic in Medicine 2008;27:1133-1163.

## 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
- 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
- Winner's curse