Weak instrument bias is the bias that occurs when the instrumental variable (IV) being used in an MR analysis is only weakly associated with the exposure.

The strength of IV in MR analyses is determined by the magnitude and precision of association of the genetic IVs with the exposure of interest. The R-squared and F-statistic for the association of the genetic IV with the exposure provide an indication of the strength of the IV or "instrument strength" (i.e., the higher the value of both, the stronger the IVand the greater statistical power in MR analyses). Genetic IVs were traditionally considered to be of sufficient power if the corresponding F-statistic was >10; however, this is not a rigid rule and an F-statistic <10 does not indicate that this IV should not be used, rather that weak instrument bias should be considered as an issue in analysis. In one-sample MR, weak IVs tend to bias towards the confounded association between the exposure and outcome; 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
- Conditional F-statistic for multiple exposures
- Confounding
- 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
- Winner's curse