The F-statistic tests whether a model (e.g., a linear or logistic regression model) with independent variables explains variation in the dependent variable, compared to a model with no independent variables.

In MR analyses, the first-stage F-statistic (or just "F-statistic") can be used to test the strength of the association between the genetic instrumental variable (IV) and exposure of interest and the extent of the relative bias that is likely to occur in estimating the causal effect of the exposure on the outcome using the genetic IV. As a general rule, an F-statistic >10 indicates that the level of weak instrument bias is likely to be small. F-statistics should not be used to select IVs to avoid overfitting the estimation model. For example, an F-statistic of <10 does not indicate that an IV should not be used but, instead, it should be noted in the analysis that weak instrument bias should be a considered limitation. See Conditional F-statistic.

## References

- Sanderson E, Glymour MM, Holmes MV, Kang H, Morrison J, MunafĂ˛ MR, Palmer T, Schooling MC, Wallace C, Zhao Q, Davey Smith G. Mendelian randomization. Nat Rev Methods Primers 2022; 2: 6.
- Yarmolinsky J, Bonilla C, Haycock PC, Langdon RJQ, Lotta LA, Langenberg C, et al. Circulating Selenium and Prostate Cancer Risk: A Mendelian Randomization Analysis. J Natl Cancer Inst. 2018; 110: 1035-1038.
- Brion MJ, Shakhbazov K, Visscher PM. Calculating statistical power in Mendelian randomization studies. Int J Epidemiol 2013; 42: 1497-501.
- Pierce BL, Ahsan H, Vanderweele TJ. Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants. Int J Epidemiol. 2011; 40: 740-52

## 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
- 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
- Weak instrument bias
- Winner's curse