- Wald ratio: The Wald Ratio is one of the most straightforward methods. In the Wald ratio method, each genetic variant is used as an instrumental variable, and the causal effect of the exposure on the outcome is estimated as the ratio of the genetic association with the outcome to the genetic association with the exposure. This is done for each genetic variant, and then the results can be combined across genetic variants, for example by taking the average.
- Maximum likelihood: the genetic effects on the exposure and outcome are modeled as a bivariate normal distribution using a maximum likelihood method, similar to IVW (fixed effect).
- MR Egger: estimates the causal effect adjusted for any directional pleiotropy by combining the Wald ratio into a meta-regression (with an intercept and slope parameter) (Bowden et al. 2015). This method is similar to the IVW approach, but allows the intercept term in the regression model to be non-zero, which can be an indication of pleiotropy. This analysis allows for the potential existence of pleiotropy, where a single gene or genetic variant affects more than one trait. The intercept from the MR-Egger regression provides a measure of the average pleiotropic effect across all genetic variants. A non-zero intercept can indicate directional pleiotropy, which could bias the MR estimates. The slope in MR-Egger regression provides a causal estimate that is corrected for pleiotropy.
- MR Egger (bootstrap): run bootstrap to obtain standard errors for MR.
- Weighted median method: This method calculates the median of the ratio estimates, but each ratio estimate is weighted by the inverse of its variance. This method provides a consistent estimate of the causal effect even when up to 50% of the information comes from invalid instrumental variables (those that violate the MR assumptions). If the weighted median estimate is similar to the standard MR estimate, it suggests that the results are robust to violations of the MR assumptions by some of the genetic variants.
- Inverse variance weighted (IVW): IVW combines two or more random variables to minimize the variance of the weighted average, which assumes no pleiotropy (Burgess et al. 2013). The basic idea here is to use each genetic variant as a separate instrumental variable and to combine the individual causal effect estimates using a meta-analysis approach. The main assumption is that the genetic variants are valid instrumental variables, i.e., they are associated with the exposure, not associated with confounders of the exposure-outcome relationship, and affect the outcome only through the exposure.
- IVW radial: fits a radial IVW model (Bowden et al. 2018)
- Inverse variance weighted (multiplicative random effects): the multiplicative random effects model permits over-dispersion in the regression model, which permits variability between the causal estimates targeted by the genetic variations.
- Inverse variance weighted (fixed effects): In a fixed-effect meta-analysis, Wald ratios are combined, with each ratio’s weight equaling the inverse of the variance of the SNP-outcome association.
- Mode-based estimate: defined as the mode of an empirical density function of the Wald ratio, either unweighted or inverse variance weighted, including simple mode, weighted mode, weighted mode with NO Measurement Error (NOME) assumption, and simple mode (NOME) (Hartwig et al. 2017).
- RAPS: robust adjusted profile score (Zhao et al. 2019)
- Sign concordance test: conducts a binomial test to determine if the proportion of positive signs is greater (in the event of a positive effect) or smaller (in the case of a negative effect) than would be predicted by chance (reference).
- Unweighted regression: similar to the IVW (fixed effects), but all SNPs are weighted equally.
Among these methods, the median estimator and MR Egger regression allow for genetic pleiotropy.
Reference:
Burgess, Stephen et al. Stat Methods Med Res. vol. 26,5 (2017)
Burgess, Stephen et al. Stat Med. vol. 35,11 (2016)
Burgess, Stephen, and Simon G Thompson. Eur J Epidemiol. vol. 32,5 (2017)
Davies, Neil M et al. BMJ (Clinical research ed.) vol. 362 k601. 12 Jul. (2018)