# What are the differences between the MR analysis methods?

• Wald ratio estimate (also known as the ratio of coefficients method) is calculated by dividing the gene-outcome association by the gene-exposure association for a specific genetic variant.
• 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).
• MR Egger (bootstrap): run bootstrap to obtain standard errors for MR.
• Median-based estimate: calculates the median of the ratio instrumental variable estimates evaluated using each genetic variant individually, including weighted mean, simple mean, and penalized weighted median methods.
• 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).
• 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.