Table 1 Description of the MR methods used in the main and sensitivity analyses.

 Wald ratio

• Ratio of the effect of the SNP-outcome association by the SNP-exposure association.

• Main MR method used for genetic instruments including a single SNP.

• Provides valid estimates if the genetic instrument satisfies all IV assumptions.

 Inverse-variance weighted (IVW) regression [61]

• Linear regression of the SNP-outcome associations on the SNP-exposure associations, weighted by the inverse-variance of the SNP-outcome associations and with intercept constrained to zero.

• Main MR method used to combine effect estimates for genetic instruments including ≥ 2 SNPs.

• Provides valid estimates if the genetic instrument satisfies all IV assumptions.

• Accounts for balanced pleiotropy (i.e., average pleiotropic effect equals to zero), but susceptible to unbalanced pleiotropy (i.e., average pleiotropic effect is positive or negative).

 MR-Egger regression [62]

• Weighted linear regression similar to IVW, but with intercept unconstrained.

• Provides an estimate of unbalanced horizontal pleiotropy and can yield accurate MR estimates even if all instruments are invalid.

• The intercept represents the average unbalanced horizontal pleiotropic effect across SNPs.

• Makes IV1, IV2, and InSIDE assumptions (i.e., the SNP-exposure associations are independent of the direct effects of the genetic variants on the outcome).

• Relaxes IV3 assumption.

• But suffers from low power and is sensitive to outliers.

 Weighted median method [63]

• Weighted median estimator for combining effect estimates from multiple genetic variants (instead of weighted mean as in IVW).

• The median of effect estimates is more robust to outliers than the corresponding mean (pleiotropy often manifests in the presence of genetic variants with outlying effect estimates).

• Provides accurate MR estimates when the majority of the information (>50%) comes from valid instruments.

• Makes IV1 and IV2 assumptions.

• Relaxes IV3 assumption.

 Weighted mode method [64]

• Weighted mode estimator for combining effect estimates from multiple genetic variants (instead of weighted mean as in IVW).

• Like the median, the mode is more robust to outliers than the corresponding mean.

• Provides accurate MR estimates if the largest subset of SNPs with a similar effect ratio (i.e., mode) is formed by valid instruments, even if the majority of SNPs are invalid.

• Makes IV1 and IV2 assumptions.

• Relaxes IV3 assumption.

 MR-PRESSO [65]

• Performs 3 tests: (1) detection of horizontal pleiotropy (global test); (2) correction for horizontal pleiotropy by removal of outliers (outlier test); (3) test for significant differences in the MR estimates before and after outlier removal (distortion test).

• Identifies and removes horizontal pleiotropic outliers in instruments including multiple SNPs.

• Makes IV1 and IV2 assumptions.

• Relaxes IV3 assumption.

• Best suited when horizontal pleiotropy occurs in < 50% of instruments.

 Robust adjusted profile score (MR-RAPS) [66]

• SNPs are assigned different weights according to the strength of their associations.

• Allows for the use of weaker instruments, which is not recommended for other methods.

• In our study, MR-RAPS is only used for the G2 instruments, which have been constructed using a more liberal p-value threshold and are therefore more susceptible to weak instrument bias.

• Makes IV2 and IV3 assumptions.

• Relaxes IV1 assumption.

 Steiger directionality test and filtering [67]

• Steiger Z-test assesses whether the absolute correlation of the genetic variants with the exposure is larger than that with the outcome.

• If Z-value > 0, X causes Y; if Z-value < 0, Y causes X; if Z = 0, neither direction is accepted.

• Steiger filtering can then be used to correct for potential misspecification of the direction of effect by removing genetic variants that explain more variation in the outcome than the exposure.

• Indicates the direction of the causal association (sign of Z-value) and the confidence level of the direction (p-value).

• Identifies and removes genetic variants whose direction of effect has been misspecified.

• Results may be biased in the presence of horizontal pleiotropy or different levels of measurement error between the exposure and the outcome.