Table 2.

Overview of referenced methods.

Method	Brief description
Basic multivariant MR methods
Two-stage least squares [3]	General instrumental variable analysis model for single-sample MR
IVW mean [3]	Estimates inverse-variance weighted (IVW) mean of the ${\beta }_j$
Heterogeneity testing
GSMR [14]	Combination of IVW mean with HEIDI heterogeneity test
GLIDE [15]	Heterogeneity test, using set of simultaneous regression equations
MR-PRESSO [16]	Heterogeneity test, using discrepancy between each variant and IVW estimate based on rest of variants
Implicit subset MR methods
Bowden et al. [17]	Estimates weighted median of the ${\beta }_j$
Hartwig et al. [18]	Estimates weighted mode of the ${\beta }_j$ using empirically smoothed densities
Burgess et al. [19]	Estimates weighted mode of the ${\beta }_j$ using heterogeneity weighted average density of IVW estimates of all subsets of variants
MR-Mix [20]	Models the set variants as an implicit mixture of valid and invalid instruments, and derives the estimate from the valid component of the mixture
Modeled pleiotropy MR methods
MR-Egger [21]	Estimation via weighted linear regression of ${\gamma }_{Yj}$ on ${\gamma }_{Xj}$
BayesMR [22]	Bayesian model selection on forward and reverse causation models
CAUSE [24]	Bayesian mixture model allowing a subset of variants to correspond to a mediated confounding scenario (whole-genome analysis)
LHC-MR [23]	Mixture model allowing different subsets of variants to correspond to mediated confounding and reverse causation scenarios (whole-genome analysis)
Explicit confounder MR methods
Multivariable MR-Egger [26]	MR-Egger approach that includes additional ${\gamma }_{Cj}$ in the model
MR-TRYX [25]	Large-scale evaluation of potential confounding using GWAS summary statistics database
Negative control population MR methods
PRMR [32]	Estimates the total component of ${\gamma }_{Yj}$ not mediated by $X$ using a negative control population