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. Author manuscript; available in PMC: 2023 Jun 14.
Published in final edited form as: Nat Rev Methods Primers. 2022 Feb 10;2:6. doi: 10.1038/s43586-021-00092-5

Table 1. List of MR estimation methods.

Category Core IV assumption relaxed Individual level data Summary data
‘Basic’ MR method None Wald ratio estimation, two-stage least squares regression analysis (2SLS)a Wald ratio estimation, inverse variance weightinga,38
Weak instrument robust methods IV1; allows for weak instruments Limited information maximum likelihood (LIML)27, allele score approaches27 MR RAPS88, dIVW190, MR GRAPPLE89, NOME adjustment191, two-sample AR192
Outlier/variant selection and removal IV3; allows for balanced/sparse pleiotropy Weighted median193 Weighted mediana,83
Outlier/variant selection and removal IV3; allows for (some) directional pleiotropy sisVIVE71, adaptive LASSO72, weighted mode193 Weighted modea,84, MR LASSO85, Steiger filteringa,94, Welch-weighted Egger95, contamination mixture194, GSMR80, MR-Clust195, Bayesian MIMR196, CIV73
Outlier/variant adjustment IV3; allows for balanced pleiotropy Limited approaches currently available MR RAPS88, MRCIP197
Outlier/variant adjustment IV3; allows for (some) directional pleiotropy Limited approaches currently available MR TRYX86, MR Robust85, MR CAUSE90, MR PRESSO87, MR GRAPPLE89, MRMix198, MR-LDP199, IMRP200, regularization201, MR-PATH202
Estimation adjustment IV3; allows for balanced pleiotropy Limited approaches currently available dIVW190
Estimation adjustment IV3; allows for (some) directional pleiotropy Constrained instrumental variables203, multivariable MR74 MR Egger91, multivariable MR74,92, MR Link204, hJAM205, GIV206, Bayesian network analysis207, BMRE208, BayesMR209
Environmental control adjustment IV3; allows for (some) directional pleiotropy MR GxE76,77, MR GENIUS78 Limited approaches currently available
a

Most commonly used methods; note that each method relies on strong assumptions and may not be the most appropriate in any particular setting. These categories are not mutually exclusive and the classification of some methods may be ambiguous. Each method will impose some alternative version of the IV condition that is relaxed for consistent estimation with that method. Methods that are robust to directional pleiotropy impose (often strong) assumptions on the nature of that pleiotropy to enable estimation. Novel MR estimation methods are being developed continually and will generally fit into one or more of these categories.