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Bremen Colloquium Epidemiology - Public Health

Dr. Tom Palmer (Lancaster University) will give a lecture on "Corrected standard errors for two-stage residual inclusion estimators and a Stata package for MR-Egger regression type analyses" on April 20th, 2017. The Colloquium will take place at BIPS in room 1.550 and will start at 3 p.m.


Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroskedasticity robust standard errors (SEs) for these estimates.

In our simulations Newey (1987), Terza (2016), bootstrap, and corrected two-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error.

MR-Egger regression analyses are becoming increasingly common in Mendelian randomization studies (MR) (Bowden et al. 2015). MR-Egger analyses use summary level data, as reported by genome-wide association studies. Such data is conveniently available from the MR-base platform (Hemani et al. 2016).

MR-Egger and related methods treat a multiple instrument MR analysis as a meta-analysis across the multiple genotypes. In the MR-Egger approach, bias from the pleiotropic effects of the multiple genotypes is treated as small study reporting bias in meta-analysis. They represent an important quality control check for any MR analysis incorporating multiple genotypes.

We implemented several of these methods (inverse-variance weighted [IVW], MR-Egger and weighted median approaches, as well as a relevant plot) in a package for Stata called mrrobust (pleiotropy robust methods for MR). There are also implementations of these methods in R (Yavorska and Burgess 2016).

mrrobust is freely available from, which includes instructions on how to install the package from within Stata. We plan to add features overtime.


Bowden J, Davey Smith G, Burgess S. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression. International Journal of Epidemiology, 2015, 44, 2, 512- 525.

Hemani G, Zheng J, Wade KH, et al., Davey Smith G, Gaunt TR, Haycock PC. The MR-Base Collaboration. MR-Base: a platform for systematic causal inference across the phenome using billions of genetic associations. bioRxiv, 2016, doi:; .

Newey WK. Efficient estimation of limited dependent variable models with endogenous explanatory variables. Journal of Econometrics, 1987, 36, 3, 231-250.

Terza JV. Simpler standard errors for two-stage optimization estimators. Stata Journal, 2016, 16, 2, 368-385.

Yavorska O, Burgess S. MendelianRandomization: Mendelian Randomization Package. 2016, version 0.2.0.