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    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in American Journal of Epidemiology following peer review. The definitive publisher-authenticated version Tom M Palmer, Michael V Holmes, Brendan J Keating, Nuala A Sheehan; Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies, American Journal of Epidemiology, Volume 186, Issue 9, 1 November 2017, Pages 1104–1114, https://doi.org/10.1093/aje/kwx175 is available online at: https://academic.oup.com/aje/article/186/9/1104/3860090

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Correcting the standard errors of two-stage residual inclusion estimators for Mendelian randomization studies

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<mark>Journal publication date</mark>1/11/2017
<mark>Journal</mark>American Journal of Epidemiology
Issue number9
Volume186
Number of pages11
Pages (from-to)1104-1114
Publication StatusPublished
Early online date1/06/17
<mark>Original language</mark>English

Abstract

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.
We compare several different forms of the SE for linear and logistic TSRI estimates in simulations and in real data examples. Amongst others we consider SEs modified from the approach of Newey (1987), Terza (2016), and bootstrapping.
In our simulations Newey, Terza, 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. In the real data examples the Newey SEs were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators respectively.
We show that TSRI estimators with modified SEs have correct type I error under the null. Researchers should report TSRI estimates with modified SEs instead of reporting unadjusted or heteroskedasticity robust SEs.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in American Journal of Epidemiology following peer review. The definitive publisher-authenticated version Tom M Palmer, Michael V Holmes, Brendan J Keating, Nuala A Sheehan; Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies, American Journal of Epidemiology, Volume 186, Issue 9, 1 November 2017, Pages 1104–1114, https://doi.org/10.1093/aje/kwx175 is available online at: https://academic.oup.com/aje/article/186/9/1104/3860090