Secondary Logo

Institutional members access full text with Ovid®

Eliminating Survivor Bias in Two-stage Instrumental Variable Estimators

Vansteelandt, Stijna,b; Walter, Stefanc,d; Tchetgen Tchetgen, Erice

doi: 10.1097/EDE.0000000000000835

Mendelian randomization studies commonly focus on elderly populations. This makes the instrumental variables analysis of such studies sensitive to survivor bias, a type of selection bias. A particular concern is that the instrumental variable conditions, even when valid for the source population, may be violated for the selective population of individuals who survive the onset of the study. This is potentially very damaging because Mendelian randomization studies are known to be sensitive to bias due to even minor violations of the instrumental variable conditions. Interestingly, the instrumental variable conditions continue to hold within certain risk sets of individuals who are still alive at a given age when the instrument and unmeasured confounders exert additive effects on the exposure, and moreover, the exposure and unmeasured confounders exert additive effects on the hazard of death. In this article, we will exploit this property to derive a two-stage instrumental variable estimator for the effect of exposure on mortality, which is insulated against the above described selection bias under these additivity assumptions.

From the aDepartment of Applied Mathematics, Computer Sciences and Statistics, Ghent University, Ghent, Belgium

bDepartment of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom

cDepartment of Epidemiology and Biostatistics, University of California, San Francisco, CA

dFundación de Investigación Biomédica, Hospital Universitario de Getafe, Madrid, Spain

eDepartment of Statistics, The Wharton School, University of Pennsylvania, PA.

Submitted February 1, 2017; accepted March 28, 2018.

Data sets are publicly available at given prior authorization by the HRS Restricted Data Application Process. Code for reproducing the form of the analysis is available in eAppendix B;

S.V.’s work was funded by the Fund for Scientific Research (Flanders, Belgium) (grant G.0111.12).

The authors report no conflicts of interest.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

Correspondence: Stijn Vansteelandt, Department of Applied Mathematics, Computer Sciences and Statistics,, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium. E-mail:

Copyright © 2018 Wolters Kluwer Health, Inc. All rights reserved.