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IJE Advance Access published online on May 7, 2008
International Journal of Epidemiology, doi:10.1093/ije/dyn080
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Published by Oxford University Press on behalf of the International Epidemiological Association © The Author 2008; all rights reserved.

Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses

Tom M Palmer1,*, John R Thompson1, Martin D Tobin2, Nuala A Sheehan2 and Paul R Burton2

1Department of Health Sciences, University of Leicester, UK.
2Departments of Health Sciences and Genetics, University of Leicester, UK.

*Corresponding author. University of Leicester, Department of Health Sciences, 2nd Floor, Adrian Building, University Road, Leicester LE1 7RH, UK. E-mail: tmp8{at}le.ac.uk


  Abstract

Background Mendelian randomization uses a carefully selected gene as an instrumental-variable (IV) to test or estimate an association between a phenotype and a disease. Classical IV analysis assumes linear relationships between the variables, but disease status is often binary and modelled by a logistic regression. When the linearity assumption between the variables does not hold the IV estimates will be biased. The extent of this bias in the phenotype-disease log odds ratio of a Mendelian randomization study is investigated.

Methods Three estimators termed direct, standard IV and adjusted IV, of the phenotype-disease log odds ratio are compared through a simulation study which incorporates unmeasured confounding. The simulations are verified using formulae relating marginal and conditional estimates given in the Appendix.

Results The simulations show that the direct estimator is biased by unmeasured confounding factors and the standard IV estimator is attenuated towards the null. Under most circumstances the adjusted IV estimator has the smallest bias, although it has inflated type I error when the unmeasured confounders have a large effect.

Conclusions In a Mendelian randomization study with a binary disease outcome the bias associated with estimating the phenotype-disease log odds ratio may be of practical importance and so estimates should be subject to a sensitivity analysis against different amounts of hypothesized confounding.

Keywords Instrumental-variable analysis, Mendelian randomization, bias, unobserved confounding

Accepted 3 April 2008


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