Re-evaluating the robustness of Mendelian randomisation to measurement error
Authors: Woolf Benjamin , Yarmolinsky James , Karhunen Ville , Tilling Kate , Gill Dipender 
Published: October 2022

Background

Mendelian randomisation (MR) uses germline genetic variation as a natural experiment to investigate causal relations between traits. MR is robust to non-differential random measurement error in exposures or outcomes. However, the effect of differential measurement error, and non-differential measurement error on the variant selection process, remains unclear.

Methods

We use Monte-Carlo simulations and an applied example to explore the effect of differential measurement error on MR estimates for a continuous exposure and outcome, and the application of multivariable MR to reduce bias. We then explore the effect of non-differential measurement error during variant selection on MR analysis, using simulated and real-world data in the UK Biobank.

Results

Causal differential measurement error biased MR estimates when it occurred in the outcome, or in an exposure with a true causal effect on the outcome. This bias was mitigated by including the variable causing the error in a multivariable MR analysis. Unlike standard regression, MR was not biased by non-causal differential measurement error, i.e. when a third variable caused the exposure (or outcome) and the error in the outcome (or exposure). Non-differential measurement error in the phenotype during variant selection reduced the precision of MR estimates and induced bias. This bias was attenuated by using three-sample MR, or Winner’s curse corrections.

Conclusion

MR estimates can be biased by differential measurement error, but in fewer circumstances than standard regression. Multivariable MR can be used to attenuate differential measurement error if the error mechanism is known. Three-sample MR is recommended particularly for error-prone exposures.

Key Messages

Previous research demonstrates that Mendelian randomization (MR) is unbiased by (classical) non-differential measurement error in the exposure or outcome once the genetic instruments have been identified.

MR estimates can be biased by causal differential measurement error in a continuous outcome, or in a continuous exposure when there is a true causal effect of the exposure on the outcome. As with observational studies, this bias could lead to an over-or under-estimation of the true effect estimate.

Unlike standard regression, MR is not biased by non-causal differential measurement error between the exposure and outcome, or causal differential measurement error in the exposure under the null hypothesis.

When all the requisite assumptions are met, multivariable MR can be used to attenuate bias due to differential measurement error in an exposure or outcome, if the variables causing the error are known. Else, a smaller sample, which is less susceptible to differential measurement error, would produce more accurate estimates, despite decreased power.

Non-differential measurement error in the exposure will reduce precision and can cause bias in MR when it occurs during the instrument selection process. The bias caused by non-differential measurement error in instrument selection can be mitigated by using non-overlapping samples for instrument selection and the instrument-exposure estimation, or statistical correction for Winner’s curse.