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Expanding the range of inference and estimation in Multivariable Mendelian Randomization

Bristol Medical School

About the Project

Many of an individual’s traits and characteristics are observationally associated with their health outcomes, however these relationships are often confounded, meaning it is not possible to determine the causal effect of particular traits on different outcomes. Mendelian Randomization (MR) is a form of instrumental variable analysis which can be to estimate causal effects in the presence of unobserved confounding. MR uses genetic variants which vary between individuals and have been shown to associate with the exposure as instruments to estimate causal effects. MR can be conducted either using data on individuals or as ‘Two-sample summary data MR’ using summary data on the association between the genetic variant and the exposure and outcome of interest taken from analyses of separate samples.

Multivariable MR is an extension of MR estimation that includes multiple exposures and can estimate the direct effect of each exposure on the outcome. Multivariable MR can be applied in settings where MR would give a biased estimate of the exposure on the outcome such as when genetic variants associated with the exposure of interest are thought to also be associated with other phenotypes, or to help unpick more complicated networks of relationships between multiple exposures.

Multivariable MR has grown in popularity recently and is now applied in a wide range of settings, however the implications on the estimation from the data available not meeting the ‘ideal’ setting for multivariable MR are not currently well understood. This PhD will investigate a variety of different ‘non-ideal’ scenarios to understand how they affect the results obtained from a multivariable MR estimation and how these effects could be mitigated. Examples of the sorts of scenarios that will be considered include; what is the best strategy for multivariable MR estimation when there are many genetic variants available for one exposure but only a few for another exposure, what are the implications on the estimated effects of all exposures when one (but not all) of them violates a key assumption of the analysis, and what is estimated when the observed value of one exposure has been adjusted for another exposure included in a two-sample multivariable MR?

This project will involve simulation studies to explore these issues as well as analysis of both individual-level and summary-level data. Although it will be primarily methodological in focus, the student will have the opportunity to develop a relevant application linked to the issues explored based on their personal applied research interests. Prospective applicants should have an interest in developing methods for causal analysis within a population health setting and will be expected to develop a robust understanding of the statistical basis of MR and instrumental variables analysis, however, no background knowledge of any particular topic is required.


Lawlor, Debbie A., et al. "Mendelian randomization: using genes as instruments for making causal inferences in epidemiology." Statistics in medicine 27.8 (2008): 1133-1163.

Sanderson, Eleanor, et al. "An examination of multivariable Mendelian randomization in the single-sample and two-sample summary data settings." International journal of epidemiology 48.3 (2019): 713-727.

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