  Mendelian randomization is a powerful tool for inferring the presence, or
otherwise, of causal effects from observational data. However, the nature of
genetic variants is such that pleiotropy remains a barrier to valid causal
effect estimation. There are many options in the literature for pleiotropy
robust methods when studying the effects of a single risk factor on an outcome.
However, there are few pleiotropy robust methods in the multivariable setting,
that is, when there are multiple risk factors of interest. In this paper we
introduce three methods which build on common approaches in the univariable
setting: MVMR-Robust; MVMR-Median; and MVMR-Lasso. We discuss the properties of
each of these methods and examine their performance in comparison to existing
approaches in a simulation study. MVMR-Robust is shown to outperform existing
outlier robust approaches when there are low levels of pleiotropy. MVMR-Lasso
provides the best estimation in terms of mean squared error for moderate to
high levels of pleiotropy, and can provide valid inference in a three sample
setting. MVMR-Median performs well in terms of estimation across all scenarios
considered, and provides valid inference up to a moderate level of pleiotropy.
We demonstrate the methods in an applied example looking at the effects of
intelligence, education and household income on the risk of Alzheimer's
disease.
