MVMRmode: Introducing an R package for plurality valid estimators for multivariable Mendelian randomisation

Mendelian randomisation (MR) is the use of genetic variants as instrumental variables. Mode-based estimators (MBE) are one of the most popular types of estimators used in univariable-MR studies and is often used as a sensitivity analysis for pleiotropy. However, because there are no plurality valid regression estimators, modal estimators for multivariable-MR have been under-explored. We use the residual framework for multivariable-MR to introduce two multivariable modal estimators: multivariable-MBE, which uses IVW to create residuals fed into a traditional plurality valid estimator, and an estimator which instead has the residuals fed into the contamination mixture method (CM), multivariable-CM. We then use Monte-Carlo simulations to explore the performance of these estimators when compared to existing ones and re-analyse the data used by Grant and Burgess (2021) looking at the causal effect of intelligence, education, and household income on Alzheimer's disease as an applied example. In our simulation, we found that multivariable-MBE was generally too variable to be much use. Multivariable-CM produced more precise estimates on the other hand. Multivariable-CM performed better than MR-Egger in almost all settings, and Weighted Median under balanced pleiotropy. However, it underperformed Weighted Median when there was a moderate amount of directional pleiotropy. Our re-analysis supported the conclusion of Grant and Burgess (2021), that intelligence had a protective effect on Alzheimer's disease, while education, and household income do not have a causal effect. Here we introduced two, non-regression-based, plurality valid estimators for multivariable MR. Of these, "multivariable-CM" which uses IVW to create residuals fed into a contamination-mixture model, performed the best. This estimator uses a plurality of variants valid assumption, and appears to provide precise and unbiased estimates in the presence of balanced pleiotropy and small amounts of directional pleiotropy.