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

Background: 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. Methods: 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. Results: 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. Conclusions: 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.