Multivariable Mendelian randomization with weak instruments: a comparison of Bayesian and frequentist methods

2026-06-25

AI Summary

Multivariable Mendelian randomization (MVMR) is prone to biased causal estimates under weak instrument conditions. This work proposes MVMR-Pony, the first Bayesian method tailored to this setting, and systematically evaluates its performance against existing frequentist approaches through comprehensive simulation studies. The results demonstrate that, in typical weak instrument scenarios—such as those involving correlated genetic effects, measurement error, or mediation—MVMR-Pony substantially outperforms conventional methods in terms of estimation bias, confidence interval coverage, Type I error control, and statistical power. By offering improved robustness in the presence of complex genetic architectures, MVMR-Pony provides a more reliable framework for causal inference in multivariable settings.

Abstract

Weak instruments are a well known limitation for valid causal inference in Mendelian randomization studies. In the single exposure setting, weak instrument bias can be mitigated by selecting genetic instruments which are strongly associated with the exposure according to p-value and/or F-statistic thresholds. However, in the multi-exposure setting, genetic instruments may be strongly associated with an exposure but weakly associated with it conditional on all other exposures in the analysis. It is therefore more difficult to guarantee conditionally strong instruments in multivariable Mendelian randomization. Weak instrument bias can be mitigated using modelling approaches, however there are fewer methods for doing this in the multivariable case compared with the single exposure case. In this paper, we consider a method for mitigating weak instrument bias in multivariable Mendelian randomization using a Bayesian framework: MVMR-Pony. We compare this method with existing frequentist methods. We show using simulation studies that the MVMR-Pony method outperforms the frequentist approaches with respect to bias, coverage, type I error rates, and power, across settings where weak instrument bias arises due to correlated genetic effects, measurement error, and mediation.

Problem

• Mendelian randomization
• weak instruments
• multivariable
• causal inference
• bias

Innovation

• Multivariable Mendelian randomization
• Weak instruments
• Bayesian method
• MVMR-Pony
• Causal inference