A comparison of robust methods for Mendelian randomization using multiple genetic variants

We report the results of a Mendelian randomization study in which multiple genetic variants are used as instrumental variables to estimate the causal effect of body mass index on personal income in the presence of unobserved confounding. The data come from Understanding Society, a large-scale longitudinal household survey, and the GIANT consortium study. Mendelian randomization studies are known to be affected by both weak instrument bias and the pleiotropic bias that arises when some genetic variants are invalid instrument variables. We review and compare some of the recently developed techniques for using multiple genetic variants as instrumental variables. Our principal focus, however, is to assess the "some invalid some valid instrumental variable estimator" (sisVIVE) developed by Kang et al. (2016). We conduct a comprehensive simulation study to assess sisVIVE for Understanding Society-like data, and find that it outperforms alternative methods across a range of scenarios. However, its performance is poor in absolute terms when the presence of indirect pleiotropy leads to failure of the key "InSIDE" condition, despite this not being explicitly required for identification. We argue that this is because the consistency criterion for sisVIVE does not identify the true causal effect if InSIDE fails. In the application to Understanding Society, we find no evidence for pleiotropic bias, and the negative effect of body mass index on income to be around five times larger than the observational association. However, this conclusion depends on the unverifiable assumption that InSIDE holds.