Assessing the robustness of sisVIVE in a Mendelian randomization study to estimate the causal effect of body mass index on income using multiple SNPs from understanding society.

The "some invalid, some valid instrumental variable estimator" (sisVIVE) is a lasso-based method for instrumental variables (IVs) regression of outcome on an exposure. In principle, sisVIVE is robust to some of the IVs in the analysis being invalid, in the sense of being related to the outcome variable through pathways not mediated by the exposure. In this paper, we consider the application of sisVIVE to a Mendelian randomization study in which multiple genetic variants are used as IVs to estimate the causal effect of body mass index on personal income in the presence of unobserved confounding. In addition to analyzing data from the large-scale longitudinal household survey Understanding Society, we conduct a simulation study to (a) assess the performance of sisVIVE in relation to that of competing robust methods like "MR-Egger" and "MR-Median" and (b) identify scenarios under which its absolute performance is poor. We find that sisVIVE outperforms alternative robust methods, in terms of mean-square error, across a wide range of scenarios, but that its performance is poor in absolute terms when the presence of indirect pleiotropy leads to failure of the "InSIDE" condition, which is not explicitly required for identification. We argue that this is because the consistency criterion for sisVIVE does not identify the true causal effect when InSIDE fails.