Bounding IV Estimates Using Mediation Analysis Thinking

In this paper we initially demonstrate that the well-known assumptions for conducting IV-analyses can equivalently be expressed using natural effects from mediation analysis. Viewing the assumptions, an indeed the whole IV analysis, from a mediation analysis perspective opens up a novel possibility for bounding the true causal effect of the exposure when the distributional assumptions of the IV analysis fail; eg. if there is an interactions between the unmeasured confounders and exposure. The procedure works across all effect scales (risk difference, hazard ratio etc.) and types of violations of the distributional assumptions. The proposed method can also be viewed as a sensitivity analysis for the IV-analysis where there is only a single tuning parameter, which can be straightforwardly interpreted. For the purely binary case the proposed bounds converges to the Balke and Pearl bounds when the tuning parameter tends to infinity (ie. when even the most extreme misspecification is considered). As the proposed method is computationally demanding some time is spent on implementation considerations.