Improved sensitivity bounds for mediation under unmeasured mediator–outcome confounding

It is often of interest to decompose a total effect into an indirect effect, relayed through a particular mediator, and a direct effect. However, these effect components are not identified if there are unmeasured confounding of the mediator and the outcome. We derive nonparametric bounds on the natural direct and indirect effects, and Cornfield inequalities that the unmeasured confounders must satisfy to explain away an “observed” effect. We demonstrate, analytically and by simulation, that these bounds and Cornfield inequalities are sharper than those previously proposed in the literature. We illustrate the methods with an application to cholestyramine treatment for coronary heart disease.