Sharp nonparametric bounds for decomposition effects with two binary mediators

TL;DR

This paper develops sharp, valid bounds for mediation effects involving two sequential mediators in randomized trials, even with unmeasured confounding, enhancing causal inference in complex mediation scenarios.

Contribution

It introduces five main bounds and thirty supplementary bounds for various decompositions of effects with two mediators, addressing unmeasured confounding.

Findings

Derived sharp bounds for mediation effects with two mediators

Adding bounds of components often yields non-sharp, non-informative results

Illustrated bounds interpretation through simulations and real data

Abstract

In randomized trials, once the total effect of the intervention has been estimated, it is often of interest to explore mechanistic effects through mediators along the causal pathway between the randomized treatment and the outcome. In the setting with two sequential mediators, there are a variety of decompositions of the total risk difference into mediation effects. We derive sharp and valid bounds for a number of mediation effects in the setting of two sequential mediators both with unmeasured confounding with the outcome. We provide five such bounds in the main text corresponding to two different decompositions of the total effect, as well as the controlled direct effect, with an additional thirty novel bounds provided in the supplementary materials corresponding to the terms of twenty-four four-way decompositions. We also show that, although it may seem that one can produce sharp bounds by adding or subtracting the limits of the sharp bounds for terms in a decomposition, this almost always produces valid, but not sharp bounds that can even be completely noninformative. We investigate the properties of the bounds by simulating random probability distributions under our causal model and illustrate how they are interpreted in a real data example.