Bounds for causal mediation effects

TL;DR

This paper develops and compares bounds for causal mediation effects under various frameworks, especially when unmeasured confounders exist, and demonstrates their application using data from a peanut allergy study.

Contribution

It derives sharp symbolic bounds for mediation effects under unmeasured confounding within natural and separable effects frameworks, extending existing bounds.

Findings

Bounds are identical for separable and natural effects with unmeasured confounders.

Compared bounds under different assumptions on cross-world independence.

Applied bounds to real trial data on peanut allergy development.

Abstract

Several frameworks have been proposed for studying causal mediation analysis. What these frameworks have in common is that they all make assumptions for point identifications that can be violated even when treatment is randomized. When a causal effect is not point-identified, one can sometimes derive bounds, i.e. a range of possible values that are consistent with the observed data. In this work, we study causal bounds for mediation effects under both the natural effects framework and the separable effects framework. In particular, we show that when there are unmeasured confounders for the intermediate variables(s) the sharp symbolic bounds on separable (in)direct effect coincide with existing bounds for natural (in)direct effects in the analogous setting. We compare these bounds to valid bounds for the natural direct effects when only the cross-world independence assumption does not hold. Furthermore, we demonstrate the use and compare the results of the bounds on data from a trial investigating the effect of peanut consumption on the development of peanut allergy in infants through specific pathways of measured immunological biomarkers.