TY - JOUR

T1 - Sharp Nonparametric Bounds for Decomposition Effects with Two Binary Mediators

AU - Gabriel, Erin E.

AU - Sachs, Michael C.

AU - Sjölander, Arvid

N1 - Publisher Copyright: © 2022 The Author(s). Published with license by Taylor & Francis Group, LLC.

PY - 2023

Y1 - 2023

N2 - 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 30 novel bounds provided in the supplementary materials corresponding to the terms of 24 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. Supplementary materials for this article are available online.

AB - 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 30 novel bounds provided in the supplementary materials corresponding to the terms of 24 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. Supplementary materials for this article are available online.

KW - Causal bounds

KW - Effect decomposition

KW - Mediation analysis

KW - Natural effects

KW - Randomized trials

U2 - 10.1080/01621459.2022.2057316

DO - 10.1080/01621459.2022.2057316

M3 - Journal article

AN - SCOPUS:85129839149

VL - 118

SP - 2446

EP - 2453

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 544

ER -