Abstract

Mediation analysis aims at disentangling the effects of a treatment on an outcome through alternative causal mechanisms and has become a popular practice in biomedical and social science applications. The causal framework based on counterfactuals is currently the standard approach to mediation, with important methodological advances introduced in the literature in the last decade, especially for simple mediation, that is with one mediator at the time. Among a variety of alternative approaches, Imai et al. showed theoretical results and developed an R package to deal with simple mediation as well as with multiple mediation involving multiple mediators conditionally independent given the treatment and baseline covariates. This approach does not allow to consider the often encountered situation in which an unobserved common cause induces a spurious correlation between the mediators. In this context, which we refer to as mediation with uncausally related mediators, we show that, under appropriate hypothesis, the natural direct and joint indirect effects are non-parametrically identifiable. Moreover, we adopt the quasi-Bayesian algorithm developed by Imai et al. and propose a procedure based on the simulation of counterfactual distributions to estimate not only the direct and joint indirect effects but also the indirect effects through individual mediators. We study the properties of the proposed estimators through simulations. As an illustration, we apply our method on a real data set from a large cohort to assess the effect of hormone replacement treatment on breast cancer risk through three mediators, namely dense mammographic area, nondense area and body mass index.

Highlights

  • Causal mediation analysis comprises statistical methods to study the mechanisms underlying the relationships between a cause, an outcome and a set of intermediate variables

  • We show that, under assumptions alternative to Sequential Ignorability, the direct effect and the joint indirect effect through the vector of all mediators can be expressed by a formula involving observed variables only, while the indirect effect through each individual mediator is given by a formula involving both observed and counterfactual variables

  • We compare our estimates of the mediation causal effects to the true effects and to the estimates obtained by running simple mediation analyses, one for each mediator

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Summary

Introduction

Causal mediation analysis comprises statistical methods to study the mechanisms underlying the relationships between a cause, an outcome and a set of intermediate variables. We adopt the point of view and formalism of Imai, Keele, and Tingley (2010a), Imai, Keele, and Yamamoto (2010b), who put forward a general approach based on counterfactuals to define, identify and estimate causal mediation effects without assuming any specific statistical model in the particular case of a single mediator. Their theoretical results are based on a strong set of assumptions known as Sequential Ignorability. N (0, 1) AΓ: the transpose of a matrix or vector A

Brief review of simple mediation
Extension to multiple causally unrelated mediators
B Assumptions
C Identifiability
D Continuous outcome
E Binary outcome
F Estimation algorithm
Simulation studies
A Data simulation method
C Empirical study of the properties of the proposed estimators
Application
A Regression models
B Multiple mediation analysis
Discussion
A Indirect effect via the mediator of interest
B Joint indirect effect
Findings
D Models
Full Text
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