  The presence of intermediate confounders, also called recanting witnesses, is
a fundamental challenge to the investigation of causal mechanisms in mediation
analysis, preventing the identification of natural path-specific effects.
Proposed alternative parameters (such as randomizational interventional
effects) are problematic because they can be non-null even when there is no
mediation for any individual in the population; i.e., they are not an average
of underlying individual-level mechanisms. In this paper we develop a novel
method for mediation analysis in settings with intermediate confounding, with
guarantees that the causal parameters are summaries of the individual-level
mechanisms of interest. The method is based on recently proposed ideas that
view causality as the transfer of information, and thus replace recanting
witnesses by draws from their conditional distribution, what we call "recanting
twins". We show that, in the absence of intermediate confounding, recanting
twin effects recover natural path-specific effects. We present the assumptions
required for identification of recanting twins effects under a standard
structural causal model, as well as the assumptions under which the recanting
twin identification formulas can be interpreted in the context of the recently
proposed separable effects models. To estimate recanting-twin effects, we
develop efficient semi-parametric estimators that allow the use of data driven
methods in the estimation of the nuisance parameters. We present numerical
studies of the methods using synthetic data, as well as an application to
evaluate the role of new-onset anxiety and depressive disorder in explaining
the relationship between gabapentin/pregabalin prescription and incident opioid
use disorder among Medicaid beneficiaries with chronic pain.
