Identifying Direct and Indirect Effects in a Non-Counterfactual Framework

Abstract

Identifying direct and indirect effects is a common problem in the social science and medical literature and can be described as follows. A treatment is administered and a response is recorded. However, another variable mediates the effect of the treatment on the response, in some way "channelling" a part of the treatment effect. The question is how to extricate the direct and channelled (indirect) effects from one another when it is not possible to intervene on the mediating variable. The aim of the paper is to tackle this problem by using a model for direct and indirect effects based on the decision theoretic framework for causal inference. Copyright 2007 Royal Statistical Society.

The Mediation Formula: A Guide to the Assessment of Causal Pathways in Nonlinear Models

“…Conversely, attempts to define and understand mediation using the notion of "principal-strata direct effect" have encountered basic conceptual difficulties (Lauritzen, 2004;Robins et al, 2007Robins et al, , 2009Pearl, 2009b), concluding that "it is not always clear that knowing about the presence of principal stratification effects will be of particular use" (VanderWeele, 2008). As a result, it is becoming widely recognized that the controlled, natural and indirect effects discussed in this paper are of greater interest, both for the purposes of making treatment decisions and for the purposes of explanation and identifying causal mechanisms (Joffe et al, 2007;Albert and Nelson, 2011;Mortensen et al, 2009;Imai et al, 2010a;Geneletti, 2007;Robins et al, 2007Robins et al, , 2009Petersen et al, 2006;Hafeman and Schwartz, 2009;Kaufman, 2010;Cai et al, 2008).…”

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“…We might view this as the controlled direct effect of treatment controlling for death (by setting it to 0). A less drastic intervention might involve equalizing death between different levels of treatment (Robins and Greenland, 1989); this might be formulated in terms of natural or pure direct effects (Robins and Greenland, 1992;Pearl, 2001) or in terms of stochastic interventions on death (Geneletti, 2007); such approaches would still be unattractive because of the vagueness of the counterfactuals or hypothetical interventions.…”