Counterfactual Graphical Models for Longitudinal Mediation Analysis With Unobserved Confounding

Abstract

Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the "difference method" (Judd & Kenny, 1981), more common in epidemiology, or the "product method" (Baron & Kenny, 1986), more common in the social sciences. In this article, we first discuss a known, but perhaps often unappreciated, fact that these parametric approaches are a special case of a general counterfactual framework for reasoning about causality first described by Neyman (1923) and Rubin (1974) and linked to causal graphical models by Robins (1986) andPearl (2000). We then show a number of advantages of this framework. First, it makes the strong assumptions underlying mediation analysis explicit. Second, it avoids a number of problems present in the product and difference methods, such as biased estimates of effects in certain cases. Finally, we show the generality of this framework by proving a novel result which allows mediation analysis to be applied to longitudinal settings with unobserved confounders.Keywords: Causal inference; Counterfactuals; Mediation analysis; Longitudinal studies; Direct and indirect effects; Path-specific effects; Graphical modelsThe aim of empirical research in many disciplines is establishing the presence of effects by means of either randomized trials or observational studies if randomization is not possible. For example, a celebrated success of empirical research in epidemiology is the discovery of a causal connection between smoking and lung cancer (Doll & Hill, 1950).Once the presence of an effect is established, the precise mechanism of the effect becomes a topic of interest as well. A particularly popular type of mechanism analysis Correspondence should be sent to Ilya Shpitser, Mathematical Sciences,

Interpretable Conditions for Identifying Direct and Indirect Effects

“…10 would lead to identifiable effects, while suppressing the W → Y or M → Y processes will not. Shpitser (2013) generalizes this result and gives a complete algorithm for path specific effects with multiple treatments, multiple outcomes, and hidden variables. Figure 10 can in fact be regarded as having two interacting mediators, M and W , and the results of Avin et al (2005) highlight a fundamental difference between the two.…”

“…These three steps are echoed in the informal conditions articulated in the next section. (See also Shpitser and VanderWeele (2011) and especially Shpitser (2013) for refinements and elaborations.) the factors that influence T are independent of all factors that influence Y when T is held fixed.…”

Anti-discrimination learning: a causal modeling-based framework

“…The explicit statement of these steps is omitted here. We recommend the reader to refer to the original papers [2,31]. As an example, in Fig.…”

“…The complete criterion for the identifiability of the post-intervention distribution is given by the do-calculus [25]. Regarding the path-specific effect, Shpitser [31] has given the generalized version of the recanting witness criterion that holds in the semi-Markovian model, known as the recanting district criterion. Any anti-discrimination technique designed for models with unobserved confounders, i.e., semi-Markovian models, must be adapted to the differences in the causal inference techniques.…”

The Deductive Approach to Causal Inference

“…Due to these two provisions, assumption set A significantly broadens the class of problems in which the natural effects are identifiable [23]. Shpitser [24] further provides complete algorithms for identifying natural direct and indirect effects and extends these results to path-specific effects with multiple treatments and multiple outcomes.…”