Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn

The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements -- effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this paper is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference between the causal inference and traditional approaches to mediation analysis and making a case for the need for explicit causal thinking and the causal inference approach in mediation analysis. It then explains in as-plain-as-possible language existing effect types, paying special attention to motivating these effects with different types of research questions, and using concrete examples for illustration. This presentation differentiates two perspectives (or purposes of analysis): the explanatory perspective (aiming to explain the total effect) and the interventional perspective (asking questions about hypothetical interventions on the exposure and mediator, or hypothetically modified exposures). For the latter perspective, the paper proposes tapping into a general class of interventional effects that contains as special cases most of the usual effect types -- interventional direct and indirect effects, controlled direct effects and also a generalized interventional direct effect type, as well as the total effect and overall effect. This general class allows flexible effect definitions which better match many research questions than the standard interventional direct and indirect effects

On Partial Identification of the Pure Direct Effect

In causal mediation analysis, nonparametric identification of the pure (natural) direct effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called "cross-world-counterfactuals" independence and (ii) no exposure- induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient's adherence, and show that inference on this effect is somewhat sensitive to model assumptions.Comment: 24 pages, 4 figure

Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis

While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon evaluating the total effect of the exposure, investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure, through a mediator variable or not, that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.Comment: Published in at http://dx.doi.org/10.1214/12-AOS990 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Counterfactual Graphical Models for Longitudinal Mediation Analysis with Unobserved Confounding

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 paper 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 J. Robins (1986), and Pearl (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.Comment: To appear in the 2012 Rumelhart prize special issue of Cognitive Science honoring Judea Pear

Exploring mechanisms of action in clinical trials of complex surgical interventions using mediation analysis.

BACKGROUND: Surgical interventions allow for tailoring of treatment to individual patients and implementation may vary with surgeon and healthcare provider. In addition, in clinical trials assessing two competing surgical interventions, the treatments may be accompanied by co-interventions. AIMS: This study explores the use of causal mediation analysis to (1) delineate the treatment effect that results directly from the surgical intervention under study and the indirect effect acting through a co-intervention and (2) to evaluate the benefit of the surgical intervention if either everybody in the trial population received the co-intervention or nobody received it. METHODS: Within a counterfactual framework, relevant direct and indirect effects of a surgical intervention are estimated and adjusted for confounding via parametric regression models, for the situation where both mediator and outcome are binary, with baseline stratification factors included as fixed effects and surgeons as random intercepts. The causal difference in probability of a successful outcome (estimand of interest) is calculated using Monte Carlo simulation with bootstrapping for confidence intervals. Packages for estimation within standard statistical software are reviewed briefly. A step by step application of methods is illustrated using the Amaze randomised trial of ablation as an adjunct to cardiac surgery in patients with irregular heart rhythm, with a co-intervention (removal of the left atrial appendage) administered to a subset of participants at the surgeon's discretion. The primary outcome was return to normal heart rhythm at one year post surgery. RESULTS: In Amaze, 17% (95% confidence interval: 6%, 28%) more patients in the active arm had a successful outcome, but there was a large difference between active and control arms in the proportion of patients who received the co-intervention (55% and 30%, respectively). Causal mediation analysis suggested that around 1% of the treatment effect was attributable to the co-intervention (16% natural direct effect). The controlled direct effect ranged from 18% (6%, 30%) if the co-intervention were mandated, to 14% (2%, 25%) if it were prohibited. Including age as a moderator of the mediation effects showed that the natural direct effect of ablation appeared to decrease with age. CONCLUSIONS: Causal mediation analysis is a useful quantitative tool to explore mediating effects of co-interventions in surgical trials. In Amaze, investigators could be reassured that the effect of the active treatment, not explainable by differential use of the co-intervention, was significant across analyses

Nonlinear mediation analysis with high‐dimensional mediators whose causal structure is unknown

With multiple possible mediators on the causal pathway from a treatment to an outcome, we consider the problem of decomposing the effects along multiple possible causal path(s) through each distinct mediator. Under a path-specific effects framework, such fine-grained decompositions necessitate stringent assumptions, such as correctly specifying the causal structure among the mediators, and no unobserved confounding among the mediators. In contrast, interventional direct and indirect effects for multiple mediators can be identified under much weaker conditions, while providing scientifically relevant causal interpretations. Nonetheless, current estimation approaches require (correctly) specifying a model for the joint mediator distribution, which can be difficult when there is a high-dimensional set of possibly continuous and noncontinuous mediators. In this article, we avoid the need to model this distribution, by developing a definition of interventional effects previously suggested for longitudinal mediation. We propose a novel estimation strategy that uses nonparametric estimates of the (counterfactual) mediator distributions. Noncontinuous outcomes can be accommodated using nonlinear outcome models. Estimation proceeds via Monte Carlo integration. The procedure is illustrated using publicly available genomic data to assess the causal effect of a microRNA expression on the 3-month mortality of brain cancer patients that is potentially mediated by expression values of multiple genes