For dichotomous outcomes, the authors discuss when the standard approaches to mediation analysis used in epidemiology and the social sciences are valid, and they provide alternative mediation analysis techniques when the standard approaches will not work. They extend definitions of controlled direct effects and natural direct and indirect effects from the risk difference scale to the odds ratio scale. A simple technique to estimate direct and indirect effect odds ratios by combining logistic and linear regressions is described that applies when the outcome is rare and the mediator continuous. Further discussion is given as to how this mediation analysis technique can be extended to settings in which data come from a case-control study design. For the standard mediation analysis techniques used in the epidemiologic and social science literatures to be valid, an assumption of no interaction between the effects of the exposure and the mediator on the outcome is needed. The approach presented here, however, will apply even when there are interactions between the effect of the exposure and the mediator on the outcome.

Recent advances in the causal inference literature on mediation have extended traditional approaches to direct and indirect effects to settings that allow for interactions and non-linearities. In this paper, these approaches from causal inference are further extended to settings in which multiple mediators may be of interest. Two analytic approaches, one based on regression and one based on weighting are proposed to estimate the effect mediated through multiple mediators and the effects through other pathways. The approaches proposed here accommodate exposure-mediator interactions and, to a certain extent, mediator-mediator interactions as well. The methods handle binary or continuous mediators and binary, continuous or count outcomes. When the mediators affect one another, the strategy of trying to assess direct and indirect effects one mediator at a time will in general fail; the approach given in this paper can still be used. A characterization is moreover given as to when the sum of the mediated effects for multiple mediators considered separately will be equal to the mediated effect of all of the mediators considered jointly. The approach proposed in this paper is robust to unmeasured common causes of two or more mediators.

Concepts concerning mediation in the causal inference literature are reviewed. Notions of direct and indirect effects from a counterfactual approach to mediation are compared with those arising from the standard regression approach to mediation of Baron and Kenny (1986), commonly utilized in the social science literature. It is shown that concepts of direct and indirect effect from causal inference generalize those described by Baron and Kenny and that under appropriate identification assumptions these more general direct and indirect effects from causal inference can be estimated using regression even when there are interactions between the primary exposure of interest and the mediator. A number of conceptual issues are discussed concerning the interpretation of identification conditions for mediation, the notion of counterfactuals based on hypothetical interventions and the so called consistency and composition assumptions.

An important problem within both epidemiology and many social sciences is to break down the effect of a given treatment into different causal pathways and to quantify the importance of each pathway. Formal mediation analysis based on counterfactuals is a key tool when addressing this problem. During the last decade, the theoretical framework for mediation analysis has been greatly extended to enable the use of arbitrary statistical models for outcome and mediator. However, the researcher attempting to use these techniques in practice will often find implementation a daunting task, as it tends to require special statistical programming. In this paper, the authors introduce a simple procedure based on marginal structural models that directly parameterize the natural direct and indirect effects of interest. It tends to produce more parsimonious results than current techniques, greatly simplifies testing for the presence of a direct or an indirect effect, and has the advantage that it can be conducted in standard software. However, its simplicity comes at the price of relying on correct specification of models for the distribution of mediator (and exposure) and accepting some loss of precision compared with more complex methods. Web Appendixes 1 and 2, which are posted on the Journal's Web site (http://aje.oupjournals.org/), contain implementation examples in SAS software (SAS Institute, Inc., Cary, North Carolina) and R language (R Foundation for Statistical Computing, Vienna, Austria).

Methods from causal mediation analysis have generalized the traditional approach to direct and indirect effects in the epidemiologic and social science literature by allowing for interaction and non-linearities. However, the methods from the causal inference literature have themselves been subject to a major limitation in that the so-called natural direct and indirect effects that are employed are not identified from data whenever there is a variable that is affected by the exposure, which also confounds the relationship between the mediator and the outcome. In this paper we describe three alternative approaches to effect decomposition that give quantities that can be interpreted as direct and indirect effects, and that can be identified from data even in the presence of an exposure-induced mediator-outcome confounder. We describe a simple weighting-based estimation method for each of these three approaches, illustrated with data from perinatal epidemiology. The methods described here can shed insight into pathways and questions of mediation even when an exposure-induced mediator-outcome confounder is present.