A Simple Unified Approach for Estimating Natural Direct and Indirect Effects

Abstract

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).

medflex: An R Package for Flexible Mediation Analysis using Natural Effect Models

“…A drawback of direct application of the mediation formula, however, is that combinations of simple models for the mediator and for the outcome often result in complex expressions for natural direct and indirect effects (Lange et al 2012;Vansteelandt et al 2012b). For instance, when using logistic regression models…”

“…This is also illustrated in Figure 1, which depicts estimates for the natural indirect effect odds ratio, as obtained by applying the mediation formula to these models fitted to our example dataset (using a dichotomized version of the mediator and baseline covariates C including gender, age and education level). As pointed out before by Lange et al (2012) and Vansteelandt et al (2012b), these convoluted expressions render results difficult to report and hypothesis testing (e.g., testing for moderated mediation) infeasible, as it may turn out impossible to find plausible models for the mediator and outcome that combine into effect expressions that do not depend on covariate levels. In certain cases, this complexity can pose a major impediment to routine application of the mediation formula.…”

“…More specifically, we make use of novel socalled natural effect models (Lange, Vansteelandt, and Bekaert 2012;Lange, Rasmussen, and Thygesen 2014;Loeys, Moerkerke, De Smet, Buysse, Steen, and Vansteelandt 2013;Vansteelandt, Bekaert, and Lange 2012b), which directly parameterize the target causal estimands on their most natural scale. This renders formal testing and interpretation more straightforward compared to other approaches as implemented in the aforementioned software applications.…”

Effects of leisure-time and occupational physical activities on 20-year incidence of acute myocardial infarction: mediation and interaction

“…Further discussions of these assumptions can be found elsewhere (49). We used recently proposed inverse-probability weighted fitting of marginal structural models for causal mediation analysis (24) to estimate the marginal pure direct effect of baseline OPA on AMI and the marginal total indirect effect of baseline OPA via baseline LTPA (figure 1). Pure direct effect was defined as the HR comparing high to low OPA levels while allowing LTPA to attain the natural value under the low OPA level.…”

“…More specifically, and separately for men with and without preexisting IHD at baseline, our study aimed to: (i) assess both multiplicative and additive interaction between OPA and LTPA and their combined effect on 20-year incidence of AMI and (ii) examine the potential mediating role of LTPA on the pathway from OPA to AMI, using causal mediation analysis that allowed for exposure-mediator interaction (24,25).…”