In his paper in this issue,1 Stijn Vansteelandt has performed an excellent service for epidemiologists who carry out statistical modeling, in general, and those who do mediation analyses with observational studies, in particular. In light of his paper, a number of important distinctions are worth addressing: (1) confounders versus postexposure factors with any type of regression modeling; (2) assessment of temporal order of factors; (3) exposures and mediators that are physically controllable versus those that are not; (4) linear and log-linear versus logistic modeling of causal associations; and (5) assessment of interactions in general versus in terms of mediation analyses.
Vansteelandt is raising the visibility of mediation analyses in epidemiology. Mediation analysis is much more prevalent in the social sciences where the focus is on the evaluation of the mechanisms of complex treatments or behavioral interventions. A Google search shows 9 times as many hits for the combination of “mediation analyses” and “psychology” as for “mediation analyses” and “epidemiology.” Similar results can be obtained with Medline. Furthermore, Vansteelandt makes a significant contribution to all fields using mediation analyses by resolving the important but obscure problem of bias due to postexposure covariates, in a way that requires no more assumptions than do standard mediation methods.
Even for those with less interest in studying the mechanisms of exposures to risk factors through mediation analyses, Vansteelandt's paper re-enforces the importance of strategic causal planning when modeling exposure on outcome. We are to be mindful of true confounders for which adjustment is imperative, versus postexposure factors such as mediators not necessarily in need of adjustment, unless one wants to understand how the exposure affects outcomes through a mediator. Furthermore, Vansteelandt's discussion confirms the importance of conceptual causal models to guide any set of hypotheses and corresponding analyses.
Implementing such strategies can be difficult because of the difficulty in ensuring the temporal order of the causal factors. For example, Vansteelandt's simulations are based on drinking as the exposure (E), smoking as the postexposure covariate (L), and HDL cholesterol as the mediator (M). In any study context, it would be very difficult to ensure that the drinking occurred first, followed by smoking, followed by prospectively collected or registry-based HDL. Furthermore, the causal relationships among these factors may be complicated by multiple feedback mechanisms. Such relationships are mentioned by Vansteelandt with respect to just the causal effects of the mediator on outcome. Of course, the statistical methodology has not progressed to the point where causal inference based on these feedback mechanisms is possible under the rigorous conditions that Vansteelandt has applied to the “simple” conceptual models in Figure 1.1
Inference under the standard mediation models (as well as most causal models such as Vansteeland's) requires that the mediator be “set” in an experimental context to specific levels (eg, setting HDL to a specific level of 57 mg/dL), even if it is not done in the study situation itself.2,3 For certain factors such as smoking and drinking, there may be plausible mechanisms to control whether an individual smokes or drinks (eg, rigorously supervised restriction or access). In contrast, a corresponding mechanism for controlling HDL is less plausible. That is, how would one set a person's HDL to 57 mg/dL in an experiment?
Vansteelandt does recognize this issue in the discussion of “natural” effects, for which there is no manipulation of the mediator of any sort because the value of the mediator is the value a given participant would have had in the absence of exposure or treatment (regardless of whether the participant actually received the treatment). Accordingly, some have interpreted this as the natural effect of the exposure that would be observed if a participant were randomized to a particular mediator level in the absence of exposure.3
Alternatively, a very different mediation model is the “principal stratification model.” This model stratifies the population into latent classes (ie, principal strata) based on this “randomization” of mediator levels. Natural direct effects of the exposure in certain principal strata are then obtained.4 This alternative mediation approach requires strong model assumptions in place of standard assumptions such as “no unmeasured confounders of the mediator-outcome relationship.” This situation represents a tradeoff of the assumption made with Vansteelandt's mediation approach, where model assumptions are relaxed but at the cost of making the “no unmeasured confounding” assumption, which is also required for most of the mediation literature. Moreover, the principal-stratification approach provides effects of the exposure for subgroups, whereas most other mediation approaches yield effects for the full population but under assumptions of no interaction.
The causal mediation methods described by Vansteelandt and others for linear and log-linear models are not applicable to logistic or probit models for binary or ordinal outcomes, nor to the Cox Proportional Hazards models for survival outcomes. One mediation strategy is to compare the main effect of the baseline intervention in the outcome model without the mediator to the corresponding main effect adjusting for the mediator. This approach can reveal a true difference in these 2 main effects even when there is no mediation (as is the case with confounding, as well). That is, such a population difference may occur when there is no association between the baseline intervention and the mediator due to the nonlinear link function. This property is sometimes called “lack of collapsibility.”5–7 We note that the natural effects approaches (eg, principal stratification and natural direct effects) are not vulnerable to this problem.8,9
Finally, Vansteelandt addresses the important mediation assumption of no mediator-exposure interaction. However, the presence of an interaction in the mediation model with or without postexposure covariates presents a problem for estimation and testing. It turns out that even under the no-confounding assumptions, this may still be problems of identification and bias if the baseline intervention affects the mediator, as is required for mediation. While there has been no formal work in this area, Kraemer et al10 note the problem, and there is research being conducted to derive the bias analytically with confirmation by simulations.
ABOUT THE AUTHOR
THOMAS TENHAVE is Professor of Biostatistics, Associate Director of Biostatistics in the Center for Clinical Epidemiology and Biostatistics. Dr. TenHave's research interests represent the intersection of causal statistical methods with research on behavioral interventions. More specifically, his statistical research addresses treatment nonadherence, causal mediation, and moderation by mechanisms of behavioral interventions, and designs and statistical analyses to accommodate patient preferences and adaptive treatment regimes.
1. Vansteelandt S. Estimating direct effects in cohort and case-control studies. Epidemiology
2. Pearl J. Direct and indirect effects. In: Besnard P, Hanks S, eds. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence
. San Francisco: Morgan Kaufmann; 2001:411–420.
3. Robins JM. Semantics of causal DAG models and the identification of direct and indirect effects. In: Green P, Hjort NL, Richardson S, eds. Highly Structured Stochastic Systems
. Oxford: Oxford University Press; 2003:70–81.
4. Frangakis C, Rubin D. Principal stratification in causal inference. Biometrics
5. Gail MH, Wieand S, Piantadosi S. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika
6. Robins J, Rotnitzky A. Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models. Biometrika
7. Vansteelandt S, Goetghebeur E. Causal inference with generalized structural mean models. J Roy Stat Soc Ser B: Stat Methodol
8. Hirano K, Rubin D, Zhao XH. Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics
9. Huang B, Sivaganesan S, Succop P, Goodman E. Statistical assessment of mediational effects for logistic mediational models. Stat Med
10. Kraemer H, Wilson G, Fairburn C. Mediators and moderators of treatment effects in randomized clinical trials. Arch Gen Psychiatry