Causal Mediation Analysis

Causal Mediation Analysis is a set of counterfactual methods for asking how and why an exposure affects an outcome, by separating the portion of the effect that passes through a specified intermediate variable, the mediator, from the portion that does not. In epidemiology it is used to examine, for example, whether the effect of education on mortality runs through smoking, or whether a drug lowers cardiovascular risk by reducing blood pressure. The field grew from the regression-based approach of Baron and Kenny in 1986, was given formal counterfactual foundations by Robins and Greenland in 1992 and by Pearl in 2001, and was extended to exposure–mediator interaction and sensitivity analysis by VanderWeele and others. Its main lesson is that mediation questions demand more assumptions than total-effect questions, and that those assumptions are rarely guaranteed by study design.

Baron and Kenny proposed a sequence of regressions. The exposure A is regressed on the mediator M to obtain a coefficient α, and the outcome Y is regressed on A and M jointly to obtain a direct coefficient θ and a mediator coefficient β. The indirect effect is estimated as the product αβ, and the direct effect as θ. When all models are linear without exposure–mediator interaction, the total effect equals θ + αβ, and the proportion mediated is αβ divided by the total.

The approach is simple and remains widely taught, but it has three limitations. It has no definition of the effects outside linear models, so it cannot handle binary outcomes, survival times, or interactions without ad hoc extensions. It does not state the confounding assumptions required for a causal reading. And it treats testing the significance of the individual paths as a criterion for mediation, which has low power for small indirect effects.

Let Y_a denote the outcome that would occur if the exposure were set to a, and M_a the mediator that would occur under exposure a. Let Y_a,m be the outcome under joint intervention on exposure and mediator.

• The controlled direct effect is Y_1,m − Y_0,m, comparing exposure levels while fixing the mediator at a value m for everyone.
• The natural direct effect is Y_1,M0 − Y_0,M0, comparing exposure levels while each individual's mediator is held at the value it would have taken without exposure.
• The natural indirect effect is Y_1,M1 − Y_1,M0, the change in outcome when the mediator is shifted from its unexposed to its exposed value while exposure is held at 1.

The total effect is the sum of the natural direct and natural indirect effects. Robins and Greenland described these quantities as pure and total direct effects and discussed when they can be identified. Pearl introduced the natural effect terminology and the mediation formula, which expresses the natural direct effect as a weighted average of conditional exposure contrasts, where the weights are the distribution of the mediator under no exposure.

Identifying natural effects from observational data requires four conditions, conditional on measured covariates C:

1. No unmeasured confounding of the exposure–outcome relation.
2. No unmeasured confounding of the mediator–outcome relation.
3. No unmeasured confounding of the exposure–mediator relation.
4. No mediator–outcome confounder that is itself affected by the exposure.

The fourth is the most difficult in practice. A confounder of the mediator and outcome that lies downstream of exposure, such as an intermediate disease state, blocks identification of natural effects, although controlled direct effects can still be estimated using methods such as the marginal structural model. Condition 4 is related to a deeper problem: natural effects involve cross-world counterfactuals, such as the outcome under exposure 1 with the mediator from the world in which exposure was 0. No experiment can observe both worlds for one person, so the joint distribution is unidentifiable without further assumption, and the identification result is justified through an independence condition between Y_1,m and M₀ given covariates. Critics, among them Robins and Richardson, argued that this cannot be verified even in principle by a randomized trial and therefore carries a metaphysical component. Interventional effects defined with respect to a randomly drawn mediator value from its conditional distribution were proposed as alternatives that avoid cross-world independence.

When exposure and mediator interact on the outcome, natural effects alone obscure the mechanism. VanderWeele's 2014 four-way decomposition splits the total effect into components:

• A controlled direct effect, which occurs regardless of the mediator.
• A reference interaction, which occurs only when the mediator is at its natural level without exposure and interaction is present.
• A mediated interaction, which requires both exposure's effect on the mediator and interaction with it.
• A pure indirect effect, which arises through the mediator without any interaction.

The proportion attributable to interaction, to mediation, to both, or to neither then gives a more informative account than a single proportion mediated. The decomposition holds on the risk-difference scale without modeling assumptions beyond the identification conditions, and has been applied in genetic epidemiology and in studies of social determinants of disease.

Given identification, several estimators exist. The regression approach fits models for the outcome and the mediator and combines them analytically, with closed forms for common cases. The weighting approach reweights the unexposed by the mediator density ratio. A simulation-based approach follows the g-computation formula: fit an outcome model, fit a mediator model, simulate mediator values under each exposure level, and average predicted outcomes. Doubly robust and targeted estimators combine both models and remain consistent if either is correct. When the exposure is itself confounded by unmeasured variables, an instrument can be combined with mediation techniques, although the combined assumptions are demanding; see instrumental variable estimation and its application in Mendelian randomization, where genetic variants for the exposure and the mediator are used in multivariable designs.

Because unmeasured mediator–outcome confounding cannot be ruled out by design, sensitivity analysis is considered an essential component of any mediation report. Methods include the product-method approach of Imai, Keele, and Yamamoto, which varies the correlation between the error terms of the mediator and outcome models, and the E-value approach of VanderWeele and Ding, which reports the strength of association an unmeasured confounder would need with both mediator and outcome to explain away the estimate. Adjusting for a collider on the path between mediator and outcome can introduce bias of its own; see collider bias.

Mediation analysis has been applied to explain disparities, to decompose genetic effects on disease through intermediate traits, and to evaluate trials in which an intervention targets a hypothesized mechanism. Common pitfalls include treating a measurement of the mediator taken at the same time as the outcome as if it preceded it, ignoring measurement error in the mediator, which biases the indirect effect toward zero, and interpreting a large proportion mediated as proof that intervening on the mediator would remove most of the effect. The last point conflates natural indirect effects with the effect of an intervention on the mediator, which is a controlled-type quantity.

1. Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research. Journal of Personality and Social Psychology, 51(6), 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173
2. Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3(2), 143–155. https://doi.org/10.1097/00001648-199203000-00013
3. Pearl, J. (2001). Direct and indirect effects. Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, 411–420. https://arxiv.org/abs/1301.2300
4. VanderWeele, T. J. (2014). A unification of mediation and interaction: a four-way decomposition. Epidemiology, 25(5), 749–761. https://doi.org/10.1097/EDE.0000000000000121