Causal mediation and moderation analysis

It adds the answer to two questions the association leaves open: through what mechanism the effect might operate, if the causal hypothesis is justified (mediation), and under what conditions or in which subgroups it changes (moderation). It applies when showing an association between exposure and outcome is only the first step, and reviewers, committees or policy makers want to know the how and the for whom. Mediation decomposes the total effect into a direct part and an indirect part that passes through an intermediate mechanism, and quantifies what proportion of the effect operates through that mediator. Moderation assesses whether the size of the effect depends on a third factor, identifying subpopulations in which the relationship is stronger or weaker. Knowing that A is related to B is not enough to ground a clinical decision or the design of an intervention; understanding the mechanism and the conditions is. That is what separates a documented association from an actionable understanding of the effect.

Causal mediation decomposes the effect of an exposure on an outcome into a direct effect and an indirect effect that operates through a mediator and, where it is interpretable, estimates what proportion of the total effect is indirect. It applies when an exposure is suspected of influencing the outcome through a specific intermediate pathway that you want to quantify. You receive the ACME (average causal mediation effect, the indirect part) and the ADE (average direct effect), with confidence intervals obtained by bootstrap rather than normal approximations, and models suited to the type of outcome, continuous or binary. The proportion mediated is also reported when it offers an interpretable reading, always with caution, because it is a quantity that is sensitive to the scale and the model. What you receive is not just a number for the indirect effect, but its quantification with uncertainty and its interpretation within the framework of the question. The decomposition of the effect is the result; the bootstrap and the right models are what make it defensible.

We use the counterfactual framework for causal mediation, specifically the Imai, Keele and Tingley approach, which estimates direct and indirect effects on an explicit causal basis, instead of the Baron and Kenny method, which has been displaced by more current causal approaches. It applies if you know the classic regression-steps procedure and want to know why it is no longer the standard. The classic approach does not handle non-continuous outcomes well, does not formalise the causal assumptions the decomposition needs, and offers no clean route to inference or to sensitivity analysis. The counterfactual framework does: it defines the effects as causal quantities, accommodates continuous and binary outcomes, and produces bootstrap confidence intervals. The difference is not one of fashion but of validity: the current framework makes explicit the assumptions under which the proportion mediated means what it is claimed to mean. Relying only on the classic procedure can be a weak point with methodologically demanding reviewers.

Validity is decided before estimating, by formalising the causal hypothesis in a DAG and checking that the structure of the problem allows a mediation analysis. It applies to every mediation study, where a technically sound model may still fail to answer the question if the assumptions do not hold. Before estimating, we check the temporal order of exposure, mediator and outcome, and look for mediator–outcome confounding or a measurement of the mediator that does not respect that required temporal order: situations that invalidate the decomposition. If the causal structure does not justify the analysis, we say so before running the model, not after. The central assumption, sequential ignorability, cannot be verified empirically, so it comes with a sensitivity analysis that assesses how far the conclusion would depend on possible unmeasured confounding. An ACME estimated without examining these assumptions is a number that is hard to interpret causally; what makes it defensible is the explicit examination of the conditions under which it can be interpreted.

Moderation assesses whether the effect of an exposure on an outcome changes with the level of a third factor, whereas mediation decomposes that effect into the pathway through which it occurs. It applies when the question is not "why" the effect occurs, but "for whom" or "under what conditions" it is stronger or weaker. These are different questions that are frequently confused. A mediator lies on the causal path between exposure and outcome; a moderator modifies the size or direction of that relationship and is not interpreted as part of the main causal pathway. Moderation is analysed with interaction terms and interpreted with visualisations of conditional effects, such as simple slopes or Johnson-Neyman, distinguishing statistical interaction from biological interaction, which are not the same thing. When the design justifies it, the two are combined in moderated mediation or mediated moderation. Confusing them leads to answering a different question from the one you had, which is why we establish from the outset which one the study is asking.

Causal mediation and moderation analysis is a specialised part of causal inference, focused on decomposing an effect into its pathways (direct and indirect) and on assessing how it varies across subgroups. Causal inference and observational study design is the broader framework: estimating the total or marginal effect of an intervention, exposure or policy when there is no randomisation, with DAGs, propensity scores, difference-in-differences, g-computation and sensitivity analysis. They do not answer quite the same question. General causal inference estimates whether X affects Y and by how much; mediation and moderation, assuming or estimating that effect, decompose it into its mechanism and its conditions under additional causal assumptions. If you are looking specifically for "mediation analysis", this is your service; if your causal question is broader, the starting point is causal inference. The two are handled in coordination: this service is the special case, and that one is the umbrella.

You need the dataset with the exposure, the mediator or moderator, the outcome and the relevant covariates, plus the domain knowledge that underpins the causal hypothesis. The client provides the data, the temporal order of the variables and the clinical or contextual knowledge that gives the proposed mechanism its meaning; the service formalises the hypothesis in a DAG, specifies the models, estimates the effects, assesses the assumptions and interprets the results. The DAG is built jointly, because the causal structure depends on the research team's domain knowledge, not on a statistical decision. A key check before the analysis is temporal order: the exposure must precede the mediator, and the mediator the outcome, because a temporal order incompatible with the model invalidates the decomposition. What you receive is the estimate and its methodological defence; the causal question and its authorship remain the client's.

You receive the effect decomposition, interpreted and documented: the direct and indirect effects with their bootstrap confidence intervals, the proportion mediated with its caveats, the moderation analysis where applicable with its conditional effects visualised, the DAG that formalises the hypothesis and the sensitivity analysis for unmeasured confounding. It applies if you need to respond to reviewers and committees who demand evidence on mechanisms, not just on associations. The material includes the methods section written in line with the reporting guidelines that apply to the design, such as STROBE or RECORD where relevant, and a discussion of the limitations inherent in the observational design, which is usually what a methodologically demanding reviewer scrutinises. A significant ACME does not stand on its own: it is placed in the context of what it implies for clinical practice or intervention design. The research team signs and leads the manuscript; the service provides the estimate, its interpretation and the arguments against foreseeable methodological objections.