Mediation, Direct Effects, and Mechanism Questions

Something worked. The employment numbers moved, the program is being renewed, and the next meeting is about why. Which part of it did the work? What could be dropped without losing the result?

That is not one question. Hold the middle variable at a level you choose for everybody and you learn one thing. Leave it wherever it would have landed on its own and you learn another. Shift its distribution rather than its value and you learn a third. Each of those is a defensible question. Each has a different answer. The answers can point in different directions on the same data.

So the sentence "we measured the mechanism" is unfinished. It stays unfinished until you say which of those three questions you asked. The procedure most analyses reach for — the one in the next section, cited tens of thousands of times — never asks you to say.

The procedure is neither anonymous nor rare. Put the outcome on the left. Put the treatment and the mediator on the right. Read mediation off what happens to the treatment coefficient. Baron and Kenny set that out in 1986. Their own definition: “In general, a given variable may be said to function as a mediator to the extent that it accounts for the relation between the predictor and the criterion.” The paper lists three conditions for mediation. Condition (c) is that “when Paths a and b are controlled, a previously significant relation between the independent and dependent variables is no longer significant”. Three regression equations operationalise it. Crossref indexes the paper at 67,977 citations, OpenAlex at 71,222, as of 21 August 2026. Whatever else it is, it is the default.

Now suppose the treatment itself caused something that moves both the mediator and the outcome. That is a mediator-outcome confounder affected by the exposure. Adding it to the right-hand side is the obvious repair. It is not a repair. VanderWeele and colleagues showed in 2014 that in that situation “the so-called natural direct and indirect effects that are used are not identified from data whenever there is a mediator-outcome confounder that is also affected by the exposure”.

Read that again, because it is stronger than a warning about a badly chosen control. The quantity being reported is not a noisy version of the right answer. It is not a function of the data at all. The same paper sets out exactly three alternative decompositions that do stay identifiable in that case, each with a weighting-based estimator, illustrated on perinatal epidemiology data. Nothing in the regression output tells you which of the two worlds you are standing in. The coefficient prints either way.

A mediator is a variable standing on the road from treatment to outcome, carrying part of the effect rather than distorting it. What splits that effect into a direct and an indirect share is not the data. It is what you decide to do to the mediator.

Fix it at a chosen level and you get a controlled direct effect. Compare the values it would have taken under each treatment condition and you get natural effects. Move its distribution instead of its individual values and you get interventional effects. Separable effects reframe the treatment itself into components, and never intervene on the mediator at all.

That the arithmetic everyone runs is the wrong arithmetic is not a recent methodological taste. Robins and Greenland published it in 1992: “We show that adjustment for the intermediate variable, which is the most common method of estimating direct effects, can be biased.” The same paper established that direct and indirect effects are not separately identifiable when only exposure is randomized. Where they can be recovered, the estimation has to run through the G-computation algorithm, because conventional adjustment stays biased. That correction carries 1,420 Crossref citations as of 21 August 2026. The procedure it corrects carries 67,977.

The fourth estimand is the youngest. Robins and two co-authors set out separable effects in 2020, and published them in 2022. The treatment is decomposed into several separable components on an expanded graph. That graph, the abstract says, “provides a self-contained framework for discussing mediation without reference to cross-world (nested) counterfactuals or interventions on the mediator.” Removing the cross-world counterfactual turns the mediation question into something a future randomized trial could test. Not something you can only assume.

Working backwards from the failed procedure gives the order of commitments. Say what the mechanism question is for: explanation, an intervention on the mediator, or attribution across pathways. Say what the mediator actually is — when it is measured, which version of it counts, whether it can be manipulated at all. Choose the estimand: controlled, natural, interventional, separable. Map the confounding, keeping baseline causes of the mediator and outcome separate from anything the treatment itself caused. Then estimate with methods built for that structure, the G-computation algorithm rather than a single regression. Then stress the result with sensitivity analysis, and with the possibility that several mediators are in play.

Once the estimand is stated, a second question decides whether the answer is useful. Could anyone set this mediator on purpose? And would setting it by other means reproduce what the treatment did? The Cardiac Arrhythmia Suppression Trial answered the second half in the most expensive way available.

Its preliminary report, in the New England Journal of Medicine in 1989, describes 2,309 patients entering drug titration. In 1,727 of them — 75 percent — the ventricular arrhythmia was suppressed, and those patients were randomized. The mediator moved exactly as the theory required. After an average of 10 months, total mortality was 56 of 730 on encainide or flecainide, or 7.7 percent. On placebo it was 22 of 725, or 3.0 percent. That is a relative risk of 2.5, 95 percent confidence interval 1.6 to 4.5. Deaths from arrhythmia and nonfatal cardiac arrests ran 33 of 730 (4.5 percent) against 9 of 725 (1.2 percent), relative risk 3.6 (95 percent confidence interval 1.7 to 8.5). That arm of the trial was discontinued.

The investigators wrote: “We conclude that neither encainide nor flecainide should be used in the treatment of patients with asymptomatic or minimally symptomatic ventricular arrhythmia after myocardial infarction, even though these drugs may be effective initially in suppressing ventricular arrhythmia.” The drugs did what the mechanism story asked of them. More patients died.

Take the vague version of the question — how does it work? — and force it into a sentence that names an intervention on the mediator. Baron and Kenny's three equations never ask for that sentence. That is why an analysis can run all the way to a published share without anyone noticing it was never written.

State which mediator, measured when, in which version. State what would be done to it and to whom, in words a colleague could act on. State the contrast: the mediator held at one level against another, or its distribution shifted from one to another. Then list what has to be true for the data to answer that. Separate the baseline confounders of mediator and outcome from anything the treatment itself caused. If the treatment caused it, adding it as a control is the move Robins and Greenland showed “can be biased” in 1992. It is also the move that in 2014 was shown to leave the natural effects unidentified altogether.

If the sentence cannot be finished, that is the finding. The mediator is not manipulable, or not measured well enough to say what manipulating it would mean. No amount of estimation supplies what the sentence was missing.

These four slide into each other in review, and each substitution changes what was claimed.

The natural effects have a birthplace. Pearl defined them in 2001, in a paper called Direct and Indirect Effects, and its abstract states the asymmetry the four terms turn on. “The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant.” A controlled direct effect and a natural indirect effect are two different questions. They are not two computations of one quantity.

Mediation earns its place when it sharpens a theory, when it suggests a complementary intervention worth building, or when it points to the pathway the next experiment should test directly. Those are real uses. None of them requires the percentage the meeting asked for.

What the estimate is evidence about is the mediator intervention you defined, and nothing wider. ILLUMINATE, reported in the New England Journal of Medicine in 2007, randomized 15,067 patients at high cardiovascular risk and was terminated early. At 12 months the pathway variables had moved precisely as the mechanism story required. Torcetrapib had raised HDL cholesterol by 72.1 percent and lowered LDL by 24.9 percent. Cardiovascular events rose anyway: hazard ratio 1.25, 95 percent CI 1.09 to 1.44, P=0.001. So did death from any cause: hazard ratio 1.58, 95 percent CI 1.14 to 2.19, P=0.006. The conclusion of the abstract is one sentence long. “Torcetrapib therapy resulted in an increased risk of mortality and morbidity of unknown mechanism.”

An indirect effect is not proof that a biological or psychological mechanism operates the way the story says. It is a statement about what happens under one specified way of moving one specified variable.

And when that variable cannot be moved meaningfully or measured well, the honest report is the association along the pathway, plus the reason a causal decomposition was not attempted. That paragraph is worth more than any share a redesign could be built around.