Mediator controls: state whether you want total or direct effects
A variable measured after an intervention can be part of the mechanism through which the intervention works. Controlling for it changes the question. A smaller adjusted coefficient is not automatically a better estimate of the original total effect, and it is not automatically a valid direct effect either.
The deliverable is a path ledger that separates the total intervention effect from a controlled direct effect at a stated mediator value. State the structural assumptions, identification conditions and estimation method separately. An ordinary regression coefficient should receive a causal label only when those additional steps justify it.
Define the intervention, mediator and outcome in time
Consider a hypothetical standardized research-review intervention X, coded 0 or 1 at baseline. M is a subsequent normalized review-intensity score, and Y is a later quality score. The temporal order is X before M before Y. The normalized score is a continuous model quantity, not a literal count of reviews.
The proposed paths are X → M → Y and X → Y. For this teaching model, assume both interventions on X and the stated setting of M are well-defined. In a real workflow, “set the score to m” may not specify a reproducible action; the relevant intervention would need operational detail before a controlled-effect interpretation becomes meaningful.
Hernán and Robins, Causal Inference: What If, August 19, 2026 version, Technical Point 22.1, defines controlled direct effects through joint interventions on treatment and mediator. Technical Point 22.2 and chapter 23 distinguish natural or pure effects and their extra assumptions. The equations below are an original transparent structural example, not empirical evidence that review interventions have these effects.
Calculate two targets in an explicit structural model
Assume these causal structural equations remain valid under the interventions being considered:
M = 2X + U;
Y = 3M + X + V.
Let U and V have mean zero, be independent of one another and independent of randomized X, with positive finite variance in U. The last condition allows M to vary within levels of X. The coefficients are stipulated features of the hypothetical mechanism, not values identified merely by fitting the two equations to observational records.
For the total effect of changing X from 0 to 1, let M respond naturally. For the same underlying U, M increases by 2. Y changes by 3×2+1=7. Equivalently, substitution gives Y=7X+3U+V, so the average intervention contrast is 7 under this model.
For a controlled direct effect, intervene to set M to the same fixed value m under both X values. The corresponding outcomes are Y(1,m)=3m+1+V and Y(0,m)=3m+V. Their difference is 1 for every m in this no-interaction model.
| Target | What happens to M? | Model-implied contrast |
|---|---|---|
| Total effect | follows 2X+U | 7 |
| Controlled direct effect at m | fixed to the same m | 1 |
| Difference between these targets | mechanism allowed versus blocked | 6 |
The seven and one answer different intervention questions. Controlling M in pursuit of the total effect blocks a genuine modeled path; calling the removed six “confounding correction” would misdescribe the mechanism. The decomposition is simple because the stated model is additive and has no interaction.
Separate structural arithmetic from identification and estimation
The structural calculation tells us what follows if those equations and error assumptions are true. Identification asks whether the corresponding causal quantities can be recovered from observed distributions. For the simple unconfounded example, consistency, appropriate positivity and exchangeability for the relevant X and M interventions are needed, alongside the model conditions.
Randomizing X does not randomize M. Mediator-outcome common causes can remain after X is assigned. Temporal order alone also does not establish that no such causes exist. Record what measured baseline factors, design features and substantive evidence support the identification argument.
Only after specifying that argument should an estimation method be selected. Under the main model’s independence and correct linear form, regressions can recover the relevant coefficients in the population, subject to sampling error. A program returning a coefficient near 1 does not test all the causal assumptions that make it a controlled direct effect.
A hidden common cause can reverse the adjusted coefficient
For a distinct boundary, retain M=2X+U but change the outcome equation to Y=3M+X+2U+V, with X still randomized and independent of the errors. U now affects both M and Y. The causal effect of setting X while fixing M remains 1 because the 2U component does not change under that joint intervention.
However, substituting U=M−2X gives Y=5M−3X+V. A population regression of Y on X and M in this example yields an X coefficient −3, although the controlled direct effect is +1. The total intervention effect remains 7: substituting the natural M instead gives Y=7X+5U+V.
Thus even randomized X plus a measured mediator does not make the adjusted X coefficient a direct effect. Conditioning on M also relates X to the unmeasured U in this structure. More precise estimation of −3 would not repair its causal interpretation.
The counterexample is not a claim that a real dataset contains exactly this U. It shows why mediator-outcome confounding must be addressed explicitly rather than assumed absent because an intervention was randomized or a regression includes many variables.
Interactions and natural effects change the accounting
For another structural boundary, suppose the outcome is Y=3M+X+XM+V while M=2X+U and E[U]=0. Fixing M at m now gives controlled direct effect 1+m: at m0 it is 1 and at m2 it is 3. Letting M respond naturally gives average total effect 9, not 7.
The target must therefore name the fixed mediator level. A single constant direct coefficient and a simple product-of-coefficients decomposition are not universal descriptions of mediation.
A natural direct effect instead compares outcomes with each individual’s mediator set to the value it would have had under a specified reference X. That is different from assigning everyone one common m. In the main additive independent-error model the numerical direct effects can coincide, but their definitions and identification requirements do not become identical. Do not use “natural,” “controlled” and “adjusted” as interchangeable labels.
Build an adjustment record a reviewer can use
| Check | Evidence to retain | Action when unresolved |
|---|---|---|
| Specify the target | total or controlled effect, contrast and mediator level | avoid a generic “effect” label |
| Fix timing | intervention, mediator and outcome dates | distinguish baseline causes from post-treatment variables |
| Define interventions | reproducible X and M actions | withhold an ill-defined controlled-effect claim |
| Assess identification | confounding, consistency and support | state the remaining causal gap |
| Choose estimation | model form, interactions and uncertainty | do not promote a fitted coefficient automatically |
| Report pathways | allowed and blocked paths | explain which question adjustment answers |
If mediator measurements are missing, do not silently estimate a direct effect only among convenient complete cases. Investigate whether missingness relates to X, M or Y and how that selection changes the population. Measurement error in M can also leave parts of the mechanism uncontrolled while introducing additional bias.
Update the judgment when a previously unknown common cause is measured, the mediator intervention is better defined, interactions are supported, or the target changes from total to controlled effects. Preserve both the original question and the revised adjustment set. The purpose of mediator review is to keep the intervention question intact, not to reward whichever regression produces the smallest residual error or most impressive coefficient.
Direct means direct relative to the specified mediator
A controlled effect not through M can still operate through other pathways omitted from that mediator definition. If M measures review intensity, the remaining X→Y path might include changes in source selection or reviewer knowledge. Calling it “direct” does not establish an immediate biological or operational mechanism, and it does not prove that every intermediate process was held fixed.
Keep the mediator definition, measurement window and implementation version with the effect estimate. Expanding M from one score to a bundle of actions changes the intervention and potentially the controlled contrast. Likewise, a pre-intervention review score can be a baseline adjustment variable, while a later score affected by X can be a mediator. Identical column names do not make their causal roles identical. Reconcile timestamps and the intended action before treating an adjusted coefficient as an answer to either question.
FAQ
Is controlling for a mediator a better way to estimate the total effect?
Not generally. It blocks a pathway included in the total effect and can introduce further bias under mediator-outcome confounding.
Does randomized treatment make every adjusted coefficient causal?
No. The mediator remains nonrandomized unless the design also addresses it, and direct-effect identification needs its own assumptions.