Why Adjusting for Mediators Changes the Causal Question

Why a Mediator Changes the Question

A treatment can affect an outcome through more than one route. It may have an effect that does not operate through a particular intermediate variable, and it may also change that intermediate variable, which in turn changes the outcome. That intermediate variable is called a mediator. For example, a program may affect blood pressure partly by changing exercise habits. If the goal is the program’s overall effect, comparing people at the same observed exercise level is not the same question as comparing their outcomes under the program versus no program.

The central distinction is between the total treatment effect, which includes all pathways from treatment to outcome, and effects defined while holding the mediator fixed or changing it between treatment conditions. Adjusting for a mediator in a regression can block some of the treatment pathway. It can also produce a coefficient that does not equal the causal effect one intended to estimate.

These potential outcomes define several distinct causal effects. The total effect compares the outcome under treatment with the outcome under no treatment, allowing the mediator to take its corresponding value in each condition:

A controlled direct effect at a specified mediator value \(m\) compares treatment conditions while setting the mediator to that same value in both:

The phrase “direct effect” here means an effect not operating through the mediator as defined; it does not mean that treatment has no other mechanisms. Two further quantities make the pathway distinction explicit. The natural direct effect holds the mediator at the value it would take without treatment, while the natural indirect effect changes the mediator from its untreated to treated value while treatment is held at one:

With these definitions, \(TE=NDE+NIE\): add and subtract \(Y(1,M(0))\) inside the total-effect contrast. This is an algebraic decomposition, not by itself a recipe for identifying the effects from observed data. In particular, observing the mediator does not reveal both \(M(0)\) and \(M(1)\) for the same person. Claims about causal mediation therefore require assumptions beyond simply fitting a regression with \(A\) and \(M\).

An Additive Model Shows the Pathways

A simple model makes the pathway arithmetic transparent. Suppose the mediator and outcome potential outcomes follow:

Here \(\alpha_1\) is the treatment-related change in the mediator in this model, \(\beta_2\) is the mediator’s outcome effect under the model, and \(\beta_1\) is the treatment effect when the mediator is held fixed. The model assumes additive relationships with no treatment-by-mediator interaction. The same underlying \(U_M\) and \(U_Y\) apply to an individual’s potential outcomes across interventions. They may be dependent on each other; the causal contrasts below do not require their independence.

The total effect follows by substituting the mediator potential outcomes into the outcome equation and subtracting:

The first term is the effect when the mediator is fixed; the second is the effect transmitted through the change in the mediator. In this additive model, \(CDE(m)=\beta_1\) for every \(m\), \(NDE=\beta_1\), and \(NIE=\beta_2\alpha_1\). This model-based decomposition is useful for understanding what a total-effect analysis includes. It does not mean that a regression including \(M\) automatically estimates \(\beta_1\).

Why a Mediator-Adjusted Regression Is Not Automatically a Direct Effect

A regression of \(Y\) on \(A\) and \(M\) describes outcome differences conditional on the included variables, under its modeling assumptions. Its treatment coefficient is not automatically the controlled direct effect, the natural direct effect, or the structural parameter \(\beta_1\). Conditioning on a mediator compares people who have the same observed mediator value, but those people may differ in why they reached that value. In addition, the adjustment blocks the part of the treatment effect that operates through changes in \(M\), if the analysis succeeds in isolating a direct contrast.

In the additive structural model, the conditional-mean requirement \(E[U_Y\mid A,M]=0\), together with correct linear specification and adequate variation to estimate the coefficients, is a sufficient condition for the regression treatment coefficient to equal \(\beta_1\). Randomization makes treatment independent of pretreatment causes on average; it does not guarantee that \(U_Y\) is unrelated to \(M\) after conditioning on treatment. If mediator and outcome causes are shared, the required conditional-mean assumption can fail.

The Direct Effect Can Depend on the Mediator Level

The additive model’s constant direct effect is a simplifying assumption. If treatment and mediator interact in their effects on the outcome, the controlled direct effect can vary with the mediator value. In that case, a single treatment coefficient may obscure which mediator level or population is relevant, even apart from confounding or model misspecification.

Choosing an Analysis and Checking Its Limits

The right decision depends first on the causal question. If the target is the total effect, adjusting for a mediator is generally inappropriate: it removes part of the pathway that the total effect is meant to include and may introduce additional bias. Adjustment for suitable pretreatment covariates can address baseline differences or improve precision under the relevant assumptions, but a mediator is measured after treatment and is not a baseline covariate.

If the target is a direct or indirect effect, define that effect precisely before choosing a model. A controlled direct effect concerns an intervention that sets the mediator to \(m\); it is not defined merely as the difference between people observed at the same \(M\). Natural direct and indirect effects refer to potential mediator values under different treatment conditions. Their identification from observational mediator and outcome data requires substantive assumptions about treatment assignment, mediator–outcome confounding, and the counterfactual quantities involved. Treatment randomization by itself does not supply all those assumptions.

Useful checks include verifying the time ordering of treatment, mediator, and outcome; stating whether the target is total or direct; considering whether the model allows treatment–mediator interaction; and asking whether measured causes of both mediator and outcome could remain uncontrolled. A conditional regression fit or a balanced treatment comparison cannot, by itself, verify those causal assumptions.

The main alternatives answer different questions. An unadjusted randomized treatment contrast, or one adjusted only for appropriate pretreatment variables, targets the total effect when its design and analysis assumptions hold. A mediator-adjusted regression describes a conditional association unless additional assumptions justify a causal interpretation. A mediation analysis targets explicitly defined direct and indirect effects and requires assumptions suited to those targets. These approaches are not interchangeable ways to obtain a more “fully adjusted” answer.