Why Causal Mediation Is More Important Than I Previously Thought

This is my summary of the Causal Mediation chapter in the book Causal Inference: What If by Hernán and Robins.

It is quite common in medicine not to know how some total effect is mediated. Perhaps we should ignore these mediators M less often.

In the spirit of target trial emulation (and other reasons), it is better to think about separable components of the intervention so that one component affects through the mediator and the other doesn’t. These components have a deterministic relationship so the arrows are actually quite different from the usual arrows. The mediator itself doesn’t need to be a well-defined intervention.

And then we can measure mediators and think about the direct and indirect effects like

• the total indirect effect of the form mean(Y(n == 1, o == 1)) - mean(Y(n == 0, o == 1)) which is the effect of component N through M since the component O is received o == 1 in both situations
• the pure direct effect of the form mean(Y(n == 1, o == 1)) - mean(Y(n == 1, o == 0)) which is the effect of the component O since component N is received n == 1 in both situations.

But let’s first talk about experiments. Because experiments can deal with mediation issues just by using placebos and blinding.

Placebo-controls are considered important for good reasons. They provide a comparator that allows removing the irrelevant components of the total intervention that affect through irrelevant behavioral mediators so that only the remaining relevant mediators can be estimated. In general, a good control intervention only allows some specific relevant difference between the total interventions given in practice. By total intervention, I mean not just the “drug in the blood stream” but also all the other things that are needed to get to that point. People who are given placebos have very different experiences compared to people who continue their lives as usual.

It is sometimes argued that placebos are not options in real decision-making situations (true) and therefore they shouldn’t be used in trials that often (less true). But just think about a drug that acts only by causing some mild harms which leads people to change their behavior which then improves their health. Should you really use this drug? Of course not. If behavioral change is the relevant mediator of the total effect, you would obviously consider some new interventions directed towards behavior change. Infact in this case only knowing a realistic total effect of the drug could lock you into a situation where a harmful drug treatment is prefered over plausibly more effective behavior change interventions.

Now let’s turn back to mediation analysis.

In principle, if you could measure all the mechanisms of interest, it would be the same as using a perfect placebo. You can measure potential mediators and estimate direct and indirect effects using g-methods. For example, the g-formula for the counterfactual outcome mean(Y(n == 0, o == 1)) (direct effect and no mediated effect) given the graph above would be a weighted average of the observed outcome mean(Y(A == 1, M == m)) with weights P(M == m | A == 0) for each observed mediator m. In other words, the mediator is adjusted like a confounder in order to close the path through the mediator, except the weights are conditional on the control intervention A == 0 which you could perhaps imagine making the mediator “inactivated” instead of closing the path.

Sometimes mediators can even help to identify causal effect when mediation analysis is not the main interest. In this case the mediator works like a confounder that can be used to identify an effect through it.

This graph has an unmeasured confounder U so estimating the effect of A on Y seems hopeless. However, if we can measure some mediator M and again think of an intervention N that works through it, we can estimate this mediated effect of A on Y using g-methods. For example, the g-formula for the counterfactual outcome mean(Y(n == 1)) is the weighted average of the observed means mean(Y(A == a, M == m) over the weights P(A == a) and P(M == m|A == 1). The weights show that the cause A is adjusted like a regular confounder and this closes the path to it’s deterministic component N through the unmeasured confounder U. Then the mediator is adjusted similarly except conditional on the cause of interest A == 1 – perhaps imagine the mediator to be “activated”.