“It is commonly accepted (and can be proved in a variety of causal frameworks) that if we conduct a randomized controlled trial comparing these two treatments and collect data on the outcome Y we will be able to find out which if any of the two treatments is better, and to choose our future actions accordingly.
Much of the causal literature basically deals with this kind of causal question (or some more subtle versions such as sequential treatments or complier causal effects) and addresses two issues.
- If a randomized controlled trial cannot be carried out (e.g. for ethical or financial reasons) under what assumptions can we still consistently estimate this causal effect from observational data?
- What methods will give us consistent, efficient and robust estimates of this causal effect (e.g. adjustment for confounding, inverse probability weighting, propensity scores and G-estimation)?
These are important questions, but they assume that there is already a very specific causal hypothesis to be investigated (which treatment is better).
Cox (2000) pointed out that if the only evidence we had was that, say, treatment A performed better in a randomized trial than treatment B, without a clue why this is so, most scientists would not be comfortable with recommending treatment A. In fact, this seems like a black box approach that hardly promotes causal understanding. Breslow (2000) made the following interesting statement: ‘Counterfactual causality with its paradigm, randomization, is the ultimate black box,…’. Obviously, in practice there will be a long history of developing, experimenting with and trying out different substances that lead to the treatments, which would have given sufficient reason to want to test them in a controlled trial. It is this kind of exploration that forms the basis of causal understanding, whereas the randomized trial is ‘just’ the formal confirmation (p.3).”
“Now our modest suggestion is as follows: if a direct effect cannot reasonably be defined as a controlled or natural direct effect in the counterfactual sense because the required hypothetical manipulation of the mediator is inconceivable, then we can alternatively view these effects as being represented by flow in a dynamic system, so that the direct effect corresponds to the flow not passing through the mediator. The indirect effect could similarly be understood as that passing through the mediator. Some precision can be made to this concept in a mathematical setting.”
Happy reading and happy friday.