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In a DAG, why does a randomized controlled trial ensure there are no backdoor paths from treatment to response and hence no omitted variable bias?

Sadie Maple
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  • Hello and welcome to Cross Validated! Could you please be specific about what you mean by a DAG? Could you also please provide an example of what you mean? A diagram would be very helpful. Have a look at [How do I ask a good question?](https://stats.stackexchange.com/help/how-to-ask) to increase the likelihood of someone answering your question. – mhdadk Oct 16 '21 at 21:21
  • Thank you! A DAG is a so called directed acyclic graph used for causal inference. Sadly it is a bit difficult to provide an example and diagram as the concept is very general. – Sadie Maple Oct 16 '21 at 21:33

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Quite simply an RCT ensures no backdoor paths (technically it reduces the possibility of backdoor confounding to a chance which is inversely related to sample size) from outcome $Y$ to treatment $A$, because by definition random assignment $R$ is the only prior cause of treatment:

$$\boxed{R} \to A \to Y$$

In the simple DAG above, randomization is the only cause of treatment. If there were a backdoor path through some third variable like disease severity, or smoking history, then randomization would not actually assign treatment.

In this DAG notation, the box around $R$ (the randomizing process) indicates that it has no prior cause (i.e. it is a purely probabilistic phenomenon).

This specific fact about random assignment—that it reduces the role of confounding via a backdoor path to chance—is rather the entire point of random assignment to treatment.

Alexis
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  • Thank you so much for the detailed and intuitive explanation, I really appreciate the help! – Sadie Maple Oct 17 '21 at 15:00
  • @SadieMaple You are quite welcome. :) Please feel free to up-vote by clicking the up arrow, as well as accepting. :) – Alexis Oct 17 '21 at 16:23