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I understand how a properly administered RCT rules out confounders because there are no variables influencing the treatment/control group assignment except randomization (meaning no backdoor paths from the outcome to the treatment variables).

Does this mean when conducting an RCT it's not necessary to draw a causal diagram (DAG) in order to identify confounders, colliders, mediators, etc. as you would with an observational causal inference study?

Are there special cases where you would want to take the time to build a DAG?

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3 Answers 3

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In short, yes there are cases where one may want to draw a DAG. I will offer a simplified example.

As you mention, (proper) randomization ensures there are no confounders so we don't need to worry about that.

Colliders are the interesting bit however. Subjects can be randomized to certain interventions in hopes that the intervention can encourage the subject to get a particular outcome. Education interventions are good examples (e.g., teach someone why smoking is bad and maybe they won't smoke and hence avoid lung cancer). Its tempting to only analyze those subjects who actually engaged with the intervention (e.g., read the pamphlet on smoking and cancer) but this could potentially introduce bias. To see why, we need to draw a dag

enter image description here

Engaging with the education (Edu in our DAG) means we have conditioned on a collider hence inducing a (potentially erroneous) correlation between cancer and education. While it is plausible to identify this pitfall through reason alone, a DAG makes it immediately clear that conditioning on post treatment outcomes is a bad idea. It also makes it clear that the treatment effect estimated in this hypothetical experiment is the effect of offering the education on cancer prevention and not the effect of the education itself.

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    $\begingroup$ Could you explain what's "U" in your DAG? $\endgroup$ Dec 22, 2023 at 11:19
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    $\begingroup$ "U" in this case is often used to represent Unmeasured variables / unmeasured confounders $\endgroup$ Dec 22, 2023 at 12:05
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    $\begingroup$ @RobertF Yes that is correct! Using Txt instead of Edu is called the ITT principle (Intention to Treat) $\endgroup$ Dec 22, 2023 at 14:33
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    $\begingroup$ @RobertF Not increased variability per se, but the ATE of the treatment on Cancer will underestimate the effect of Education on Cancer because some subjects will not engage with the treatment (e.g. will not be treated by reading the pamphlet) $\endgroup$ Dec 22, 2023 at 17:24
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    $\begingroup$ @RobertF In principle you could, but it is almost better to use treatment as an instrumental variable, as per Frank's answer, to estimate the effect of education on treatment. I'm dubious of conditioning on the right confounders in this case $\endgroup$ Dec 22, 2023 at 17:41
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Classic randomized clinical trial analysis uses the intention to treat approach in which all patients are analyzed and they are analyzed using the randomization codes. Secondary analyses may require methods of causal inference. In Demetri’s excellent example, estimation of what would happen were a person to actually engage with the educational intervention requires understanding of causal methods, and in that case there is a perfect instrumental variable (the randomization code) that can lead to unbiased causal estimation of the target effect through an instrumental variable analysis.

For the standard primary intent-to-treat analysis no causal inference calculus is needed to make a causal inference about the effect of the plan to give treatment B instead of treatment A. That’s because there are no alternate explanations for the B-A effect other than the planned treatment. This is true in the Bayesian sense of data generating mechanisms or in the frequentist sense of getting the right B-A estimate on the average (over samples). When randomization is properly carried out (including masking when needed), there are no post-randomization exclusions, and there are no post-randomization covariates being adjusted for, the interpretation of the estimated B-A effect is simple and is causal.

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Even in an RCT, a DAG can be useful to examine colliders and mediators

In general, there are two types of variables that might might adversely impact an RCT and which may require consideration and analysis: colliders and mediators. Randomisation in an RCT (what makes it an RCT) only severs the causal pathways from would-be confounders, but other protocols are required to deal with mediator variables, and care must also be taken in dealing with colliders. DAGs can be useful to facilitate this analysis and to communicate it to others. Here are some reasons that a DAG might still be useful even if you have constructed an RCT:

  • DAGs facilitate analysis of colliders: As pointed out in the other answer, collider variables are still a potential problem in an RCT, and a DAG is a potentially useful way to formally consider/analyse this possibility. As pointed out in the other answers here, even the distinction between intention-to-treat and actual engagement with the treatment can be related to a collider and can therefore raise some tricky causal questions. Consideration of this type of issue can be facilitated by formal analysis with a DAG, and potentially problematic situations can also be illustrated well with a DAG to your reader.

enter image description here

  • DAGs facilitate analysis of mediators due to post-treatment actions: While you are correct that you don't need to worry about confounders in a properly administered RCT, there is an awful lot to think about in the idea of "properly administered". Remember that the randomisation of the treatment only shuts off the back-doors that would have a causal impact prior to treatment assignment. There can also be mediator variables that confound the analysis by operating after the treatment assignment if the assigned treatment is able to have a causal impact on things it shouldn't (thereby having an indirect causal effect on the outcome variable of a type we don't want to measure). This can occur in the absence of proper blinding protocols --- e.g., patient finds out what treatment group they are randomly assigned to and it affects their behaviour/effort in ways that act as a mediator, treating doctor finds out what treatment group patient is in and it affects selected treatments/effort in ways that act as a mediator, etc. The construction of a proper RCT often involves consideration of potential mediators that could confound the analysis based on causality that occurs after treatment assignment, and the construction of a "properly administered" RCT typically requires the imposition of protocols to deal with this (e.g., blinding, double-blinding, etc.)

enter image description here

  • DAGs facilitate analysis of mediators due to indirect effects: In addition to dealing with potential mediators that arise from post-assignment actions, a "properly administered" RCT often needs to deal with mediator variables that involve indirect effects from the treatment to the outcome. Often the goal of the study is to measure a particular direct effect and the presence of mediators interferes with what we want to measure. The archetypal example of this is the "placebo effect" that can result from a patient observing their treatment assignment, which can then passively impact the outcome in a way that is not the direct causal result of the treatment that we want to measure. In such cases we again require protocols to remove the mediator variable (e.g., adding a placebo-treatment for the control group to aid blinding). Again, the construction of a proper RCT often involves consideration of potential mediators that could confound the analysis based on causality that occurs after treatment assignment, and the construction of a "properly administered" RCT typically requires the imposition of protocols to deal with this (e.g., placebo-treatment, etc.).

enter image description here

  • DAGs can illustrate potential problematic situations: For the various problematic situations that arise from potential colliders, confounders and mediators (described above), it is possible to explain these textually, but they can usually be illustrated in a fruitful way with a DAG. Analysis of any of these situations can potentially be aided by a DAG and so can communication of potentially problematic situations and the protocols to deal with these.
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  • $\begingroup$ I think your first graph is not a DAG of an RCT: if "treatment" is caused by "collider" (i.e. anything other than "randomization"), then treatment is not randomized, yeah? $\endgroup$
    – Alexis
    Dec 25, 2023 at 21:40
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    $\begingroup$ @Alexis: Thanks for noticing --- updated to correct. $\endgroup$
    – Ben
    Dec 25, 2023 at 22:39

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