I once helped organize a meeting at Harvard where we invited both Don Rubin and Tyler Vanderweele (a proponent of DAGs) to give talks on the merits of the graphical approach to causal inference. We had students both from the Statistics department at the Graduate School of Arts and Sciences (generally on Rubin's side) and from the departments of Epidemiology and Biostatistics at the School of Public Health (which is heavily graphical due to the influence of Jamie Robins). Part of the purpose of this meeting was to help us understand how the other side thinks, and clarify what we really disagree about.

Since I'm an epidemiologist and not a statistician, some of Rubin's arguments may have gone over my head. However, my main take home message was that Rubin very strongly believes in the dictum "No causation without manipulation", ie that it is not meaningful to talk about non-manipulable variables as being causes of anything. My understanding is that he dislikes DAGs because these graphs implicitly label confounders as "causes" of the exposure and of the outcome, in violation of this philosophy.

The following is a major simplification of the differences between the two approaches to causal inference:

Both Pearl and Rubin have provided frameworks for stating assumptions about how the data was generated, and for using those assumptions to prove that an observational quantity will be equal to the causal effect. These frameworks are both valid in the sense that if the assumptions (unconfoundedness) are true, then the conclusions (identification of the causal effect) follow.

• In Pearl's framework, the investigator starts from an assumption that the data was generated by a particular directed acyclic graph, and then proves that if he is able to block all backdoor paths between the exposure and the outcome by conditioning on certain covariates, then controlling for those variables is sufficient to eliminate confounding.

• In Rubin's framework, the investigator starts from the assumption that treatment is assigned by a "treatment assignment mechanism", and then proves that if conditional on certain covariates this mechanism does not depend on the counterfactual outcome , then controlling for those covariates is sufficient to eliminate confounding.

Pearl claims that these approaches are equivalent. The logical implication from Pearl's definition of confounding to Rubin's definition seems uncontroversial. I am not sure exactly what background assumptions (if any) you have to make in order for the converse to hold, but I don't think those assumptions are restrictive.

Both approaches are logically valid. However, there are infinitely many possible assumptions you can use as starting points for your chain of reasoning to prove identification. The real question is therefore whether either framework allows you to start your reasoning from a foundation that facilitates clear communication about whether the assumptions that are necessary for identification are true for a given study.

This is what I see as Pearl's advantage. His DAGs really are optimized for allowing scientists to clarify exactly how they believe the data was generated, and present those assumptions in a transparent form so that they can be evaluated, discussed and criticized by other scientists. I think it would be very challenging to have such a conversation using only the language of counterfactual variables and treatment assignment mechanisms.

I believe that Pearl's framework is better suited for the purpose of being the language in which we conduct discussions about what variables to control for. I believe users of the graphical language will be better equipped to communicate subtle points that will influence the choice of analytic method and the credibility of the estimates. Since this is the major source of uncertainty in observational research, I believe DAGs will ultimately win out in the marketplace of ideas.

Of course, being a student in the graphical camp at HSPH, I am obviously pretty biased.