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Someone asked on reddit (bit.ly/2S5tOPA) about the "amicable disagreements" between @yudapearl & @_MiguelHernan are, and what the do-operator is. Here's my summary: (1)
The do-operator represents an idealized intervention. In cases where the "treatment" is something that is well-defined (i.e. the exposure in a randomized control trial, such as taking aspirin), the two camps are in agreement. However, in cases where the "treatment" is ... (2)
non-manipulable by itself in the real-world (i.e. obesity), the two camps diverge. Hernan's camp believes that 1. the value of E(Mortality | do(Obesity = 1)) has no real bearing to the real world, hence "extrascientific" and "magical." (3)
Obesity, in the physical world, always has to be manipulated by some intervention (i.e. liposuction, diet, genetics, etc.). He argues that the counterfactual outcome E(Mortality^{obesity=1}) is different for each treatment, which breaks a key tenet of the Potential Outcomes (4)
framework of consistency. As an epidemiologist, he's concerned with what tangible policies people can adapt, so it is understandable that he is more concerned about the question of "Does drinking 3 cans of soda a day increase mortality rates?" (5)
instead of "Does decreasing obesity lower mortality rates?" Judea's Structural Causal Model (SCM), on the other hand, treats non-manipulable variables as first-class citizens. (6)
In the cases of non-manipulable variables, he likens them to complex numbers -- they don't exist in the physical world, but they are useful. For example, imagine that treatment A causes non-manipulable variable B, (7)
, and non-manipulable variable B causes C, and A has no effect on C, assuming linear relationships between the variables. If we know that B's effect on C is small, then no matter how strong A's relationship with B is, the effect of A on C is always going to be small (8)
(i.e. effect of B on C acts as a limit). See "On the Interpretation of do(x)": ftp.cs.ucla.edu/pub/stat_ser/r… In that paper, he also discusses indirect tests for validating the estimate of the effect of a non-manipulable variable. (9)
Judea also clarifies that, even though there's an apparent "inconsistency" about "consistency," the two frameworks coexist: (10)
Miguel's papers: Does Obesity Shorten Life? (nature.com/articles/ijo20…). Does Water Kill? (ncbi.nlm.nih.gov/pmc/articles/P…) Judea's responses: Does Obesity Shorten Life? Or is it that can of soda? (ftp.cs.ucla.edu/pub/stat_ser/r…) On the interpretation of do(x): (ftp.cs.ucla.edu/pub/stat_ser/r…) (11-END)
