Causal and Treatment Effects

Unconfounded Graph

Judea Pearl defines a "causal effect" as what happens to some variable of interest "Y" when some policy variable "X" is purposely changed.  For example, the causal effect of the treatment "FolFox" is equal to what happens to colon cancer when a patient's treatment is changed to FolFox by some policy.

Don Rubin defines a "causal effect" as the difference in the patient's "potential" outcome under the proposed treatment and their outcome under the current treatment.  The causal effect of FolFox on patient survival is equal to the patient's survival on FolFox less what the patient's survival would have been if they had not received FolFox.

While Pearl's definition is very practical and makes perfect sense, Rubin's definition is closest to what economists call the "treatment effect" and will generally be preferred here.

The average treatment effect is the average over each patient's treatment effect.  If the data is unconfounded then the average treatment effect is equal to the difference in the average from each trial arm.  Rubin calls this the "typical causal effect."

References

1.  Causality (2009) by Judea Pearl.
2.  Estimating Causal Effects of Treatments from Randomized and Nonrandomized Studies (1974) by Don Rubin.