Effect of Treatment on the Treated
Antonio Forcina writes:
I have tried to read Judea and Ilya's paper on effect of treatment on the treated which sound much more general than anything else I have read on the subject before. Unfortunately I was unable to follow their proof and could not find an instance where the ETT effect is identifiable. The only instance where I new that ETT was identifiable is with an instrumental variable under certain restrictions, instead I imagine that identifiability here means without restrictions other than those encoded in the DAG.The most clear treatment of the subject I new until now is in a paper by Hernan and Robins in Epidemiology 2006; and I do not understand why the discussion on Forcina's paper by Robins, Vander Weele and RIchardson is so popular.
Dear Antonio,
There are many common instances where ETT is indentifiable.
The three most common ones are:
1. Whenever ATE (Average Treatment Effect) is identifiable through adjustment for a set S of covariates.
2. Whenever treatment is binary and ATE is identifiable by any method whatsoever
3. In linear systems, whenever the total effect is identifiable.
The proof takes two lines, and also appears in chapter 11 of causality 2nd edition.
You are right, identifiability here means without restrictions other than those encoded in the DAG.I have not read the papers by Hernan and Robins in Epidemiology 2006; and Robins, Vander Weele and Richardson. Perhaps you can give us a pointer and a summary.
Comment by judea pearl — August 4, 2009 @ 1:24 pm