1/4 In view of the dominant role that re-weighing plays in
extrapolating effects across populations, and the many
Twitter requests for a concise graphical criterion
that gives re-weighing its legitimacy, I am retweeting
the criterion (called "S-admissibility"), in next 4 tweets.
extrapolating effects across populations, and the many
Twitter requests for a concise graphical criterion
that gives re-weighing its legitimacy, I am retweeting
the criterion (called "S-admissibility"), in next 4 tweets.
2/ It works on a selection diagram in which S nodes represent disparities between the target (*) population and study population (experimental). Z is a set of measurements. To test if Z is S-admissible
(1) Remove all arrows pointing to X
(2) Check if {X, Z} d-separates S from Y
(1) Remove all arrows pointing to X
(2) Check if {X, Z} d-separates S from Y
3/4 If Z passes this test, then the reweighing formula is valid:
P*(y|do(x)) = SUM_z P(y|do(x),z)P*(z)
In words: Effect at target equals the Z-specific effects at study, averaged over Z, using the target distribution P*(z) as weight.
Warning, this is merely a sufficient test.
P*(y|do(x)) = SUM_z P(y|do(x),z)P*(z)
In words: Effect at target equals the Z-specific effects at study, averaged over Z, using the target distribution P*(z) as weight.
Warning, this is merely a sufficient test.
4/4 Many more opportunities are available for situations in which a S-admissible set cannot be found. see ucla.in/2N7S0K9 and ucla.in/2Jc1kdD #Bookofwhy
(And dont dismiss "trivial transportability," described in ucla.in/2N7S0K9) Graphs are fun! #Bookofwhy
(And dont dismiss "trivial transportability," described in ucla.in/2N7S0K9) Graphs are fun! #Bookofwhy
