Identifiability of
Path-specific Effects
AZT Example
AZT
Headaches
Pneumonia
Antibiotics
Painkillers
Survival
Indirect
Effect
Direct Effect
Path-specific Effects
AZT
AZT
Headaches
Pneumonia
Painkillers
Antibiotics
Survival
Painkiller contribution to the
total effect of AZT on survival
Headaches
Pneumonia
Painkillers
Antibiotics
Survival
Antibiotics contribution to the
total effect of AZT on survival
Problem Statement


Experimental Identifiability – can path-specific
effects of interest be uniquely determined
from results of experiments.
Experimental non-Identifiability – can there
be two causal models which are
experimentally indistinguishable while
producing different path-specific effects?
Methodology



Path-specific effects we are interested in are
expressions in counterfactual logic (with
associated probabilities).
We convert these expressions into DAGs
with sets of ‘cut’ edges.
Our subsequent reasoning and results are
stated in terms of these graphs rather than
the underlying logic.
Effect-invariant Graph
Transformations
Rule 1
Rule 2
Main Result


Applying the two rules results in one of two
cases:
Case 1: we obtain a ‘kite pattern.’ Then the
path-specific effect is not identifiable.
Z
R - Recanting witness
Y
Main Result (cont.)

Case 2: all blocked edges emanate from the
root node. Then the effect is identifiable.
X
W
Z
Y
Z’
Z”
AZT Example Revisited
AZT
AZT
Headaches
Pneumonia
Painkillers
Antibiotics
Survival
Painkiller contribution to the
total effect of AZT on survival
Headaches
Pneumonia
Painkillers
Antibiotics
Survival
Antibiotics contribution to the
total effect of AZT on survival
Recanting Witness
AZT
R-Recanting
Witness
Headaches
Pneumonia
Painkillers
Antibiotics
R behave as I
Survival
R behave as II
Antibiotics contribution to the
total effect of AZT on survival
P(RX,RX*) is not experimental identifiable