Identifiability of Pathspecific Effects AZT Example AZT Headaches

Identifiability of Path-specific Effects

AZT Example AZT Headaches Pneumonia Antibiotics Painkillers Survival Indirect Effect Direct Effect

Path-specific Effects 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 l l 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 l l l 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 l l 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. ) l 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 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