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In causal mediation analysis, nonparametric identification of the pure(natural) direct effect typically relies on, in addition to no unobservedpre-exposure confounding, fundamental assumptions of (i) so-called"cross-world-counterfactuals" independence and (ii) no exposure- inducedconfounding. When the mediator is binary, bounds for partial identificationhave been given when neither assumption is made, or alternatively when assumingonly (ii). We extend existing bounds to the case of a polytomous mediator, andprovide bounds for the case assuming only (i). We apply these bounds to datafrom the Harvard PEPFAR program in Nigeria, where we evaluate the extent towhich the effects of antiretroviral therapy on virological failure are mediatedby a patient's adherence, and show that inference on this effect is somewhatsensitive to model assumptions.

On Partial Identification of the Pure Direct Effect