Abstract:
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Analyzing effects of an HIV drug administered over time, versus effects of patient adherence, is a longitudinal mediation problem. Mediated effects have generally been considered for point treatments only, and there exist well-known obstacles to identifying these effects in longitudinal settings, even in observational studies with no hidden variables. We give a framework which unifies mediated effects, and effects on the untreated in this setting, in terms of a hierarchy of interventions associated with graphical features (nodes, edges, and paths). We show a natural correspondence between this hierarchy, and the causal models FFRCISTG of Robins, and NPSEM-IE of Pearl. Finally, we show a correspondence between some total effects with hidden causes of treatments, and mediated effects, and show that certain types of longitudinal mediated effects are identified under the NPSEM-IE, even when some types of unobserved confounding is present. We show how our results can be used to resolve policy questions in the HIV setting.
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