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We consider continuous-time survival or more general event-history settings,where the aim is to infer the causal effect of a time-dependent treatmentprocess. This is formalised as the effect on the outcome event of a (possiblyhypothetical) intervention on the intensity of the treatment process, i.e. astochastic intervention. To establish whether valid inference about theinterventional situation can be drawn from typical observational, i.e.non-experimental, data we propose graphical rules indicating whether theobserved information is sufficient to identify the desired causal effect bysuitable re-weighting. In analogy to the well-known causal directed acyclicgraphs, the corresponding dynamic graphs combine causal semantics with localindependence models for multivariate counting processes. Importantly, wehighlight that causal inference from censored data requires structuralassumptions on the censoring process beyond the usual independent censoringassumption, which can be represented and verified graphically. Our resultsestablish general non-parametric identifiability and do not rely on particularsurvival models. We illustrate our proposal with a data example on HPV-testingfor cervical cancer screening, where the desired effect is estimated byre-weighted cumulative incidence curves.

Graphical criteria for the identification of marginal causal effects in continuous-time survival and event-history analyses