Temporal Causal Mediation through a Point Process: Direct and Indirect
  Effects of Healthcare Interventions
Çağlar Hızlı ST John Anne Juuti Tuure Saarinen Kirsi Pietiläinen Pekka Marttinen
Deciding on an appropriate intervention requires a causal model of a
treatment, the outcome, and potential mediators. Causal mediation analysis lets
us distinguish between direct and indirect effects of the intervention, but has
mostly been studied in a static setting. In healthcare, data come in the form
of complex, irregularly sampled time-series, with dynamic interdependencies
between a treatment, outcomes, and mediators across time. Existing approaches
to dynamic causal mediation analysis are limited to regular measurement
intervals, simple parametric models, and disregard long-range mediator--outcome
interactions. To address these limitations, we propose a non-parametric
mediator--outcome model where the mediator is assumed to be a temporal point
process that interacts with the outcome process. With this model, we estimate
the direct and indirect effects of an external intervention on the outcome,
showing how each of these affects the whole future trajectory. We demonstrate
on semi-synthetic data that our method can accurately estimate direct and
indirect effects. On real-world healthcare data, our model infers clinically
meaningful direct and indirect effect trajectories for blood glucose after a
surgery.