  A treatment policy defines when and what treatments are applied to affect
some outcome of interest. Data-driven decision-making requires the ability to
predict what happens if a policy is changed. Existing methods that predict how
the outcome evolves under different scenarios assume that the tentative
sequences of future treatments are fixed in advance, while in practice the
treatments are determined stochastically by a policy and may depend, for
example, on the efficiency of previous treatments. Therefore, the current
methods are not applicable if the treatment policy is unknown or a
counterfactual analysis is needed. To handle these limitations, we model the
treatments and outcomes jointly in continuous time, by combining Gaussian
processes and point processes. Our model enables the estimation of a treatment
policy from observational sequences of treatments and outcomes, and it can
predict the interventional and counterfactual progression of the outcome after
an intervention on the treatment policy (in contrast with the causal effect of
a single treatment). We show with real-world and semi-synthetic data on blood
glucose progression that our method can answer causal queries more accurately
than existing alternatives.
